Patent Publication Number: US-2022224941-A1

Title: Three-dimensional data encoding method, three-dimensional data decoding method, three-dimensional data encoding device, and three-dimensional data decoding device

Description:
CROSS REFERENCE TO RELATED APPLICATIONS 
     This application is a U.S. continuation application of PCT International Patent Application Number PCT/JP2020/038359 filed on Oct. 9, 2020, claiming the benefit of priority of U.S. Provisional Patent Application No. 62/912,865 filed on Oct. 9, 2019 and U.S. Provisional Patent Application No. 62/913,466 filed on Oct. 10, 2019, the entire contents of which are hereby incorporated by reference. 
    
    
     BACKGROUND 
     1. Technical Field 
     The present disclosure relates to a three-dimensional data encoding method, a three-dimensional data decoding method, a three-dimensional data encoding device, and a three-dimensional data decoding device. 
     2. Description of the Related Art 
     Devices or services utilizing three-dimensional data are expected to find their widespread use in a wide range of fields, such as computer vision that enables autonomous operations of cars or robots, map information, monitoring, infrastructure inspection, and video distribution. Three-dimensional data is obtained through various means including a distance sensor such as a rangefinder, as well as a stereo camera and a combination of a plurality of monocular cameras. 
     Methods of representing three-dimensional data include a method known as a point cloud scheme that represents the shape of a three-dimensional structure by a point cloud in a three-dimensional space. In the point cloud scheme, the positions and colors of a point cloud are stored. While point cloud is expected to be a mainstream method of representing three-dimensional data, a massive amount of data of a point cloud necessitates compression of the amount of three-dimensional data by encoding for accumulation and transmission, as in the case of a two-dimensional moving picture (examples include Moving Picture Experts Group-4 Advanced Video Coding (MPEG-4 AVC) and High Efficiency Video Coding (HEVC) standardized by MPEG). 
     Meanwhile, point cloud compression is partially supported by, for example, an open-source library (Point Cloud Library) for point cloud-related processing. 
     Furthermore, a technique for searching for and displaying a facility located in the surroundings of the vehicle by using three-dimensional map data is known (for example, see International Publication WO 2014/020663). 
     SUMMARY 
     There has been a demand for improving coding efficiency in coding three-dimensional data. 
     The present disclosure has an object to provide a three-dimensional data encoding method, a three-dimensional data decoding method, a three-dimensional data encoding device, or a three-dimensional data decoding device that is capable of improving coding efficiency. 
     A three-dimensional data encoding method according to one aspect of the present disclosure includes: setting one prediction mode out of two or more prediction modes each for calculating a predicted value of an item of first geometry information of a first three-dimensional point using one or more items of second geometry information of one or more second three-dimensional points surrounding the first three-dimensional point; calculating a predicted value of the one prediction mode set; calculating a prediction residual that is a difference between the item of first geometry information and the predicted value calculated; and generating a first bitstream including the one prediction mode set and the prediction residual. In the setting, the one prediction mode is set based on a depth of the first three-dimensional point in the hierarchical structure. 
     A three-dimensional data decoding method according to one aspect of the present disclosure includes: obtaining a first bitstream including an encoded prediction mode of a first three-dimensional point among the three-dimensional points and an encoded prediction residual; decoding a prediction mode value indicating the encoded prediction mode, and the encoded prediction residual; calculating a predicted value of a prediction mode obtained in the decoding and indicated by the prediction mode value; and calculating an item of first geometry information of the first three-dimensional point by adding the predicted value and a prediction residual obtained in the decoding. The encoded prediction mode included in the first bitstream is a prediction mode set based on a depth of the first three-dimensional point in the hierarchical structure. 
     The present disclosure provides a three-dimensional data encoding method, a three-dimensional data decoding method, a three-dimensional data encoding device, or a three-dimensional data decoding device that is capable of improving coding efficiency. 
    
    
     
       BRIEF DESCRIPTION OF DRAWINGS 
       These and other objects, advantages and features of the disclosure will become apparent from the following description thereof taken in conjunction with the accompanying drawings that illustrate a specific embodiment of the present disclosure. 
         FIG. 1  is a diagram illustrating a configuration of a three-dimensional data encoding and decoding system according to Embodiment 1; 
         FIG. 2  is a diagram illustrating a structure example of point cloud data according to Embodiment 1; 
         FIG. 3  is a diagram illustrating a structure example of a data file indicating the point cloud data according to Embodiment 1; 
         FIG. 4  is a diagram illustrating types of the point cloud data according to Embodiment 1; 
         FIG. 5  is a diagram illustrating a structure of a first encoder according to Embodiment 1; 
         FIG. 6  is a block diagram illustrating the first encoder according to Embodiment 1; 
         FIG. 7  is a diagram illustrating a structure of a first decoder according to Embodiment 1; 
         FIG. 8  is a block diagram illustrating the first decoder according to Embodiment 1; 
         FIG. 9  is a block diagram of a three-dimensional data encoding device according to Embodiment 1; 
         FIG. 10  is a diagram showing an example of geometry information according to Embodiment 1; 
         FIG. 11  is a diagram showing an example of an octree representation of geometry information according to Embodiment 1; 
         FIG. 12  is a block diagram of a three-dimensional data decoding device according to Embodiment 1; 
         FIG. 13  is a block diagram of an attribute information encoder according to Embodiment 1; 
         FIG. 14  is a block diagram of an attribute information decoder according to Embodiment 1; 
         FIG. 15  is a block diagram showing a configuration of the attribute information encoder according to the variation of Embodiment 1; 
         FIG. 16  is a block diagram of the attribute information encoder according to Embodiment 1; 
         FIG. 17  is a block diagram showing a configuration of the attribute information decoder according to the variation of Embodiment 1; 
         FIG. 18  is a block diagram of the attribute information decoder according to Embodiment 1; 
         FIG. 19  is a diagram illustrating a structure of a second encoder according to Embodiment 1; 
         FIG. 20  is a block diagram illustrating the second encoder according to Embodiment 1; 
         FIG. 21  is a diagram illustrating a structure of a second decoder according to Embodiment 1; 
         FIG. 22  is a block diagram illustrating the second decoder according to Embodiment 1; 
         FIG. 23  is a diagram illustrating a protocol stack related to PCC encoded data according to Embodiment 1; 
         FIG. 24  is a diagram illustrating structures of an encoder and a multiplexer according to Embodiment 2; 
         FIG. 25  is a diagram illustrating a structure example of encoded data according to Embodiment 2; 
         FIG. 26  is a diagram illustrating a structure example of encoded data and a NAL unit according to Embodiment 2; 
         FIG. 27  is a diagram illustrating a semantics example of pcc_nal_unit_type according to Embodiment 2; 
         FIG. 28  is a diagram illustrating an example of a transmitting order of NAL units according to Embodiment 2; 
         FIG. 29  is a flowchart of processing performed by a three-dimensional data encoding device according to Embodiment 2; 
         FIG. 30  is a flowchart of processing performed by a three-dimensional data decoding device according to Embodiment 2; 
         FIG. 31  is a flowchart of multiplexing processing according to Embodiment 2; 
         FIG. 32  is a flowchart of demultiplexing processing according to Embodiment 2; 
         FIG. 33  is a diagram showing a structure of a distribution system according to Embodiment 3; 
         FIG. 34  is a diagram showing an example structure of a bitstream of an encoded three-dimensional map according to Embodiment 3; 
         FIG. 35  is a diagram for describing an advantageous effect on encoding efficiency according to Embodiment 3; 
         FIG. 36  is a flowchart of processes performed by a server according to Embodiment 3; 
         FIG. 37  is a flowchart of processes performed by a client according to Embodiment 3; 
         FIG. 38  is a diagram showing an example syntax of a submap according to Embodiment 3; 
         FIG. 39  is a diagram schematically showing a switching process of an encoding type according to Embodiment 3; 
         FIG. 40  is a diagram showing an example syntax of a submap according to Embodiment 3; 
         FIG. 41  is a flowchart of a three-dimensional data encoding process according to Embodiment 3; 
         FIG. 42  is a flowchart of a three-dimensional data decoding process according to Embodiment 3; 
         FIG. 43  is a diagram schematically showing an operation of a variation of the switching process of the encoding type according to Embodiment 3; 
         FIG. 44  is a diagram schematically showing an operation of a variation of the switching process of the encoding type according to Embodiment 3; 
         FIG. 45  is a diagram schematically showing an operation of a variation of the switching process of the encoding type according to Embodiment 3; 
         FIG. 46  is a diagram schematically showing an operation of a variation of a calculation process of a differential value according to Embodiment 3; 
         FIG. 47  is a diagram schematically showing an operation of a variation of the calculation process of the differential value according to Embodiment 3; 
         FIG. 48  is a diagram schematically showing an operation of a variation of the calculation process of the differential value according to Embodiment 3; 
         FIG. 49  is a diagram schematically showing an operation of a variation of the calculation process of the differential value according to Embodiment 3; 
         FIG. 50  is a diagram showing an example syntax of a volume according to Embodiment 3; 
         FIG. 51  is a diagram illustrating an example of three-dimensional points according to Embodiment 4; 
         FIG. 52  is a diagram illustrating an example of setting LoDs according to Embodiment 4; 
         FIG. 53  is a diagram illustrating an example of setting LoDs according to Embodiment 4; 
         FIG. 54  is a diagram illustrating an example of attribute information to be used for predicted values according to Embodiment 4; 
         FIG. 55  is a diagram illustrating examples of exponential-Golomb codes according to Embodiment 4; 
         FIG. 56  is a diagram indicating a process on exponential-Golomb codes according to Embodiment 4; 
         FIG. 57  is a diagram indicating an example of a syntax in attribute header according to Embodiment 4; 
         FIG. 58  is a diagram indicating an example of a syntax in attribute data according to Embodiment 4; 
         FIG. 59  is a flowchart of a three-dimensional data encoding process according to Embodiment 4; 
         FIG. 60  is a flowchart of an attribute information encoding process according to Embodiment 4; 
         FIG. 61  is a diagram indicating processing on exponential-Golomb codes according to Embodiment 4; 
         FIG. 62  is a diagram indicating an example of a reverse lookup table indicating relationships between remaining codes and the values thereof according to Embodiment 4; 
         FIG. 63  is a flowchart of a three-dimensional data decoding process according to Embodiment 4; 
         FIG. 64  is a flowchart of an attribute information decoding process according to Embodiment 4; 
         FIG. 65  is a block diagram of a three-dimensional data encoding device according to Embodiment 4; 
         FIG. 66  is a block diagram of a three-dimensional data decoding device according to Embodiment 4; 
         FIG. 67  is a diagram showing a first example of a table representing predicted values calculated in prediction modes according to Embodiment 5; 
         FIG. 68  is a diagram showing examples of attribute information items (pieces of attribute information) used as the predicted values according to Embodiment 5; 
         FIG. 69  is a diagram showing a second example of a table representing predicted values calculated in the prediction modes according to Embodiment 5; 
         FIG. 70  is a diagram showing a third example of a table representing predicted values calculated in the prediction modes according to Embodiment 5; 
         FIG. 71  is a diagram showing a fourth example of a table representing predicted values calculated in the prediction modes according to Embodiment 5; 
         FIG. 72  is a diagram showing a fifth example of a table representing predicted values calculated in the prediction modes according to Embodiment 5; 
         FIG. 73  is a diagram showing a sixth example of a table representing predicted values calculated in the prediction modes according to Embodiment 5; 
         FIG. 74  is a diagram showing a seventh example of a table representing predicted values calculated in the prediction modes according to Embodiment 5; 
         FIG. 75  is a diagram showing an eighth example of a table representing predicted values calculated in the prediction modes according to Embodiment 5; 
         FIG. 76  is a diagram showing a first example of a binarization table in binarizing and encoding prediction mode values according to Embodiment 5; 
         FIG. 77  is a diagram showing a second example of a binarization table in binarizing and encoding the prediction mode values according to Embodiment 5; 
         FIG. 78  is a diagram showing a third example of a binarization table in binarizing and encoding the prediction mode values according to Embodiment 5; 
         FIG. 79  is a diagram for describing an example of encoding binary data in the binarization table in binarizing and encoding the prediction modes according to Embodiment 5; 
         FIG. 80  is a flowchart of an example of encoding a prediction mode value according to Embodiment 5; 
         FIG. 81  is a flowchart of an example of decoding a prediction mode value according to Embodiment 5; 
         FIG. 82  is a diagram showing another example of a table representing predicted values calculated in the prediction modes according to Embodiment 5; 
         FIG. 83  is a diagram for describing an example of encoding binary data in the binarization table in binarizing and encoding the prediction modes according to Embodiment 5; 
         FIG. 84  is flowchart of another example of encoding a prediction mode value according to Embodiment 5; 
         FIG. 85  is a flowchart of another example of decoding a prediction mode value according to Embodiment 5; 
         FIG. 86  is a flowchart of an example of a process of determining whether or not a prediction mode value is fixed under condition A in encoding according to Embodiment 5; 
         FIG. 87  is a flowchart of an example of a process of determining whether the prediction mode value is fixed or decoded under condition A in decoding according to Embodiment 5; 
         FIG. 88  is a diagram for describing maximum absolute differential value maxdiff according to Embodiment 5; 
         FIG. 89  is a diagram showing an example of a syntax according to Embodiment 5; 
         FIG. 90  is a diagram showing an example of a syntax according to Embodiment 5; 
         FIG. 91  is a flowchart of a three-dimensional data encoding process by a three-dimensional data encoding device according to Embodiment 5; 
         FIG. 92  is a flowchart of an attribute information encoding process according to Embodiment 5; 
         FIG. 93  is a flowchart of a predicted value calculation process by the three-dimensional data encoding device according to Embodiment 5; 
         FIG. 94  is a flowchart of a prediction mode selection process according to Embodiment 5; 
         FIG. 95  is a flowchart of a prediction mode selection process that minimizes cost according to Embodiment 5; 
         FIG. 96  is a flowchart of a three-dimensional data decoding process by a three-dimensional data decoding device according to Embodiment 5; 
         FIG. 97  is a flowchart of an attribute information decoding process according to Embodiment 5; 
         FIG. 98  is a flowchart of a predicted value calculation process by the three-dimensional data decoding device according to Embodiment 5; 
         FIG. 99  is a flowchart of a prediction mode decoding process according to Embodiment 5; 
         FIG. 100  is a block diagram showing a configuration of an attribute information encoder included in the three-dimensional data encoding device according to Embodiment 5; 
         FIG. 101  is a block diagram showing a configuration of an attribute information decoder included in the three-dimensional data decoding device according to Embodiment 5; 
         FIG. 102  is a flowchart of a prediction mode determination process performed by a three-dimensional data encoding device according to Embodiment 6; 
         FIG. 103  is a diagram showing an example of a syntax of the prediction mode determination process performed by the three-dimensional data encoding device according to Embodiment 6; 
         FIG. 104  is a flowchart of a prediction mode determination process performed by a three-dimensional data decoding device according to Embodiment 6; 
         FIG. 105  is a diagram showing an example of a syntax of attribute data when a prediction mode fixing flag is provided for each three-dimensional point according to Embodiment 6; 
         FIG. 106  is a diagram showing an example of a syntax of attribute data when a prediction mode fixing flag is provided for each LoD according to Embodiment 6; 
         FIG. 107  is a flowchart of an example of a prediction mode encoding process by the three-dimensional data encoding device according to Embodiment 6; 
         FIG. 108  is a flowchart of an example of a prediction mode decoding process by the three-dimensional data decoding device according to Embodiment 6; 
         FIG. 109  is a flowchart of a three-dimensional data encoding process by the three-dimensional data encoding device according to Embodiment 6; 
         FIG. 110  is a flowchart of an attribute information encoding process shown in  FIG. 109 ; 
         FIG. 111  is a flowchart of a predicted-value calculation process shown in  FIG. 110 ; 
         FIG. 112  is a flowchart of a prediction mode selection process shown in  FIG. 111 ; 
         FIG. 113  is a flowchart of a specific example of the prediction mode selection process shown in  FIG. 112 ; 
         FIG. 114  is a flowchart of a three-dimensional data decoding process by the three-dimensional data decoding device according to Embodiment 6; 
         FIG. 115  is a flowchart of a predicted-value calculation process shown in  FIG. 114 ; 
         FIG. 116  is a flowchart of details of the predicted-value calculation process shown in  FIG. 115 ; 
         FIG. 117  is a flowchart of a calculation process of a prediction mode and a quantized value shown in  FIG. 116 ; 
         FIG. 118  is a flowchart of a process when the three-dimensional data encoding device does not fix a prediction mode according to Embodiment 6; 
         FIG. 119  is a flowchart of a process when the three-dimensional data decoding device does not fix a prediction mode according to Embodiment 6; 
         FIG. 120  is a diagram showing another example of a syntax of attribute data according to Embodiment 6; 
         FIG. 121  is a flowchart of an example of a prediction mode encoding process by the three-dimensional data encoding device according to Embodiment 6; 
         FIG. 122  is a flowchart of a prediction mode decoding process by the three-dimensional data decoding device according to Embodiment 6; 
         FIG. 123  is a flowchart of another example of the predicted-value calculation process shown in  FIG. 110 ; 
         FIG. 124  is a flowchart of a prediction mode selection process shown in  FIG. 123 ; 
         FIG. 125  is a flowchart of a specific example of the prediction mode selection process shown in  FIG. 124 ; 
         FIG. 126  is a flowchart of another example of the calculation process of a prediction mode and a quantized value shown in  FIG. 115 ; 
         FIG. 127  is a diagram showing an example of attribute information used in calculating a predicted value; 
         FIG. 128  is a diagram showing an example of the reference relationship according to Embodiment 7; 
         FIG. 129  is a diagram showing a calculation example of a QW according to Embodiment 7; 
         FIG. 130  is a diagram showing a calculation example of a predicted residual according to Embodiment 7; 
         FIG. 131  is a diagram illustrating an example of a prediction tree used in a three-dimensional data encoding method according to Embodiment 8; 
         FIG. 132  is a flowchart illustrating an example of a three-dimensional data encoding method according to Embodiment 8; 
         FIG. 133  is a flowchart illustrating an example of a three-dimensional data decoding method according to Embodiment 8; 
         FIG. 134  is a diagram for describing a method of generating a prediction tree according to Embodiment 8; 
         FIG. 135  is a diagram for describing a first example of prediction modes according to Embodiment 8; 
         FIG. 136  is a diagram illustrating a second example of a table that indicates a predicted value calculated in each prediction mode according to Embodiment 8; 
         FIG. 137  is a diagram illustrating a specific example of the second example of the table that indicates a predicted value calculated in each prediction mode according to Embodiment 8; 
         FIG. 138  is a diagram illustrating a third example of the table that indicates a predicted value calculated in each prediction mode according to Embodiment 8; 
         FIG. 139  is a diagram illustrating a fourth example of the table that indicates a predicted value calculated in each prediction mode according to Embodiment 8; 
         FIG. 140  is a diagram illustrating a fifth example of the table that indicates a predicted value calculated in each prediction mode according to Embodiment 8; 
         FIG. 141  is a diagram illustrating a sixth example of the table that indicates a predicted value calculated in each prediction mode according to Embodiment 8; 
         FIG. 142  is a diagram illustrating a seventh example of the table that indicates a predicted value calculated in each prediction mode according to Embodiment 8; 
         FIG. 143  is a diagram illustrating a first example of a binarization table in a case where a prediction mode value is binarized and encoded according to Embodiment 8; 
         FIG. 144  is a diagram illustrating a second example of the binarization table in the case where a prediction mode value is binarized and encoded according to Embodiment 8; 
         FIG. 145  is a diagram illustrating a third example of the binarization table in the case where a prediction mode value is binarized and encoded according to Embodiment 8; 
         FIG. 146  is a diagram for describing an example of encoding of binary data in a binarization table in the case where a prediction mode value is binarized and encoded according to Embodiment 8; 
         FIG. 147  is a flowchart illustrating an example of encoding of a prediction mode value according to Embodiment 8; 
         FIG. 148  is a flowchart illustrating an example of decoding of a prediction mode value according to Embodiment 8; 
         FIG. 149  is a diagram illustrating another example of the table that indicates a predicted value calculated in each prediction mode according to Embodiment 8; 
         FIG. 150  is a diagram for describing an example of encoding of binary data in a binarization table in the case where a prediction mode value is binarized and encoded according to Embodiment 8; 
         FIG. 151  is a flowchart illustrating another example of encoding of a prediction mode value according to Embodiment 8; 
         FIG. 152  is a flowchart illustrating another example of decoding of a prediction mode value according to Embodiment 8; 
         FIG. 153  is a flowchart illustrating an example of a process of determining whether or not to fix the prediction mode value according to condition A in encoding according to Embodiment 8; 
         FIG. 154  is a flowchart illustrating an example of a process of determining whether to set the prediction mode value at a fixed value or decode the prediction mode value according to condition A in decoding according to Embodiment 8; 
         FIG. 155  is a diagram illustrating an example of a syntax of a header of geometry information according to Embodiment 8; 
         FIG. 156  is a diagram illustrating an example of a syntax of geometry information according to Embodiment 8; 
         FIG. 157  is a diagram illustrating another example of the syntax of geometry information according to Embodiment 8; 
         FIG. 158  is a diagram illustrating an example of a prediction tree used in a three-dimensional data encoding method according to Embodiment 9; 
         FIG. 159  is a diagram illustrating another example of a syntax of geometry information according to Embodiment 9; 
         FIG. 160  is a diagram illustrating an example of a configuration of a prediction tree used for encoding of both geometry information and attribute information according to Embodiment 9; 
         FIG. 161  is a flowchart illustrating an example of a three-dimensional data encoding method according to a modification of Embodiment 9; 
         FIG. 162  is a flowchart illustrating an example of a three-dimensional data decoding method according to a modification of Embodiment 9; 
         FIG. 163  is a diagram illustrating an example of a syntax of a header of attribute information according to Embodiment 9; 
         FIG. 164  is a diagram illustrating another example of a syntax of attribute information according to Embodiment 9; 
         FIG. 165  is a diagram illustrating an example of a syntax of geometry information and attribute information according to Embodiment 9; 
         FIG. 166  is a flowchart of a process by a three-dimensional data encoding device according to Embodiments 8 and 9; 
         FIG. 167  is a flowchart of a process by a three-dimensional data decoding device according to Embodiments 8 and 9; 
         FIG. 168  is a block diagram of a three-dimensional data creation device according to Embodiment 10; 
         FIG. 169  is a flowchart of a three-dimensional data creation method according to Embodiment 10; 
         FIG. 170  is a diagram showing a structure of a system according to Embodiment 10; 
         FIG. 171  is a block diagram of a client device according to Embodiment 10; 
         FIG. 172  is a block diagram of a server according to Embodiment 10; 
         FIG. 173  is a flowchart of a three-dimensional data creation process performed by the client device according to Embodiment 10; 
         FIG. 174  is a flowchart of a sensor information transmission process performed by the client device according to Embodiment 10; 
         FIG. 175  is a flowchart of a three-dimensional data creation process performed by the server according to Embodiment 10; 
         FIG. 176  is a flowchart of a three-dimensional map transmission process performed by the server according to Embodiment 10; 
         FIG. 177  is a diagram showing a structure of a variation of the system according to Embodiment 10; 
         FIG. 178  is a diagram showing a structure of the server and client devices according to Embodiment 10; 
         FIG. 179  is a diagram illustrating a configuration of a server and a client device according to Embodiment 10; 
         FIG. 180  is a flowchart of a process performed by the client device according to Embodiment 10; 
         FIG. 181  is a diagram illustrating a configuration of a sensor information collection system according to Embodiment 10; 
         FIG. 182  is a diagram illustrating an example of a system according to Embodiment 10; 
         FIG. 183  is a diagram illustrating a variation of the system according to Embodiment 10; 
         FIG. 184  is a flowchart illustrating an example of an application process according to Embodiment 10; 
         FIG. 185  is a diagram illustrating the sensor range of various sensors according to Embodiment 10; 
         FIG. 186  is a diagram illustrating a configuration example of an automated driving system according to Embodiment 10; 
         FIG. 187  is a diagram illustrating a configuration example of a bitstream according to Embodiment 10; 
         FIG. 188  is a flowchart of a point cloud selection process according to Embodiment 10; 
         FIG. 189  is a diagram illustrating a screen example for point cloud selection process according to Embodiment 10; 
         FIG. 190  is a diagram illustrating a screen example of the point cloud selection process according to Embodiment 10; and 
         FIG. 191  is a diagram illustrating a screen example of the point cloud selection process according to Embodiment 10. 
     
    
    
     DETAILED DESCRIPTION OF THE EMBODIMENTS 
     A three-dimensional data encoding method according to one aspect of the present disclosure includes: setting one prediction mode out of two or more prediction modes each for calculating a predicted value of an item of first geometry information of a first three-dimensional point using one or more items of second geometry information of one or more second three-dimensional points surrounding the first three-dimensional point; calculating a predicted value of the one prediction mode set; calculating a prediction residual that is a difference between the item of first geometry information and the predicted value calculated; and generating a first bitstream including the one prediction mode set and the prediction residual. In the setting, the one prediction mode is set based on a depth of the first three-dimensional point in the hierarchical structure. 
     According to this, geometry information can be encoded using a predicted value in one prediction mode among two or more prediction modes that is set based on the depth in the hierarchical structure, so that the encoding efficiency of the geometry information can be improved. 
     In the setting, a prediction mode value that is less than or equal to a value of the depth of the first three-dimensional point in the hierarchical structure may be set, and the prediction mode value may indicate the one prediction mode. 
     The first bitstream may further include a prediction mode count indicating a total number of the two or more prediction modes. 
     In the generating, a prediction mode value indicating the one prediction mode set may be encoded using the prediction mode count, and the first bitstream may include the prediction mode value encoded as the one prediction mode set. 
     In the generating, the prediction mode value may be encoded using a truncated unary code in which the prediction mode count is set as a maximum value. 
     Therefore, the code amount of the prediction mode value can be reduced. 
     Each of the item of first geometry information and the one or more items of second geometry information may include three elements, and in the setting, a prediction mode for calculating a predicted value of each of the three elements included in the item of first geometry information may be set for the three elements in common. 
     Therefore, the code amount of the prediction mode value can be reduced. 
     Each of the item of first geometry information and the one or more items of second geometry information may include three elements, and in the setting, a prediction mode for calculating a predicted value of each of the three elements included in the item of first geometry information may be set for the three elements independently of each other. 
     Therefore, the three-dimensional data decoding device can independently decode each element. 
     Each of the item of first geometry information and the one or more items of second geometry information may include three elements, and in the setting, a prediction mode for calculating a predicted value of each of the three elements included in the item of first geometry information may be set for two elements among the three elements in common, and is set for a remaining one element independently of the two elements. 
     Therefore, the code amount of the prediction mode value can be reduced for the two elements. Therefore, the three-dimensional data decoding device can independently decode the remaining one element. 
     In the generating, when the prediction mode count is 1, the prediction mode value need not be encoded, and a second bitstream not including the prediction mode value indicating the one prediction mode may be generated. 
     Therefore, the code amount of the bitstream can be reduced. 
     In the generating, when a prediction mode in which the predicted value calculated in the calculating is 0 is set, an item of positive and negative information need not be encoded, and a third bitstream not including the item of positive and negative information may be generated, the item of positive and negative information indicating whether the prediction residual is positive or negative. 
     Therefore, the code amount of the bitstream can be reduced. 
     A three-dimensional data decoding method according to one aspect of the present disclosure includes: obtaining a first bitstream including an encoded prediction mode of a first three-dimensional point among the three-dimensional points and an encoded prediction residual; decoding a prediction mode value indicating the encoded prediction mode, and the encoded prediction residual; calculating a predicted value of a prediction mode obtained in the decoding and indicated by the prediction mode value; and calculating an item of first geometry information of the first three-dimensional point by adding the predicted value and a prediction residual obtained in the decoding. The encoded prediction mode included in the first bitstream is a prediction mode set based on a depth of the first three-dimensional point in the hierarchical structure. 
     According to this, geometry information can be encoded using a predicted value in one prediction mode among two or more prediction modes that is set based on the depth in the hierarchical structure, so that the encoding efficiency of the geometry information can be improved. 
     The prediction mode value indicating the encoded prediction mode included in the first bitstream may be less than or equal to a value of the depth of the first three-dimensional point in the hierarchical structure. 
     The first bitstream may include a prediction mode count indicating a total number of the two or more prediction modes. 
     In the decoding, the prediction mode value may be decoded using a truncated unary code in which the total number of the two or more prediction modes is set as a maximum value. 
     Each of the item of first geometry information and one or more items of second geometry information of one or more second three-dimensional points may include three elements, the one or more second three-dimensional points surrounding the first three-dimensional point, and a prediction mode for calculating a predicted value of each of the three elements included in the item of first geometry information may be set for the three elements in common. 
     Each of the item of first geometry information and one or more items of second geometry information of one or more second three-dimensional points may include three elements, the one or more second three-dimensional points surrounding the first three-dimensional point, and a prediction mode for calculating a predicted value of each of the three elements included in the item of first geometry information may be set for the three elements independently of each other. 
     Each of the item of first geometry information and one or more items of second geometry information of one or more second three-dimensional points may include three elements, the one or more second three-dimensional points surrounding the first three-dimensional point, and a prediction mode for calculating a predicted value of each of the three elements included in the item of first geometry information may be set for two elements among the three elements in common, and is set for a remaining one element independently of the two elements. 
     When a second bitstream not including the prediction mode value is obtained in the obtaining, a predicted value of a specific prediction mode may be calculated in the calculating of the predicted value. 
     When a third bitstream not including positive and negative information is obtained in the obtaining, the prediction residual may be used as 0 or a positive number in the calculating of the item of first geometry information. 
     A three-dimensional data encoding device according to one aspect of the present disclosure is a three-dimensional data encoding device that encodes three-dimensional points having a hierarchical structure and includes a processor and memory. Using the memory, the processor: sets one prediction mode out of two or more prediction modes each for calculating a predicted value of an item of first geometry information of a first three-dimensional point using one or more items of second geometry information of one or more second three-dimensional points surrounding the first three-dimensional point; calculates a predicted value of the one prediction mode set; calculates a prediction residual that is a difference between the item of first geometry information and the predicted value calculated; and generates a first bitstream including the one prediction mode set and the prediction residual. In the setting, the one prediction mode is set based on a depth of the first three-dimensional point in the hierarchical structure. 
     According to this, geometry information can be encoded using a predicted value in one prediction mode among two or more prediction modes that is set based on the depth in the hierarchical structure, so that the encoding efficiency of the geometry information can be improved. 
     A three-dimensional data decoding device according to one aspect of the present disclosure is a three-dimensional data decoding device that decodes three-dimensional points having a hierarchical structure and includes a processor and memory. Using the memory, the processor: obtains a first bitstream including an encoded prediction mode of a first three-dimensional point among the three-dimensional points and an encoded prediction residual; decodes a prediction mode value indicating the encoded prediction mode, and the encoded prediction residual; calculates a predicted value of a prediction mode obtained in the decoding and indicated by the prediction mode value; and calculates an item of first geometry information of the first three-dimensional point by adding the predicted value and a prediction residual obtained in the decoding. The encoded prediction mode included in the first bitstream is a prediction mode set based on a depth of the first three-dimensional point in the hierarchical structure. 
     According to this, geometry information can be encoded using a predicted value in one prediction mode among two or more prediction modes that is set based on the depth in the hierarchical structure, so that the encoding efficiency of the geometry information can be improved. 
     It is to be noted that these general or specific aspects may be implemented as a system, a method, an integrated circuit, a computer program, or a computer-readable recording medium such as a CD-ROM, or may be implemented as any combination of a system, a method, an integrated circuit, a computer program, and a recording medium. 
     Hereinafter, embodiments will be specifically described with reference to the drawings. It is to be noted that each of the following embodiments indicate a specific example of the present disclosure. The numerical values, shapes, materials, constituent elements, the arrangement and connection of the constituent elements, steps, the processing order of the steps, etc., indicated in the following embodiments are mere examples, and thus are not intended to limit the present disclosure. Among the constituent elements described in the following embodiments, constituent elements not recited in any one of the independent claims will be described as optional constituent elements. 
     Embodiment 1 
     When using encoded data of a point cloud in a device or for a service in practice, required information for the application is desirably transmitted and received in order to reduce the network bandwidth. However, conventional encoding structures for three-dimensional data have no such a function, and there is also no encoding method for such a function. 
     Embodiment 1 described below relates to a three-dimensional data encoding method and a three-dimensional data encoding device for encoded data of a three-dimensional point cloud that provides a function of transmitting and receiving required information for an application, a three-dimensional data decoding method and a three-dimensional data decoding device for decoding the encoded data, a three-dimensional data multiplexing method for multiplexing the encoded data, and a three-dimensional data transmission method for transmitting the encoded data. 
     In particular, at present, a first encoding method and a second encoding method are under investigation as encoding methods (encoding schemes) for point cloud data. However, there is no method defined for storing the configuration of encoded data and the encoded data in a system format. Thus, there is a problem that an encoder cannot perform an MUX process (multiplexing), transmission, or accumulation of data. 
     In addition, there is no method for supporting a format that involves two codecs, the first encoding method and the second encoding method, such as point cloud compression (PCC). 
     With regard to this embodiment, a configuration of PCC-encoded data that involves two codecs, a first encoding method and a second encoding method, and a method of storing the encoded data in a system format will be described. 
     A configuration of a three-dimensional data (point cloud data) encoding and decoding system according to this embodiment will be first described.  FIG. 1  is a diagram showing an example of a configuration of the three-dimensional data encoding and decoding system according to this embodiment. As shown in  FIG. 1 , the three-dimensional data encoding and decoding system includes three-dimensional data encoding system  4601 , three-dimensional data decoding system  4602 , sensor terminal  4603 , and external connector  4604 . 
     Three-dimensional data encoding system  4601  generates encoded data or multiplexed data by encoding point cloud data, which is three-dimensional data. Three-dimensional data encoding system  4601  may be a three-dimensional data encoding device implemented by a single device or a system implemented by a plurality of devices. The three-dimensional data encoding device may include a part of a plurality of processors included in three-dimensional data encoding system  4601 . 
     Three-dimensional data encoding system  4601  includes point cloud data generation system  4611 , presenter  4612 , encoder  4613 , multiplexer  4614 , input/output unit  4615 , and controller  4616 . Point cloud data generation system  4611  includes sensor information obtainer  4617 , and point cloud data generator  4618 . 
     Sensor information obtainer  4617  obtains sensor information from sensor terminal  4603 , and outputs the sensor information to point cloud data generator  4618 . Point cloud data generator  4618  generates point cloud data from the sensor information, and outputs the point cloud data to encoder  4613 . 
     Presenter  4612  presents the sensor information or point cloud data to a user. For example, presenter  4612  displays information or an image based on the sensor information or point cloud data. 
     Encoder  4613  encodes (compresses) the point cloud data, and outputs the resulting encoded data, control information (signaling information) obtained in the course of the encoding, and other additional information to multiplexer  4614 . The additional information includes the sensor information, for example. 
     Multiplexer  4614  generates multiplexed data by multiplexing the encoded data, the control information, and the additional information input thereto from encoder  4613 . A format of the multiplexed data is a file format for accumulation or a packet format for transmission, for example. 
     Input/output unit  4615  (a communication unit or interface, for example) outputs the multiplexed data to the outside. Alternatively, the multiplexed data may be accumulated in an accumulator, such as an internal memory. Controller  4616  (or an application executor) controls each processor. That is, controller  4616  controls the encoding, the multiplexing, or other processing. 
     Note that the sensor information may be input to encoder  4613  or multiplexer  4614 . Alternatively, input/output unit  4615  may output the point cloud data or encoded data to the outside as it is. 
     A transmission signal (multiplexed data) output from three-dimensional data encoding system  4601  is input to three-dimensional data decoding system  4602  via external connector  4604 . 
     Three-dimensional data decoding system  4602  generates point cloud data, which is three-dimensional data, by decoding the encoded data or multiplexed data. Note that three-dimensional data decoding system  4602  may be a three-dimensional data decoding device implemented by a single device or a system implemented by a plurality of devices. The three-dimensional data decoding device may include a part of a plurality of processors included in three-dimensional data decoding system  4602 . 
     Three-dimensional data decoding system  4602  includes sensor information obtainer  4621 , input/output unit  4622 , demultiplexer  4623 , decoder  4624 , presenter  4625 , user interface  4626 , and controller  4627 . 
     Sensor information obtainer  4621  obtains sensor information from sensor terminal  4603 . 
     Input/output unit  4622  obtains the transmission signal, decodes the transmission signal into the multiplexed data (file format or packet), and outputs the multiplexed data to demultiplexer  4623 . 
     Demultiplexer  4623  obtains the encoded data, the control information, and the additional information from the multiplexed data, and outputs the encoded data, the control information, and the additional information to decoder  4624 . 
     Decoder  4624  reconstructs the point cloud data by decoding the encoded data. 
     Presenter  4625  presents the point cloud data to a user. For example, presenter  4625  displays information or an image based on the point cloud data. User interface  4626  obtains an indication based on a manipulation by the user. Controller  4627  (or an application executor) controls each processor. That is, controller  4627  controls the demultiplexing, the decoding, the presentation, or other processing. 
     Note that input/output unit  4622  may obtain the point cloud data or encoded data as it is from the outside. Presenter  4625  may obtain additional information, such as sensor information, and present information based on the additional information. Presenter  4625  may perform a presentation based on an indication from a user obtained on user interface  4626 . 
     Sensor terminal  4603  generates sensor information, which is information obtained by a sensor. Sensor terminal  4603  is a terminal provided with a sensor or a camera. For example, sensor terminal  4603  is a mobile body, such as an automobile, a flying object, such as an aircraft, a mobile terminal, or a camera. 
     Sensor information that can be generated by sensor terminal  4603  includes (1) the distance between sensor terminal  4603  and an object or the reflectance of the object obtained by LiDAR, a millimeter wave radar, or an infrared sensor or (2) the distance between a camera and an object or the reflectance of the object obtained by a plurality of monocular camera images or a stereo-camera image, for example. The sensor information may include the posture, orientation, gyro (angular velocity), position (GPS information or altitude), velocity, or acceleration of the sensor, for example. The sensor information may include air temperature, air pressure, air humidity, or magnetism, for example. 
     External connector  4604  is implemented by an integrated circuit (LSI or IC), an external accumulator, communication with a cloud server via the Internet, or broadcasting, for example. 
     Next, point cloud data will be described.  FIG. 2  is a diagram showing a configuration of point cloud data.  FIG. 3  is a diagram showing a configuration example of a data file describing information of the point cloud data. 
     Point cloud data includes data on a plurality of points. Data on each point includes geometry information (three-dimensional coordinates) and attribute information associated with the geometry information. A set of a plurality of such points is referred to as a point cloud. For example, a point cloud indicates a three-dimensional shape of an object. 
     Geometry information (position), such as three-dimensional coordinates, may be referred to as geometry. Data on each point may include attribute information (attribute) on a plurality of types of attributes. A type of attribute is color or reflectance, for example. 
     One item of attribute information (in other words, a piece of attribute information or an attribute information item) may be associated with one item of geometry information (in other words, a piece of geometry information or a geometry information item), or attribute information on a plurality of different types of attributes may be associated with one item of geometry information. Alternatively, items of attribute information on the same type of attribute may be associated with one item of geometry information. 
     The configuration example of a data file shown in  FIG. 3  is an example in which geometry information and attribute information are associated with each other in a one-to-one relationship, and geometry information and attribute information on N points forming point cloud data are shown. 
     The geometry information is information on three axes, specifically, an x-axis, a y-axis, and a z-axis, for example. The attribute information is RGB color information, for example. A representative data file is ply file, for example. 
     Next, types of point cloud data will be described.  FIG. 4  is a diagram showing types of point cloud data. As shown in  FIG. 4 , point cloud data includes a static object and a dynamic object. 
     The static object is three-dimensional point cloud data at an arbitrary time (a time point). The dynamic object is three-dimensional point cloud data that varies with time. In the following, three-dimensional point cloud data associated with a time point will be referred to as a PCC frame or a frame. 
     The object may be a point cloud whose range is limited to some extent, such as ordinary video data, or may be a large point cloud whose range is not limited, such as map information. 
     There are point cloud data having varying densities. There may be sparse point cloud data and dense point cloud data. 
     In the following, each processor will be described in detail. Sensor information is obtained by various means, including a distance sensor such as LiDAR or a range finder, a stereo camera, or a combination of a plurality of monocular cameras. Point cloud data generator  4618  generates point cloud data based on the sensor information obtained by sensor information obtainer  4617 . Point cloud data generator  4618  generates geometry information as point cloud data, and adds attribute information associated with the geometry information to the geometry information. 
     When generating geometry information or adding attribute information, point cloud data generator  4618  may process the point cloud data. For example, point cloud data generator  4618  may reduce the data amount by omitting a point cloud whose position coincides with the position of another point cloud. Point cloud data generator  4618  may also convert the geometry information (such as shifting, rotating or normalizing the position) or render the attribute information. 
     Note that, although  FIG. 1  shows point cloud data generation system  4611  as being included in three-dimensional data encoding system  4601 , point cloud data generation system  4611  may be independently provided outside three-dimensional data encoding system  4601 . 
     Encoder  4613  generates encoded data by encoding point cloud data according to an encoding method previously defined. In general, there are the two types of encoding methods described below. One is an encoding method using geometry information, which will be referred to as a first encoding method, hereinafter. The other is an encoding method using a video codec, which will be referred to as a second encoding method, hereinafter. 
     Decoder  4624  decodes the encoded data into the point cloud data using the encoding method previously defined. 
     Multiplexer  4614  generates multiplexed data by multiplexing the encoded data in an existing multiplexing method. The generated multiplexed data is transmitted or accumulated. Multiplexer  4614  multiplexes not only the PCC-encoded data but also another medium, such as a video, an audio, subtitles, an application, or a file, or reference time information. Multiplexer  4614  may further multiplex attribute information associated with sensor information or point cloud data. 
     Multiplexing schemes or file formats include ISOBMFF, MPEG-DASH, which is a transmission scheme based on ISOBMFF, MMT, MPEG-2 TS Systems, or RMP, for example. 
     Demultiplexer  4623  extracts PCC-encoded data, other media, time information and the like from the multiplexed data. 
     Input/output unit  4615  transmits the multiplexed data in a method suitable for the transmission medium or accumulation medium, such as broadcasting or communication. Input/output unit  4615  may communicate with another device over the Internet or communicate with an accumulator, such as a cloud server. 
     As a communication protocol, http, ftp, TCP, UDP or the like is used. The pull communication scheme or the push communication scheme can be used. 
     A wired transmission or a wireless transmission can be used. For the wired transmission, Ethernet (registered trademark), USB, RS-232C, HDMI (registered trademark), or a coaxial cable is used, for example. For the wireless transmission, wireless LAN, Wi-Fi (registered trademark), Bluetooth (registered trademark), or a millimeter wave is used, for example. 
     As a broadcasting scheme, DVB-T2, DVB-S2, DVB-C2, ATSC3.0, or ISDB-S3 is used, for example. 
       FIG. 5  is a diagram showing a configuration of first encoder  4630 , which is an example of encoder  4613  that performs encoding in the first encoding method.  FIG. 6  is a block diagram showing first encoder  4630 . First encoder  4630  generates encoded data (encoded stream) by encoding point cloud data in the first encoding method. First encoder  4630  includes geometry information encoder  4631 , attribute information encoder  4632 , additional information encoder  4633 , and multiplexer  4634 . 
     First encoder  4630  is characterized by performing encoding by keeping a three-dimensional structure in mind. First encoder  4630  is further characterized in that attribute information encoder  4632  performs encoding using information obtained from geometry information encoder  4631 . The first encoding method is referred to also as geometry-based PCC (GPCC). 
     Point cloud data is PCC point cloud data like a PLY file or PCC point cloud data generated from sensor information, and includes geometry information (position), attribute information (attribute), and other additional information (metadata). The geometry information is input to geometry information encoder  4631 , the attribute information is input to attribute information encoder  4632 , and the additional information is input to additional information encoder  4633 . 
     Geometry information encoder  4631  generates encoded geometry information (compressed geometry), which is encoded data, by encoding geometry information. For example, geometry information encoder  4631  encodes geometry information using an N-ary tree structure, such as an octree. Specifically, in the case of an octree, a current space (target space) is divided into eight nodes (subspaces), 8-bit information (occupancy code) that indicates whether each node includes a point cloud or not is generated. A node including a point cloud is further divided into eight nodes, and 8-bit information that indicates whether each of the eight nodes includes a point cloud or not is generated. This process is repeated until a predetermined level is reached or the number of the point clouds included in each node becomes equal to or less than a threshold. 
     Attribute information encoder  4632  generates encoded attribute information (compressed attribute), which is encoded data, by encoding attribute information using configuration information generated by geometry information encoder  4631 . For example, attribute information encoder  4632  determines a reference point (reference node) that is to be referred to in encoding a current point (in other words, a current node or a target node) to be processed based on the octree structure generated by geometry information encoder  4631 . For example, attribute information encoder  4632  refers to a node whose parent node in the octree is the same as the parent node of the current node, of peripheral nodes or neighboring nodes. Note that the method of determining a reference relationship is not limited to this method. 
     The process of encoding attribute information may include at least one of a quantization process, a prediction process, and an arithmetic encoding process. In this case, “refer to” means using a reference node for calculating a predicted value of attribute information or using a state of a reference node (occupancy information that indicates whether a reference node includes a point cloud or not, for example) for determining a parameter of encoding. For example, the parameter of encoding is a quantization parameter in the quantization process or a context or the like in the arithmetic encoding. 
     Additional information encoder  4633  generates encoded additional information (compressed metadata), which is encoded data, by encoding compressible data of additional information. 
     Multiplexer  4634  generates encoded stream (compressed stream), which is encoded data, by multiplexing encoded geometry information, encoded attribute information, encoded additional information, and other additional information. The generated encoded stream is output to a processor in a system layer (not shown). 
     Next, first decoder  4640 , which is an example of decoder  4624  that performs decoding in the first encoding method, will be described.  FIG. 7  is a diagram showing a configuration of first decoder  4640 .  FIG. 8  is a block diagram showing first decoder  4640 . First decoder  4640  generates point cloud data by decoding encoded data (encoded stream) encoded in the first encoding method in the first encoding method. First decoder  4640  includes demultiplexer  4641 , geometry information decoder  4642 , attribute information decoder  4643 , and additional information decoder  4644 . 
     An encoded stream (compressed stream), which is encoded data, is input to first decoder  4640  from a processor in a system layer (not shown). 
     Demultiplexer  4641  separates encoded geometry information (compressed geometry), encoded attribute information (compressed attribute), encoded additional information (compressed metadata), and other additional information from the encoded data. 
     Geometry information decoder  4642  generates geometry information by decoding the encoded geometry information. For example, geometry information decoder  4642  restores the geometry information on a point cloud represented by three-dimensional coordinates from encoded geometry information represented by an N-ary structure, such as an octree. 
     Attribute information decoder  4643  decodes the encoded attribute information based on configuration information generated by geometry information decoder  4642 . For example, attribute information decoder  4643  determines a reference point (reference node) that is to be referred to in decoding a current point (current node) to be processed based on the octree structure generated by geometry information decoder  4642 . For example, attribute information decoder  4643  refers to a node whose parent node in the octree is the same as the parent node of the current node, of peripheral nodes or neighboring nodes. Note that the method of determining a reference relationship is not limited to this method. 
     The process of decoding attribute information may include at least one of an inverse quantization process, a prediction process, and an arithmetic decoding process. In this case, “refer to” means using a reference node for calculating a predicted value of attribute information or using a state of a reference node (occupancy information that indicates whether a reference node includes a point cloud or not, for example) for determining a parameter of decoding. For example, the parameter of decoding is a quantization parameter in the inverse quantization process or a context or the like in the arithmetic decoding. 
     Additional information decoder  4644  generates additional information by decoding the encoded additional information. First decoder  4640  uses additional information required for the decoding process for the geometry information and the attribute information in the decoding, and outputs additional information required for an application to the outside. 
     Next, an example configuration of a geometry information encoder will be described.  FIG. 9  is a block diagram of geometry information encoder  2700  according to this embodiment. Geometry information encoder  2700  includes octree generator  2701 , geometry information calculator  2702 , encoding table selector  2703 , and entropy encoder  2704 . 
     Octree generator  2701  generates an octree, for example, from input position information, and generates an occupancy code of each node of the octree. Geometry information calculator  2702  obtains information that indicates whether a neighboring node of a current node (target node) is an occupied node or not. For example, geometry information calculator  2702  calculates occupancy information on a neighboring node from an occupancy code of a parent node to which a current node belongs (information that indicates whether a neighboring node is an occupied node or not). Geometry information calculator  2702  may save an encoded node in a list and search the list for a neighboring node. Note that geometry information calculator  2702  may change neighboring nodes in accordance with the position of the current node in the parent node. 
     Encoding table selector  2703  selects an encoding table used for entropy encoding of the current node based on the occupancy information on the neighboring node calculated by geometry information calculator  2702 . For example, encoding table selector  2703  may generate a bit sequence based on the occupancy information on the neighboring node and select an encoding table of an index number generated from the bit sequence. 
     Entropy encoder  2704  generates encoded geometry information and metadata by entropy-encoding the occupancy code of the current node using the encoding table of the selected index number. Entropy encoder may add, to the encoded geometry information, information that indicates the selected encoding table. 
     In the following, an octree representation and a scan order for geometry information will be described. Geometry information (geometry data) is transformed into an octree structure (octree transform) and then encoded. The octree structure includes nodes and leaves. Each node has eight nodes or leaves, and each leaf has voxel (VXL) information.  FIG. 10  is a diagram showing an example structure of geometry information including a plurality of voxels.  FIG. 11  is a diagram showing an example in which the geometry information shown in  FIG. 10  is transformed into an octree structure. Here, of leaves shown in  FIG. 11 , leaves  1 ,  2 , and  3  represent voxels VXL 1 , VXL 2 , and VXL 3  shown in  FIG. 10 , respectively, and each represent VXL containing a point cloud (referred to as a valid VXL, hereinafter). 
     Specifically, node 1 corresponds to the entire space comprising the geometry information in  FIG. 10 . The entire space corresponding to node 1 is divided into eight nodes, and among the eight nodes, a node containing valid VXL is further divided into eight nodes or leaves. This process is repeated for every layer of the tree structure. Here, each node corresponds to a subspace, and has information (occupancy code) that indicates where the next node or leaf is located after division as node information. A block in the bottom layer is designated as a leaf and retains the number of the points contained in the leaf as leaf information. 
     Next, an example configuration of a geometry information decoder will be described.  FIG. 12  is a block diagram of geometry information decoder  2710  according to this embodiment. Geometry information decoder  2710  includes octree generator  2711 , geometry information calculator  2712 , encoding table selector  2713 , and entropy decoder  2714 . 
     Octree generator  2711  generates an octree of a space (node) based on header information, metadata or the like of a bitstream. For example, octree generator  2711  generates an octree by generating a large space (root node) based on the sizes of a space in an x-axis direction, a y-axis direction, and a z-axis direction added to the header information and dividing the space into two parts in the x-axis direction, the y-axis direction, and the z-axis direction to generate eight small spaces A (nodes A0 to A7). Nodes A0 to A7 are sequentially designated as a current node. 
     Geometry information calculator  2712  obtains occupancy information that indicates whether a neighboring node of a current node is an occupied node or not. For example, geometry information calculator  2712  calculates occupancy information on a neighboring node from an occupancy code of a parent node to which a current node belongs. Geometry information calculator  2712  may save a decoded node in a list and search the list for a neighboring node. Note that geometry information calculator  2712  may change neighboring nodes in accordance with the position of the current node in the parent node. 
     Encoding table selector  2713  selects an encoding table (decoding table) used for entropy decoding of the current node based on the occupancy information on the neighboring node calculated by geometry information calculator  2712 . For example, encoding table selector  2713  may generate a bit sequence based on the occupancy information on the neighboring node and select an encoding table of an index number generated from the bit sequence. 
     Entropy decoder  2714  generates position information by entropy-decoding the occupancy code of the current node using the selected encoding table. Note that entropy decoder  2714  may obtain information on the selected encoding table by decoding the bitstream, and entropy-decode the occupancy code of the current node using the encoding table indicated by the information. 
     In the following, configurations of an attribute information encoder and an attribute information decoder will be described.  FIG. 13  is a block diagram showing an example configuration of attribute information encoder A 100 . The attribute information encoder may include a plurality of encoders that perform different encoding methods. For example, the attribute information encoder may selectively use any of the two methods described below in accordance with the use case. 
     Attribute information encoder A 100  includes LoD attribute information encoder A 101  and transformed-attribute-information encoder A 102 . LoD attribute information encoder A 101  classifies three-dimensional points into a plurality of layers based on geometry information on the three-dimensional points, predicts attribute information on three-dimensional points belonging to each layer, and encodes a prediction residual therefor. Here, each layer into which a three-dimensional point is classified is referred to as a level of detail (LoD). 
     Transformed-attribute-information encoder A 102  encodes attribute information using region adaptive hierarchical transform (RAHT). Specifically, transformed-attribute-information encoder A 102  generates a high frequency component and a low frequency component for each layer by applying RAHT or Haar transform to each item of attribute information based on the geometry information on three-dimensional points, and encodes the values by quantization, entropy encoding or the like. 
       FIG. 14  is a block diagram showing an example configuration of attribute information decoder A 110 . The attribute information decoder may include a plurality of decoders that perform different decoding methods. For example, the attribute information decoder may selectively use any of the two methods described below for decoding based on the information included in the header or metadata. 
     Attribute information decoder A 110  includes LoD attribute information decoder A 111  and transformed-attribute-information decoder A 112 . LoD attribute information decoder A 111  classifies three-dimensional points into a plurality of layers based on the geometry information on the three-dimensional points, predicts attribute information on three-dimensional points belonging to each layer, and decodes attribute values thereof. 
     Transformed-attribute-information decoder A 112  decodes attribute information using region adaptive hierarchical transform (RAHT). Specifically, transformed-attribute-information decoder A 112  decodes each attribute value by applying inverse RAHT or inverse Haar transform to the high frequency component and the low frequency component of the attribute value based on the geometry information on the three-dimensional point. 
       FIG. 15  is a block diagram showing a configuration of attribute information encoder  3140  that is an example of LoD attribute information encoder A 101 . 
     Attribute information encoder  3140  includes LoD generator  3141 , periphery searcher  3142 , predictor  3143 , prediction residual calculator  3144 , quantizer  3145 , arithmetic encoder  3146 , inverse quantizer  3147 , decoded value generator  3148 , and memory  3149 . 
     LoD generator  3141  generates an LoD using geometry information on a three-dimensional point. 
     Periphery searcher  3142  searches for a neighboring three-dimensional point neighboring each three-dimensional point using a result of LoD generation by LoD generator  3141  and distance information indicating distances between three-dimensional points. 
     Predictor  3143  generates a predicted value of an item of attribute information on a current (target) three-dimensional point to be encoded. 
     Prediction residual calculator  3144  calculates (generates) a prediction residual of the predicted value of the item of the attribute information generated by predictor  3143 . 
     Quantizer  3145  quantizes the prediction residual of the item of attribute information calculated by prediction residual calculator  3144 . 
     Arithmetic encoder  3146  arithmetically encodes the prediction residual quantized by quantizer  3145 . Arithmetic encoder  3146  outputs a bitstream including the arithmetically encoded prediction residual to the three-dimensional data decoding device, for example. 
     The prediction residual may be binarized by quantizer  3145  before being arithmetically encoded by arithmetic encoder  3146 . 
     Arithmetic encoder  3146  may initialize the encoding table used for the arithmetic encoding before performing the arithmetic encoding. Arithmetic encoder  3146  may initialize the encoding table used for the arithmetic encoding for each layer. Arithmetic encoder  3146  may output a bitstream including information that indicates the position of the layer at which the encoding table is initialized. 
     Inverse quantizer  3147  inverse-quantizes the prediction residual quantized by quantizer  3145 . 
     Decoded value generator  3148  generates a decoded value by adding the predicted value of the item of attribute information generated by predictor  3143  and the prediction residual inverse-quantized by inverse quantizer  3147  together. 
     Memory  3149  is a memory that stores a decoded value of an item of attribute information on each three-dimensional point decoded by decoded value generator  3148 . For example, when generating a predicted value of a three-dimensional point yet to be encoded, predictor  3143  may generate the predicted value using a decoded value of an item of attribute information on each three-dimensional point stored in memory  3149 . 
       FIG. 16  is a block diagram of attribute information encoder  6600  that is an example of transformation attribute information encoder A 102 . Attribute information encoder  6600  includes sorter  6601 , Haar transformer  6602 , quantizer  6603 , inverse quantizer  6604 , inverse Haar transformer  6605 , memory  6606 , and arithmetic encoder  6607 . 
     Sorter  6601  generates the Morton codes by using the geometry information of three-dimensional points, and sorts the plurality of three-dimensional points in the order of the Morton codes. Haar transformer  6602  generates the coding coefficient by applying the Haar transform to the attribute information. Quantizer  6603  quantizes the coding coefficient of the attribute information. 
     Inverse quantizer  6604  inverse quantizes the coding coefficient after the quantization. Inverse Haar transformer  6605  applies the inverse Haar transform to the coding coefficient. Memory  6606  stores the values of items of attribute information of a plurality of decoded three-dimensional points. For example, the attribute information of the decoded three-dimensional points stored in memory  6606  may be utilized for prediction and the like of an unencoded three-dimensional point. 
     Arithmetic encoder  6607  calculates ZeroCnt from the coding coefficient after the quantization, and arithmetically encodes ZeroCnt. Additionally, arithmetic encoder  6607  arithmetically encodes the non-zero coding coefficient after the quantization. Arithmetic encoder  6607  may binarize the coding coefficient before the arithmetic encoding. In addition, arithmetic encoder  6607  may generate and encode various kinds of header information. 
       FIG. 17  is a block diagram showing a configuration of attribute information decoder  3150  that is an example of LoD attribute information decoder A 111 . 
     Attribute information decoder  3150  includes LoD generator  3151 , periphery searcher  3152 , predictor  3153 , arithmetic decoder  3154 , inverse quantizer  3155 , decoded value generator  3156 , and memory  3157 . 
     LoD generator  3151  generates an LoD using geometry information on a three-dimensional point decoded by the geometry information decoder (not shown in  FIG. 17 ). 
     Periphery searcher  3152  searches for a neighboring three-dimensional point neighboring each three-dimensional point using a result of LoD generation by LoD generator  3151  and distance information indicating distances between three-dimensional points. 
     Predictor  3153  generates a predicted value of attribute information item on a current three-dimensional point to be decoded. 
     Arithmetic decoder  3154  arithmetically decodes the prediction residual in the bitstream obtained from attribute information encoder  3140  shown in  FIG. 15 . Note that arithmetic decoder  3154  may initialize the decoding table used for the arithmetic decoding. Arithmetic decoder  3154  initializes the decoding table used for the arithmetic decoding for the layer for which the encoding process has been performed by arithmetic encoder  3146  shown in  FIG. 15 . Arithmetic decoder  3154  may initialize the decoding table used for the arithmetic decoding for each layer. Arithmetic decoder  3154  may initialize the decoding table based on the information included in the bitstream that indicates the position of the layer for which the encoding table has been initialized. 
     Inverse quantizer  3155  inverse-quantizes the prediction residual arithmetically decoded by arithmetic decoder  3154 . 
     Decoded value generator  3156  generates a decoded value by adding the predicted value generated by predictor  3153  and the prediction residual inverse-quantized by inverse quantizer  3155  together. Decoded value generator  3156  outputs the decoded attribute information data to another device. 
     Memory  3157  is a memory that stores a decoded value of an item of attribute information on each three-dimensional point decoded by decoded value generator  3156 . For example, when generating a predicted value of a three-dimensional point yet to be decoded, predictor  3153  generates the predicted value using a decoded value of an item of attribute information on each three-dimensional point stored in memory  3157 . 
       FIG. 18  is a block diagram of attribute information decoder  6610  that is an example of transformation attribute information decoder A 112 . Attribute information decoder  6610  includes arithmetic decoder  6611 , inverse quantizer  6612 , inverse Haar transformer  6613 , and memory  6614 . 
     Arithmetic decoder  6611  arithmetically decodes ZeroCnt and the coding coefficient included in a bitstream. Note that arithmetic decoder  6611  may decode various kinds of header information. 
     Inverse quantizer  6612  inverse quantizes the arithmetically decoded coding coefficient. Inverse Haar transformer  6613  applies the inverse Haar transform to the coding coefficient after the inverse quantization. Memory  6614  stores the values of items of attribute information of a plurality of decoded three-dimensional points. For example, the attribute information of the decoded three-dimensional points stored in memory  6614  may be utilized for prediction of an undecoded three-dimensional point. 
     Next, second encoder  4650 , which is an example of encoder  4613  that performs encoding in the second encoding method, will be described.  FIG. 19  is a diagram showing a configuration of second encoder  4650 .  FIG. 20  is a block diagram showing second encoder  4650 . 
     Second encoder  4650  generates encoded data (encoded stream) by encoding point cloud data in the second encoding method. Second encoder  4650  includes additional information generator  4651 , geometry image generator  4652 , attribute image generator  4653 , video encoder  4654 , additional information encoder  4655 , and multiplexer  4656 . 
     Second encoder  4650  is characterized by generating a geometry image and an attribute image by projecting a three-dimensional structure onto a two-dimensional image, and encoding the generated geometry image and attribute image in an existing video encoding scheme. The second encoding method is referred to as video-based PCC (VPCC). 
     Point cloud data is PCC point cloud data like a PLY file or PCC point cloud data generated from sensor information, and includes geometry information (position), attribute information (attribute), and other additional information (metadata). 
     Additional information generator  4651  generates map information on a plurality of two-dimensional images by projecting a three-dimensional structure onto a two-dimensional image. 
     Geometry image generator  4652  generates a geometry image based on the geometry information and the map information generated by additional information generator  4651 . The geometry image is a distance image in which distance (depth) is indicated as a pixel value, for example. The distance image may be an image of a plurality of point clouds viewed from one point of view (an image of a plurality of point clouds projected onto one two-dimensional plane), a plurality of images of a plurality of point clouds viewed from a plurality of points of view, or a single image integrating the plurality of images. 
     Attribute image generator  4653  generates an attribute image based on the attribute information and the map information generated by additional information generator  4651 . The attribute image is an image in which attribute information (color (RGB), for example) is indicated as a pixel value, for example. The image may be an image of a plurality of point clouds viewed from one point of view (an image of a plurality of point clouds projected onto one two-dimensional plane), a plurality of images of a plurality of point clouds viewed from a plurality of points of view, or a single image integrating the plurality of images. 
     Video encoder  4654  generates an encoded geometry image (compressed geometry image) and an encoded attribute image (compressed attribute image), which are encoded data, by encoding the geometry image and the attribute image in a video encoding scheme. Note that, as the video encoding scheme, any well-known encoding method can be used. For example, the video encoding scheme is AVC or HEVC. 
     Additional information encoder  4655  generates encoded additional information (compressed metadata) by encoding the additional information, the map information and the like included in the point cloud data. 
     Multiplexer  4656  generates an encoded stream (compressed stream), which is encoded data, by multiplexing the encoded geometry image, the encoded attribute image, the encoded additional information, and other additional information. The generated encoded stream is output to a processor in a system layer (not shown). 
     Next, second decoder  4660 , which is an example of decoder  4624  that performs decoding in the second encoding method, will be described.  FIG. 21  is a diagram showing a configuration of second decoder  4660 .  FIG. 22  is a block diagram showing second decoder  4660 . Second decoder  4660  generates point cloud data by decoding encoded data (encoded stream) encoded in the second encoding method in the second encoding method. Second decoder  4660  includes demultiplexer  4661 , video decoder  4662 , additional information decoder  4663 , geometry information generator  4664 , and attribute information generator  4665 . 
     An encoded stream (compressed stream), which is encoded data, is input to second decoder  4660  from a processor in a system layer (not shown). 
     Demultiplexer  4661  separates an encoded geometry image (compressed geometry image), an encoded attribute image (compressed attribute image), an encoded additional information (compressed metadata), and other additional information from the encoded data. 
     Video decoder  4662  generates a geometry image and an attribute image by decoding the encoded geometry image and the encoded attribute image in a video encoding scheme. Note that, as the video encoding scheme, any well-known encoding method can be used. For example, the video encoding scheme is AVC or HEVC. 
     Additional information decoder  4663  generates additional information including map information or the like by decoding the encoded additional information. 
     Geometry information generator  4664  generates geometry information from the geometry image and the map information. Attribute information generator  4665  generates attribute information from the attribute image and the map information. 
     Second decoder  4660  uses additional information required for decoding in the decoding, and outputs additional information required for an application to the outside. 
     In the following, a problem with the PCC encoding scheme will be described.  FIG. 23  is a diagram showing a protocol stack relating to PCC-encoded data.  FIG. 23  shows an example in which PCC-encoded data is multiplexed with other medium data, such as a video (HEVC, for example) or an audio, and transmitted or accumulated. 
     A multiplexing scheme and a file format have a function of multiplexing various encoded data and transmitting or accumulating the data. To transmit or accumulate encoded data, the encoded data has to be converted into a format for the multiplexing scheme. For example, with HEVC, a technique for storing encoded data in a data structure referred to as a NAL unit and storing the NAL unit in ISOBMFF is prescribed. 
     At present, a first encoding method (Codec1) and a second encoding method (Codec2) are under investigation as encoding methods for point cloud data. However, there is no method defined for storing the configuration of encoded data and the encoded data in a system format. Thus, there is a problem that an encoder cannot perform an MUX process (multiplexing), transmission, or accumulation of data. 
     Note that, in the following, the term “encoding method” means any of the first encoding method and the second encoding method unless a particular encoding method is specified. 
     Embodiment 2 
     In this embodiment, types of the encoded data (geometry information (geometry), attribute information (attribute), and additional information (metadata)) generated by first encoder  4630  or second encoder  4650  described above, a method of generating additional information (metadata), and a multiplexing process in the multiplexer will be described. The additional information (metadata) may be referred to as a parameter set or control information (signaling information). 
     In this embodiment, the dynamic object (three-dimensional point cloud data that varies with time) described above with reference to  FIG. 4  will be described, for example. However, the same method can also be used for the static object (three-dimensional point cloud data associated with an arbitrary time point). 
       FIG. 24  is a diagram showing configurations of encoder  4801  and multiplexer  4802  in a three-dimensional data encoding device according to this embodiment. Encoder  4801  corresponds to first encoder  4630  or second encoder  4650  described above, for example. Multiplexer  4802  corresponds to multiplexer  4634  or  4656  described above. 
     Encoder  4801  encodes a plurality of PCC (point cloud compression) frames of point cloud data to generate a plurality of pieces of encoded data (multiple compressed data) of geometry information, attribute information, and additional information. 
     Multiplexer  4802  integrates a plurality of types of data (geometry information, attribute information, and additional information) into a NAL unit, thereby converting the data into a data configuration that takes data access in the decoding device into consideration. 
       FIG. 25  is a diagram showing a configuration example of the encoded data generated by encoder  4801 . Arrows in the drawing indicate a dependence involved in decoding of the encoded data. The source of an arrow depends on data of the destination of the arrow. That is, the decoding device decodes the data of the destination of an arrow, and decodes the data of the source of the arrow using the decoded data. In other words, “a first entity depends on a second entity” means that data of the second entity is referred to (used) in processing (encoding, decoding, or the like) of data of the first entity. 
     First, a process of generating encoded data of geometry information will be described. Encoder  4801  encodes geometry information of each frame to generate encoded geometry data (compressed geometry data) for each frame. The encoded geometry data is denoted by G(i). i denotes a frame number or a time point of a frame, for example. 
     Furthermore, encoder  4801  generates a geometry parameter set (GPS(i)) for each frame. The geometry parameter set includes a parameter that can be used for decoding of the encoded geometry data. The encoded geometry data for each frame depends on an associated geometry parameter set. 
     The encoded geometry data formed by a plurality of frames is defined as a geometry sequence. Encoder  4801  generates a geometry sequence parameter set (referred to also as geometry sequence PS or geometry SPS) that stores a parameter commonly used for a decoding process for the plurality of frames in the geometry sequence. The geometry sequence depends on the geometry SPS. 
     Next, a process of generating encoded data of attribute information will be described. Encoder  4801  encodes attribute information of each frame to generate encoded attribute data (compressed attribute data) for each frame. The encoded attribute data is denoted by A(i).  FIG. 25  shows an example in which there are attribute X and attribute Y, and encoded attribute data for attribute X is denoted by AX(i), and encoded attribute data for attribute Y is denoted by AY(i). 
     Furthermore, encoder  4801  generates an attribute parameter set (APS(i)) for each frame. The attribute parameter set for attribute X is denoted by AXPS(i), and the attribute parameter set for attribute Y is denoted by AYPS(i). The attribute parameter set includes a parameter that can be used for decoding of the encoded attribute information. The encoded attribute data depends on an associated attribute parameter set. 
     The encoded attribute data formed by a plurality of frames is defined as an attribute sequence. Encoder  4801  generates an attribute sequence parameter set (referred to also as attribute sequence PS or attribute SPS) that stores a parameter commonly used for a decoding process for the plurality of frames in the attribute sequence. The attribute sequence depends on the attribute SPS. 
     In the first encoding method, the encoded attribute data depends on the encoded geometry data. 
       FIG. 25  shows an example in which there are two types of attribute information (attribute X and attribute Y). When there are two types of attribute information, for example, two encoders generate data and metadata for the two types of attribute information. For example, an attribute sequence is defined for each type of attribute information, and an attribute SPS is generated for each type of attribute information. 
     Note that, although  FIG. 25  shows an example in which there is one type of geometry information, and there are two types of attribute information, the present disclosure is not limited thereto. There may be one type of attribute information or three or more types of attribute information. In such cases, encoded data can be generated in the same manner. If the point cloud data has no attribute information, there may be no attribute information. In such a case, encoder  4801  does not have to generate a parameter set associated with attribute information. 
     Next, a process of generating encoded data of additional information (metadata) will be described. Encoder  4801  generates a PCC stream PS (referred to also as PCC stream PS or stream PS), which is a parameter set for the entire PCC stream. Encoder  4801  stores a parameter that can be commonly used for a decoding process for one or more geometry sequences and one or more attribute sequences in the stream PS. For example, the stream PS includes identification information indicating the codec for the point cloud data and information indicating an algorithm used for the encoding, for example. The geometry sequence and the attribute sequence depend on the stream PS. 
     Next, an access unit and a GOF will be described. In this embodiment, concepts of access unit (AU) and group of frames (GOF) are newly introduced. 
     An access unit is a basic unit for accessing data in decoding, and is formed by one or more pieces of data and one or more pieces of metadata. For example, an access unit is formed by geometry information and one or more pieces of attribute information associated with a same time point. A GOF is a random access unit, and is formed by one or more access units. 
     Encoder  4801  generates an access unit header (AU header) as identification information indicating the top of an access unit. Encoder  4801  stores a parameter relating to the access unit in the access unit header. For example, the access unit header includes a configuration of or information on the encoded data included in the access unit. The access unit header further includes a parameter commonly used for the data included in the access unit, such as a parameter relating to decoding of the encoded data. 
     Note that encoder  4801  may generate an access unit delimiter that includes no parameter relating to the access unit, instead of the access unit header. The access unit delimiter is used as identification information indicating the top of the access unit. The decoding device identifies the top of the access unit by detecting the access unit header or the access unit delimiter. 
     Next, generation of identification information for the top of a GOF will be described. As identification information indicating the top of a GOF, encoder  4801  generates a GOF header. Encoder  4801  stores a parameter relating to the GOF in the GOF header. For example, the GOF header includes a configuration of or information on the encoded data included in the GOF. The GOF header further includes a parameter commonly used for the data included in the GOF, such as a parameter relating to decoding of the encoded data. 
     Note that encoder  4801  may generate a GOF delimiter that includes no parameter relating to the GOF, instead of the GOF header. The GOF delimiter is used as identification information indicating the top of the GOF. The decoding device identifies the top of the GOF by detecting the GOF header or the GOF delimiter. 
     In the PCC-encoded data, the access unit is defined as a PCC frame unit, for example. The decoding device accesses a PCC frame based on the identification information for the top of the access unit. 
     For example, the GOF is defined as one random access unit. The decoding device accesses a random access unit based on the identification information for the top of the GOF. For example, if PCC frames are independent from each other and can be separately decoded, a PCC frame can be defined as a random access unit. 
     Note that two or more PCC frames may be assigned to one access unit, and a plurality of random access units may be assigned to one GOF. 
     Encoder  4801  may define and generate a parameter set or metadata other than those described above. For example, encoder  4801  may generate supplemental enhancement information (SEI) that stores a parameter (an optional parameter) that is not always used for decoding. 
     Next, a configuration of encoded data and a method of storing encoded data in a NAL unit will be described. 
     For example, a data format is defined for each type of encoded data.  FIG. 26  is a diagram showing an example of encoded data and a NAL unit. 
     For example, as shown in  FIG. 26 , encoded data includes a header and a payload. The encoded data may include length information indicating the length (data amount) of the encoded data, the header, or the payload. The encoded data may include no header. 
     The header includes identification information for identifying the data, for example. The identification information indicates a data type or a frame number, for example. 
     The header includes identification information indicating a reference relationship, for example. The identification information is stored in the header when there is a dependence relationship between data, for example, and allows an entity to refer to another entity. For example, the header of the entity to be referred to includes identification information for identifying the data. The header of the referring entity includes identification information indicating the entity to be referred to. 
     Note that, when the entity to be referred to or the referring entity can be identified or determined from other information, the identification information for identifying the data or identification information indicating the reference relationship can be omitted. 
     Multiplexer  4802  stores the encoded data in the payload of the NAL unit. The NAL unit header includes pcc_nal_unit_type, which is identification information for the encoded data.  FIG. 27  is a diagram showing a semantics example of pcc_nal_unit_type. 
     As shown in  FIG. 27 , when pcc_codec_type is codec 1 (Codec1: first encoding method), values 0 to 10 of pcc_nal_unit_type are assigned to encoded geometry data (Geometry), encoded attribute X data (AttributeX), encoded attribute Y data (AttributeY), geometry PS (Geom. PS), attribute XPS (AttrX. S), attribute YPS (AttrY. PS), geometry SPS (Geometry Sequence PS), attribute X SPS (AttributeX Sequence PS), attribute Y SPS (AttributeY Sequence PS), AU header (AU Header), and GOF header (GOF Header) in codec 1. Values of 11 and greater are reserved in codec 1. 
     When pcc_codec_type is codec 2 (Codec2: second encoding method), values of 0 to 2 of pcc_nal_unit_type are assigned to data A (DataA), metadata A (MetaDataA), and metadata B (MetaDataB) in the codec. Values of 3 and greater are reserved in codec 2. 
     Next, an order of transmission of data will be described. In the following, restrictions on the order of transmission of NAL units will be described. 
     Multiplexer  4802  transmits NAL units on a GOF basis or on an AU basis. Multiplexer  4802  arranges the GOF header at the top of a GOF, and arranges the AU header at the top of an AU. 
     In order to allow the decoding device to decode the next AU and the following AUs even when data is lost because of a packet loss or the like, multiplexer  4802  may arrange a sequence parameter set (SPS) in each AU. 
     When there is a dependence relationship for decoding between encoded data, the decoding device decodes the data of the entity to be referred to and then decodes the data of the referring entity. In order to allow the decoding device to perform decoding in the order of reception without rearranging the data, multiplexer  4802  first transmits the data of the entity to be referred to. 
       FIG. 28  is a diagram showing examples of the order of transmission of NAL units.  FIG. 28  shows three examples, that is, geometry information-first order, parameter-first order, and data-integrated order. 
     The geometry information-first order of transmission is an example in which information relating to geometry information is transmitted together, and information relating to attribute information is transmitted together. In the case of this order of transmission, the transmission of the information relating to the geometry information ends earlier than the transmission of the information relating to the attribute information. 
     For example, according to this order of transmission is used, when the decoding device does not decode attribute information, the decoding device may be able to have an idle time since the decoding device can omit decoding of attribute information. When the decoding device is required to decode geometry information early, the decoding device may be able to decode geometry information earlier since the decoding device obtains encoded data of the geometry information earlier. 
     Note that, although in  FIG. 28  the attribute X SPS and the attribute Y SPS are integrated and shown as the attribute SPS, the attribute X SPS and the attribute Y SPS may be separately arranged. 
     In the parameter set-first order of transmission, a parameter set is first transmitted, and data is then transmitted. 
     As described above, as far as the restrictions on the order of transmission of NAL units are met, multiplexer  4802  can transmit NAL units in any order. For example, order identification information may be defined, and multiplexer  4802  may have a function of transmitting NAL units in a plurality of orders. For example, the order identification information for NAL units is stored in the stream PS. 
     The three-dimensional data decoding device may perform decoding based on the order identification information. The three-dimensional data decoding device may indicate a desired order of transmission to the three-dimensional data encoding device, and the three-dimensional data encoding device (multiplexer  4802 ) may control the order of transmission according to the indicated order of transmission. 
     Note that multiplexer  4802  can generate encoded data having a plurality of functions merged to each other as in the case of the data-integrated order of transmission, as far as the restrictions on the order of transmission are met. For example, as shown in  FIG. 28 , the GOF header and the AU header may be integrated, or AXPS and AYPS may be integrated. In such a case, an identifier that indicates data having a plurality of functions is defined in pcc_nal_unit_type. 
     In the following, variations of this embodiment will be described. There are levels of PSs, such as a frame-level PS, a sequence-level PS, and a PCC sequence-level PS. Provided that the PCC sequence level is a higher level, and the frame level is a lower level, parameters can be stored in the manner described below. 
     The value of a default PS is indicated in a PS at a higher level. If the value of a PS at a lower level differs from the value of the PS at a higher level, the value of the PS is indicated in the PS at the lower level. Alternatively, the value of the PS is not described in the PS at the higher level but is described in the PS at the lower level. Alternatively, information indicating whether the value of the PS is indicated in the PS at the lower level, at the higher level, or at both the levels is indicated in both or one of the PS at the lower level and the PS at the higher level. Alternatively, the PS at the lower level may be merged with the PS at the higher level. If the PS at the lower level and the PS at the higher level overlap with each other, multiplexer  4802  may omit transmission of one of the PSs. 
     Note that encoder  4801  or multiplexer  4802  may divide data into slices or tiles and transmit each of the divided slices or tiles as divided data. The divided data includes information for identifying the divided data, and a parameter used for decoding of the divided data is included in the parameter set. In this case, an identifier that indicates that the data is data relating to a tile or slice or data storing a parameter is defined in pcc_nal_unit_type. 
     In the following, a process relating to order identification information will be described.  FIG. 29  is a flowchart showing a process performed by the three-dimensional data encoding device (encoder  4801  and multiplexer  4802 ) that involves the order of transmission of NAL units. 
     First, the three-dimensional data encoding device determines the order of transmission of NAL units (geometry information-first or parameter set-first) (S 4801 ). For example, the three-dimensional data encoding device determines the order of transmission based on a specification from a user or an external device (the three-dimensional data decoding device, for example). 
     If the determined order of transmission is geometry information-first (if “geometry information-first” in S 4802 ), the three-dimensional data encoding device sets the order identification information included in the stream PS to geometry information-first (S 4803 ). That is, in this case, the order identification information indicates that the NAL units are transmitted in the geometry information-first order. The three-dimensional data encoding device then transmits the NAL units in the geometry information-first order (S 4804 ). 
     On the other hand, if the determined order of transmission is parameter set-first (if “parameter set-first” in S 4802 ), the three-dimensional data encoding device sets the order identification information included in the stream PS to parameter set-first (S 4805 ). That is, in this case, the order identification information indicates that the NAL units are transmitted in the parameter set-first order. The three-dimensional data encoding device then transmits the NAL units in the parameter set-first order (S 4806 ). 
       FIG. 30  is a flowchart showing a process performed by the three-dimensional data decoding device that involves the order of transmission of NAL units. First, the three-dimensional data decoding device analyzes the order identification information included in the stream PS (S 4811 ). 
     If the order of transmission indicated by the order identification information is geometry information-first of “geometry information-first” in S 4812 ), the three-dimensional data decoding device decodes the NAL units based on the determination that the order of transmission of the NAL units is geometry information-first (S 4813 ). 
     On the other hand, if the order of transmission indicated by the order identification information is parameter set-first (if “parameter set-first” in S 4812 ), the three-dimensional data decoding device decodes the NAL units based on the determination that the order of transmission of the NAL units is parameter set-first (S 4814 ). 
     For example, if the three-dimensional data decoding device does not decode attribute information, in step S 4813 , the three-dimensional data decoding device does not obtain the entire NAL units but can obtain a part of a NAL unit relating to the geometry information and decode the obtained NAL unit to obtain the geometry information. 
     Next, a process relating to generation of an AU and a GOF will be described.  FIG. 31  is a flowchart showing a process performed by the three-dimensional data encoding device (multiplexer  4802 ) that relates to generation of an AU and a GOF in multiplexing of NAL units. 
     First, the three-dimensional data encoding device determines the type of the encoded data (S 4821 ). Specifically, the three-dimensional data encoding device determines whether the encoded data to be processed is AU-first data, GOF-first data, or other data. 
     If the encoded data is GOF-first data (if “GOF-first” in S 4822 ), the three-dimensional data encoding device generates NAL units by arranging a GOF header and an AU header at the top of the encoded data belonging to the GOF (S 4823 ). 
     If the encoded data is AU-first data (if “AU-first” in S 4822 ), the three-dimensional data encoding device generates NAL units by arranging an AU header at the top of the encoded data belonging to the AU (S 4824 ). 
     If the encoded data is neither GOF-first data nor AU-first data (if “other than GOF-first and AU-first” in S 4822 ), the three-dimensional data encoding device generates NAL units by arranging the encoded data to follow the AU header of the AU to which the encoded data belongs (S 4825 ). 
     Next, a process relating to access to an AU and a GOF will be described.  FIG. 32  is a flowchart showing a process performed by the three-dimensional data decoding device that involves accessing to an AU and a GOF in demultiplexing of a NAL unit. 
     First, the three-dimensional data decoding device determines the type of the encoded data included in the NAL unit by analyzing nal_unit_type in the NAL unit (S 4831 ). Specifically, the three-dimensional data decoding device determines whether the encoded data included in the NAL unit is AU-first data, GOF-first data, or other data. 
     If the encoded data included in the NAL unit is GOF-first data (if “GOF-first” in S 4832 ), the three-dimensional data decoding device determines that the NAL unit is a start position of random access, accesses the NAL unit, and starts the decoding process (S 4833 ). 
     If the encoded data included in the NAL unit is AU-first data (if “AU-first” in S 4832 ), the three-dimensional data decoding device determines that the NAL unit is AU-first, accesses the data included in the NAL unit, and decodes the AU (S 4834 ). 
     If the encoded data included in the NAL unit is neither GOF-first data nor AU-first data (if “other than GOF-first and AU-first” in S 4832 ), the three-dimensional data decoding device does not process the NAL unit. 
     Embodiment 3 
     In the present embodiment, a representation means of three-dimensional points (point cloud) in encoding of three-dimensional data will be described. 
       FIG. 33  is a block diagram showing a structure of a distribution system of three-dimensional data according to the present embodiment. The distribution system shown in  FIG. 33  includes server  1501  and a plurality of clients  1502 . 
     Server  1501  includes storage  1511  and controller  1512 . Storage  1511  stores encoded three-dimensional map  1513  that is encoded three-dimensional data. 
       FIG. 34  is a diagram showing an example structure of a bitstream of encoded three-dimensional map  1513 . The three-dimensional map is divided into a plurality of submaps and each submap is encoded. Each submap is appended with a random-access (RA) header including subcoordinate information. The subcoordinate information is used for improving encoding efficiency of the submap. This subcoordinate information indicates subcoordinates of the submap. The subcoordinates are coordinates of the submap having reference coordinates as reference. Note that the three-dimensional map including the plurality of submaps is referred to as an overall map. Coordinates that are a reference in the overall map (e.g. origin) are referred to as the reference coordinates. In other words, the subcoordinates are the coordinates of the submap in a coordinate system of the overall map. In other words, the subcoordinates indicate an offset between the coordinate system of the overall map and a coordinate system of the submap. Coordinates in the coordinate system of the overall map having the reference coordinates as reference are referred to as overall coordinates. Coordinates in the coordinate system of the submap having the subcoordinates as reference are referred to as differential coordinates. 
     Client  1502  transmits a message to server  1501 . This message includes position information on client  1502 . Controller  1512  included in server  1501  obtains a bitstream of a submap located closest to client  1502 , based on the position information included in the received message. The bitstream of the submap includes the subcoordinate information and is transmitted to client  1502 . Decoder  1521  included in client  1502  obtains overall coordinates of the submap having the reference coordinates as reference, using this subcoordinate information. Application  1522  included in client  1502  executes an application relating to a self-location, using the obtained overall coordinates of the submap. 
     The submap indicates a partial area of the overall map. The subcoordinates are the coordinates in which the submap is located in a reference coordinate space of the overall map. For example, in an overall map called A, there is submap A called AA and submap B called AB. When a vehicle wants to consult a map of AA, decoding begins from submap A, and when the vehicle wants to consult a map of AB, decoding begins from submap B. The submap here is a random-access point. To be specific, A is Osaka Prefecture, AA is Osaka City, and AB is Takatsuki City. 
     Each submap is transmitted along with the subcoordinate information to the client. The subcoordinate information is included in header information of each submap, a transmission packet, or the like. 
     The reference coordinates, which serve as a reference for the subcoordinate information of each submap, may be appended to header information of a space at a higher level than the submap, such as header information of the overall map. 
     The submap may be formed by one space (SPC). The submap may also be formed by a plurality of SPCs. 
     The submap may include a Group of Spaces (GOS). The submap may be formed by a world. For example, in a case where there are a plurality of objects in the submap, the submap is formed by a plurality of SPCs when assigning the plurality of objects to separate SPCs. The submap is formed by one SPC when assigning the plurality of objects to one SPC. 
     An advantageous effect on encoding efficiency when using the subcoordinate information will be described next.  FIG. 35  is a diagram for describing this advantageous effect. For example, a high bit count is necessary in order to encode three-dimensional point A, which is located far from the reference coordinates, shown in  FIG. 35 . A distance between the subcoordinates and three-dimensional point A is shorter than a distance between the reference coordinates and three-dimensional point A. As such, it is possible to improve encoding efficiency by encoding coordinates of three-dimensional point A having the subcoordinates as reference more than when encoding the coordinates of three-dimensional point A having the reference coordinates as reference. The bitstream of the submap includes the subcoordinate information. By transmitting the bitstream of the submap and the reference coordinates to a decoding end (client), it is possible to restore the overall coordinates of the submap in the decoder end. 
       FIG. 36  is a flowchart of processes performed by server  1501 , which is a transmission end of the submap. 
     Server  1501  first receives a message including position information on client  1502  from client  1502  (S 1501 ). Controller  1512  obtains an encoded bitstream of the submap based on the position information on the client from storage  1511  (S 1502 ). Server  1501  then transmits the encoded bitstream of the submap and the reference coordinates to client  1502  (S 1503 ). 
       FIG. 37  is a flowchart of processes performed by client  1502 , which is a receiver end of the submap. 
     Client  1502  first receives the encoded bitstream of the submap and the reference coordinates transmitted from server  1501  (S 1511 ). Client  1502  next obtains the subcoordinate information of the submap by decoding the encoded bitstream (S 1512 ). Client  1502  next restores the differential coordinates in the submap to the overall coordinates, using the reference coordinates and the subcoordinates (S 1513 ). 
     An example syntax of information relating to the submap will be described next. In the encoding of the submap, the three-dimensional data encoding device calculates the differential coordinates by subtracting the subcoordinates from the coordinates of each point cloud (three-dimensional points). The three-dimensional data encoding device then encodes the differential coordinates into the bitstream as a value of each point cloud. The encoding device encodes the subcoordinate information indicating the subcoordinates as the header information of the bitstream. This enables the three-dimensional data decoding device to obtain overall coordinates of each point cloud. For example, the three-dimensional data encoding device is included in server  1501  and the three-dimensional data decoding device is included in client  1502 . 
       FIG. 38  is a diagram showing an example syntax of the submap. NumOfPoint shown in  FIG. 38  indicates a total number of point clouds included in the submap. sub_coordinate_x, sub_coorclinate_y, and sub_coordinate_z are the subcoordinate information. sub_coordinate_x indicates an x-coordinate of the subcoordinates. sub_coorclinate_y indicates a y-coordinate of the subcoordinates. sub_coordinate_z indicates a z-coordinate of the subcoordinates. 
     diff_x[i], diff_y[i], and diff_z[i] are differential coordinates of an i-th point cloud in the submap. diff_x[i] is a differential value between an x-coordinate of the i-th point cloud and the x-coordinate of the subcoordinates in the submap. diff_y[i] is a differential value between a y-coordinate of the i-th point cloud and the y-coordinate of the subcoordinates in the submap. diff_z[i] is a differential value between a z-coordinate of the i-th point cloud and the z-coordinate of the subcoordinates in the submap. 
     The three-dimensional data decoding device decodes point_cloud[i]_x, point_cloud[i]_y, and point_cloud[i]_z, which are overall coordinates of the i-th point cloud, using the expression below. point_cloud[i]_x is an x-coordinate of the overall coordinates of the i-th point cloud. point_cloud[i]_y is a y-coordinate of the overall coordinates of the i-th point cloud. point_cloud[i]_z is a z-coordinate of the overall coordinates of the i-th point cloud. 
       point_cloud[ i ]_ x =sub_coordinate_ x +diff_ x [ i ] 
       point_cloud[ i ]_ y =sub_coorclinate_ y +diff_ y [ i ] 
       point_cloud[ i ]_ z =sub_coordinate_ z +diff_ z [ i ] 
     A switching process for applying octree encoding will be described next. The three-dimensional data encoding device selects, when encoding the submap, whether to encode each point cloud using an octree representation (hereinafter, referred to as octree encoding) or to encode the differential values from the subcoordinates (hereinafter, referred to as non-octree encoding).  FIG. 39  is a diagram schematically showing this operation. For example, the three-dimensional data encoding device applies octree encoding to the submap, when the total number of point clouds in the submap is at least a predetermined threshold. The three-dimensional data encoding device applies non-octree encoding to the submap, when the total number of point clouds in the submap is lower than the predetermined threshold. This enables the three-dimensional data encoding device to improve encoding efficiency, since it is possible to appropriately select whether to use octree encoding or non-octree encoding, in accordance with a shape and density of objects included in the submap. 
     The three-dimensional data encoding device appends, to a header and the like of the submap, information indicating whether octree encoding or non-octree encoding has been applied to the submap (hereinafter, referred to as octree encoding application information). This enables the three-dimensional data decoding device to identify whether the bitstream is obtained by octree encoding the submap or non-octree encoding the submap. 
     The three-dimensional data encoding device may calculate encoding efficiency when applying octree encoding and encoding efficiency when applying non-octree encoding to the same point cloud, and apply an encoding method whose encoding efficiency is better to the submap. 
       FIG. 40  is a diagram showing an example syntax of the submap when performing this switching. coding_type shown in  FIG. 40  is information indicating the encoding type and is the above octree encoding application information. coding_type=00 indicates that octree encoding has been applied. coding_type=01 indicates that non-octree encoding has been applied. coding_type=10 or 11 indicates that an encoding method and the like other than the above encoding methods has been applied. 
     When the encoding type is non-octree encoding (non_octree), the submap includes NumOfPoint and the subcoordinate information (sub_coordinate_x, sub_coordinate_y, and sub_coordinate_z). 
     When the encoding type is octree encoding (octree), the submap includes octree_info. octree_info is information necessary to the octree encoding and includes, for example, depth information. 
     When the encoding type is non-octree encoding (non_octree), the submap includes the differential coordinates (diff_x[i], diff_y[i], and diff_z[i]). 
     When the encoding type is octree encoding (octree), the submap includes octree_data, which is encoded data relating to the octree encoding. 
     Note that an example has been described here in which an xyz coordinate system is used as the coordinate system of the point cloud, but a polar coordinate system may also be used. 
       FIG. 41  is a flowchart of a three-dimensional data encoding process performed by the three-dimensional data encoding device. Three-dimensional data encoding device first calculates a total number of point clouds in a current submap, which is the submap to be processed (S 1521 ). The three-dimensional data encoding device next determines whether when the calculated total number of point clouds is at least a predetermined threshold (S 1522 ). 
     When the total number of point clouds is at least the predetermined threshold (YES in S 1522 ), the three-dimensional data encoding device applies octree encoding to the current submap (S 1523 ). The three-dimensional data encoding device appends, to a header of the bitstream, octree encoding application information indicating that octree encoding has been applied to the current submap (S 1525 ). 
     In contrast, when the total number of point clouds is lower than the predetermined threshold (NO in S 1522 ), the three-dimensional data encoding device applies non-octree encoding to the current submap (S 1524 ). The three-dimensional data encoding device appends, to the header of the bitstream, octree encoding application information indicating that non-octree encoding has been applied to the current submap (S 1525 ). 
       FIG. 42  is a flowchart of a three-dimensional data decoding process performed by the three-dimensional data decoding device. The three-dimensional data decoding device first decodes the octree encoding application information from the header of the bitstream (S 1531 ). The three-dimensional data decoding device next determines whether the encoding type applied to the current submap is octree encoding, based on the decoded octree encoding application information (S 1532 ). 
     When the octree encoding application information indicates that the encoding type is octree encoding (YES in S 1532 ), the three-dimensional data decoding device decodes the current submap through octree decoding (S 1533 ). In contrast, when the octree encoding application information indicates that the encoding type is non-octree encoding (NO in S 1532 ), the three-dimensional data decoding device decodes the current submap through non-octree decoding (S 1534 ). 
     Hereinafter, variations of the present embodiment will be described.  FIG. 43  to  FIG. 45  are diagrams schematically showing operations of variations of the switching process of the encoding type. 
     As illustrated in  FIG. 43 , the three-dimensional data encoding device may select whether to apply octree encoding or non-octree encoding per space. In this case, the three-dimensional data encoding device appends the octree encoding application information to a header of the space. This enables the three-dimensional data decoding device to determine whether octree encoding has been applied per space. In this case, the three-dimensional data encoding device sets subcoordinates per space, and encodes a differential value, which is a value of the subcoordinates subtracted from coordinates of each point cloud in the space. 
     This enables the three-dimensional data encoding device to improve encoding efficiency, since it is possible to appropriately select whether to apply octree encoding, in accordance with a shape of objects or the total number of point clouds in the space. 
     As illustrated in  FIG. 44 , the three-dimensional data encoding device may select whether to apply octree encoding or non-octree encoding per volume. In this case, the three-dimensional data encoding device appends the octree encoding application information to a header of the volume. This enables the three-dimensional data decoding device to determine whether octree encoding has been applied per volume. In this case, the three-dimensional data encoding device sets subcoordinates per volume, and encodes a differential value, which is a value of the subcoordinates subtracted from coordinates of each point cloud in the volume. 
     This enables the three-dimensional data encoding device to improve encoding efficiency, since it is possible to appropriately select whether to apply octree encoding, in accordance with a shape of objects or the total number of point clouds in the volume. 
     In the above description, an example has been shown in which the difference, which is the subcoordinates of each point cloud subtracted from the coordinates of each point cloud, is encoded as the non-octree encoding, but is not limited thereto, and any other type of encoding method other than the octree encoding may be used. For example, as illustrated in  FIG. 45 , the three-dimensional data encoding device may not only encode the difference from the subcoordinates as the non-octree encoding, but also use a method in which a value of the point cloud in the submap, the space, or the volume itself is encoded (hereinafter, referred to as original coordinate encoding). 
     In this case, the three-dimensional data encoding device stores, in the header, information indicating that original coordinate encoding has been applied to a current space (submap, space, or volume). This enables the three-dimensional data decoding device to determine whether original coordinate encoding has been applied to the current space. 
     When applying original coordinate encoding, the three-dimensional data encoding device may perform the encoding without applying quantization and arithmetic encoding to original coordinates. The three-dimensional data encoding device may encode the original coordinates using a predetermined fixed bit length. This enables three-dimensional data encoding device to generate a stream with a fixed bit length at a certain time. 
     In the above description, an example has been shown in which the difference, which is the subcoordinates of each point cloud subtracted from the coordinates of each point cloud, is encoded as the non-octree encoding, but is not limited thereto. 
     For example, the three-dimensional data encoding device may sequentially encode a differential value between the coordinates of each point cloud.  FIG. 46  is a diagram for describing an operation in this case. For example, in the example shown in  FIG. 46 , the three-dimensional data encoding device encodes a differential value between coordinates of point cloud PA and predicted coordinates, using the subcoordinates as the predicted coordinates, when encoding point cloud PA. The three-dimensional data encoding device encodes a differential value between point cloud PB and predicted coordinates, using the coordinates of point cloud PA as the predicted coordinates, when encoding point cloud PB. The three-dimensional data encoding device encodes a differential value between point cloud PC and predicted coordinates, using the coordinates of point cloud PB as the predicted coordinates, when encoding point cloud PC. In this manner, the three-dimensional data encoding device may set a scan order to a plurality of point clouds, and encode a differential value between coordinates of a current point cloud to be processed and coordinates of a point cloud immediately before the current point cloud in the scan order. 
     In the above description, the subcoordinates are coordinates in the lower left front corner of the submap, but a location of the subcoordinates is not limited thereto.  FIG. 47  to  FIG. 49  are diagrams showing other examples of the location of the subcoordinates. The location of the subcoordinates may be set to any coordinates in the current space (submap, space, or volume). In other words, the subcoordinates may be, as stated above, coordinates in the lower left front corner of the current space. As illustrated in  FIG. 47 , the subcoordinates may be coordinates in a center of the current space. As illustrated in  FIG. 48 , the subcoordinates may be coordinates in an upper right rear corner of the current space. The subcoordinates are not limited to being coordinates in the lower left front corner or the upper right rear corner of the current space, but may also be coordinates in any corner of the current space. 
     The location of the subcoordinates may be the same as coordinates of a certain point cloud in the current space (submap, space, or volume). For example, in the example shown in  FIG. 49 , the coordinates of the subcoordinates coincide with coordinates of point cloud PD. 
     In the present embodiment, an example has been shown that switches between applying octree encoding or non-octree encoding, but is not necessarily limited thereto. For example, the three-dimensional data encoding device may switch between applying a tree structure other than an octree or a non-tree structure other than the tree-structure. For example, the other tree structure is a k-d tree in which splitting is performed using perpendicular planes on one coordinate axis. Note that any other method may be used as the other tree structure. 
     In the present embodiment, an example has been shown in which coordinate information included in a point cloud is encoded, but is not necessarily limited thereto. The three-dimensional data encoding device may encode, for example, color information, a three-dimensional feature quantity, or a feature quantity of visible light using the same method as for the coordinate information. For example, the three-dimensional data encoding device may set an average value of the color information included in each point cloud in the submap to subcolor information, and encode a difference between the color information and the subcolor information of each point cloud. 
     In the present embodiment, an example has been shown in which an encoding method (octree encoding or non-octree encoding) with good encoding efficiency is selected in accordance with a total number of point clouds and the like, but is not necessarily limited thereto. For example, the three-dimensional data encoding device, which is a server end, may store a bitstream of a point cloud encoded through octree encoding, a bitstream of a point cloud encoded through non-octree encoding, and a bitstream of a point cloud encoded through both methods, and switch the bitstream to be transmitted to the three-dimensional data decoding device, in accordance with a transmission environment or a processing power of the three-dimensional data decoding device. 
       FIG. 50  is a diagram showing an example syntax of a volume when applying octree encoding. The syntax shown in  FIG. 50  is basically the same as the syntax shown in  FIG. 40 , but differs in that each piece of information is information in units of volumes. To be specific, NumOfPoint indicates a total number of point clouds included in the volume. sub_coordinate_x, sub_coorclinate_y, and sub_coordinate_z are the subcoordinate information of the volume. 
     diff_x[i], diff_y[i], and diff_z[i] are differential coordinates of an i-th point cloud in the volume. diff_x[i] is a differential value between an x-coordinate of the i-th point cloud and the x-coordinate of the subcoordinates in the volume. diff_y[i] is a differential value between a y-coordinate of the i-th point cloud and the y-coordinate of the subcoordinates in the volume. diff_z[i] is a differential value between a z-coordinate of the i-th point cloud and the z-coordinate of the subcoordinates in the volume. 
     Note that when it is possible to calculate a relative position of the volume in the space, the three-dimensional data encoding device does not need to include the subcoordinate information in a header of the volume. In other words, the three-dimensional data encoding device may calculate the relative position of the volume in the space without including the subcoordinate information in the header, and use the calculated position as the subcoordinates of each volume. 
     As stated above, the three-dimensional data encoding device according to the present embodiment determines whether to encode, using an octree structure, a current space unit among a plurality of space units (e.g. submaps, spaces, or volumes) included in three-dimensional data (e.g. S 1522  in  FIG. 41 ). For example, the three-dimensional data encoding device determines that the current space unit is to be encoded using the octree structure, when a total number of the three-dimensional points included in the current space unit is higher than a predetermined threshold. The three-dimensional data encoding device determines that the current space unit is not to be encoded using the octree structure, when the total number of the three-dimensional points included in the current space unit is lower than or equal to the predetermined threshold. 
     When it is determined that the current space unit is to be encoded using the octree structure (YES in S 1522 ), the three-dimensional data encoding device encodes the current space unit using the octree structure (S 1523 ). When it is determined that the current space unit is not to be encoded using the octree structure (NO in S 1522 ), the three-dimensional data encoding device encodes the current space unit using a different method that is not the octree structure (S 1524 ). For example, in the different method, the three-dimensional data encoding device encodes coordinates of three-dimensional points included in the current space unit. To be specific, in the different method, the three-dimensional data encoding device encodes a difference between reference coordinates of the current space unit and the coordinates of the three-dimensional points included in the current space unit. 
     The three-dimensional data encoding device next appends, to a bitstream, information that indicates whether the current space unit has been encoded using the octree structure (S 1525 ). 
     This enables the three-dimensional data encoding device to improve encoding efficiency since it is possible to reduce the amount of data of the encoded signal. 
     For example, the three-dimensional data encoding device includes a processor and memory, the processor using the memory to perform the above processes. 
     The three-dimensional data decoding device according to the present embodiment decodes, from a bitstream, information that indicates whether to decode, using an octree structure, a current space unit among a plurality of space units (e.g. submaps, spaces, or volumes) included in three-dimensional data (e.g. S 1531  in  FIG. 42 ). When the information indicates that the current space unit is to be decoded using the octree structure (YES in S 1532 ), the three-dimensional data decoding device decodes the current space unit using the octree structure (S 1533 ). 
     When the information indicates not to decode the current space unit using the octree structure (NO in S 1532 ), the three-dimensional data decoding device decodes the current space unit using a different method that is not the octree structure (S 1534 ). For example, in the different method, the three-dimensional data decoding device decodes coordinates of three-dimensional points included in the current space unit. To be specific, in the different method, the three-dimensional data decoding device decodes a difference between reference coordinates of the current space unit and the coordinates of the three-dimensional points included in the current space unit. 
     This enables the three-dimensional data decoding device to improve encoding efficiency since it is possible to reduce the amount of data of the encoded signal. 
     For example, three-dimensional data decoding device includes a processor and memory. The processor uses the memory to perform the above processes. 
     Embodiment 4 
     Information of a three-dimensional point cloud includes geometry information (geometry) and attribute information (attribute). Geometry information includes coordinates (x-coordinate, y-coordinate, z-coordinate) with respect to a certain point. When geometry information is encoded, a method of representing the position of each of three-dimensional points in octree representation and encoding the octree information to reduce a code amount is used instead of directly encoding the coordinates of the three-dimensional point. 
     On the other hand, attribute information includes information indicating, for example, color information (RGB, YUV, etc.) of each three-dimensional point, a reflectance, and a normal vector. For example, a three-dimensional data encoding device is capable of encoding attribute information using an encoding method different from a method used to encode geometry information. 
     In the present embodiment, a method of encoding attribute information is explained. It is to be noted that, in the present embodiment, the method is explained based on an example case using integer values as values of attribute information. For example, when each of RGB or YUV color components is of an 8-bit accuracy, the color component is an integer value in a range from 0 to 255. When a reflectance value is of 10-bit accuracy, the reflectance value is an integer in a range from 0 to 1023. It is to be noted that, when the bit accuracy of attribute information is a decimal accuracy, the three-dimensional data encoding device may multiply the value by a scale value to round it to an integer value so that the value of the attribute information becomes an integer value. It is to be noted that the three-dimensional data encoding device may add the scale value to, for example, a header of a bitstream. 
     As a method of encoding attribute information of a three-dimensional point, it is conceivable to calculate a predicted value of the attribute information of the three-dimensional point and encode a difference (prediction residual) between the original value of the attribute information and the predicted value. For example, when the value of attribute information at three-dimensional point p is Ap and a predicted value is Pp, the three-dimensional data encoding device encodes differential absolute value Diffp=|Ap−Pp|. In this case, when highly-accurate predicted value Pp can be generated, differential absolute value Diffp is small. Thus, for example, it is possible to reduce the code amount by entropy encoding differential absolute value Diffp using a coding table that reduces an occurrence bit count more when differential absolute value Diffp is smaller. 
     As a method of generating a prediction value of attribute information, it is conceivable to use attribute information of a reference three-dimensional point that is another three-dimensional point which neighbors a current three-dimensional point to be encoded. Here, a reference three-dimensional point is a three-dimensional point in a range of a predetermined distance from the current three-dimensional point. For example, when there are current three-dimensional point p=(x1, y1, z1) and three-dimensional point q=(x2, y2, z2), the three-dimensional data encoding device calculates Euclidean distance d (p, q) between three-dimensional point p and three-dimensional point q represented by (Equation A1). 
       [Math. 1] 
         d ( p,q )=√{square root over (( x 1− y 1) 2 +( x 2− y 2) 2 +( x 3− y 3) 2 )}   (Equation A1)
 
     The three-dimensional data encoding device determines that the position of three-dimensional point q is closer to the position of current three-dimensional point p when Euclidean distance d (p, q) is smaller than predetermined threshold value THd, and determines to use the value of the attribute information of three-dimensional point q to generate a predicted value of the attribute information of current three-dimensional point p. It is to be noted that the method of calculating the distance may be another method, and a Mahalanobis distance or the like may be used. In addition, the three-dimensional data encoding device may determine not to use, in prediction processing, any three-dimensional point outside the predetermined range of distance from the current three-dimensional point. For example, when three-dimensional point r is present, and distance d (p, r) between current three-dimensional point p and three-dimensional point r is larger than or equal to threshold value THd, the three-dimensional data encoding device may determine not to use three-dimensional point r for prediction. It is to be noted that the three-dimensional data encoding device may add the information indicating threshold value THd to, for example, a header of a bitstream. 
       FIG. 51  is a diagram illustrating an example of three-dimensional points. In this example, distance d (p, q) between current three-dimensional point p and three-dimensional point q is smaller than threshold value THd. Thus, the three-dimensional data encoding device determines that three-dimensional point q is a reference three-dimensional point of current three-dimensional point p, and determines to use the value of attribute information Aq of three-dimensional point q to generate predicted value Pp of attribute information Ap of current three-dimensional point p. 
     In contrast, distance d (p, r) between current three-dimensional point p and three-dimensional point r is larger than or equal to threshold value THd. Thus, the three-dimensional data encoding device determines that three-dimensional point r is not any reference three-dimensional point of current three-dimensional point p, and determines not to use the value of attribute information Ar of three-dimensional point r to generate predicted value Pp of attribute information Ap of current three-dimensional point p. 
     In addition, when encoding the attribute information of the current three-dimensional point using a predicted value, the three-dimensional data encoding device uses a three-dimensional point whose attribute information has already been encoded and decoded, as a reference three-dimensional point. Likewise, when decoding the attribute information of a current three-dimensional point to be decoded, the three-dimensional data decoding device uses a three-dimensional point whose attribute information has already been decoded, as a reference three-dimensional point. In this way, it is possible to generate the same predicted value at the time of encoding and decoding. Thus, a bitstream of the three-dimensional point generated by the encoding can be decoded correctly at the decoding side. 
     Furthermore, when encoding attribute information of each of three-dimensional points, it is conceivable to classify the three-dimensional point into one of a plurality of layers using geometry information of the three-dimensional point and then encode the attribute information. Here, each of the layers classified is referred to as a Level of Detail (LoD). A method of generating LoDs is explained with reference to  FIG. 52 . 
     First, the three-dimensional data encoding device selects initial point a0 and assigns initial point a0 to LoD0. Next, the three-dimensional data encoding device extracts point a1 distant from point a0 more than threshold value Thres_LoD[0] of LoD0 and assigns point a1 to LoD0. Next, the three-dimensional data encoding device extracts point a2 distant from point a1 more than threshold value Thres_LoD[0] of LoD0 and assigns point a2 to LoD0. In this way, the three-dimensional data encoding device configures LoD0 in such a manner that the distance between the points in LoD0 is larger than threshold value Thres_LoD[0]. 
     Next, the three-dimensional data encoding device selects point b0 which has not yet been assigned to any LoD and assigns point b0 to LoD1. Next, the three-dimensional data encoding device extracts point b1 which is distant from point b0 more than threshold value Thres_LoD[1] of LoD1 and which has not yet been assigned to any LoD, and assigns point b1 to LoD1. Next, the three-dimensional data encoding device extracts point b2 which is distant from point b1 more than threshold value Thres_LoD[1] of LoD1 and which has not yet been assigned to any LoD, and assigns point b2 to LoD1. In this way, the three-dimensional data encoding device configures LoD1 in such a manner that the distance between the points in LoD1 is larger than threshold value Thres_LoD[1]. 
     Next, the three-dimensional data encoding device selects point c0 which has not yet been assigned to any LoD and assigns point c0 to LoD2. Next, the three-dimensional data encoding device extracts point cl which is distant from point c0 more than threshold value Thres_LoD[2] of LoD2 and which has not yet been assigned to any LoD, and assigns point c1 to LoD2. Next, the three-dimensional data encoding device extracts point c2 which is distant from point c1 more than threshold value Thres_LoD[2] of LoD2 and which has not yet been assigned to any LoD, and assigns point c2 to LoD2. In this way, the three-dimensional data encoding device configures LoD2 in such a manner that the distance between the points in LoD2 is larger than threshold value Thres_LoD[2]. For example, as illustrated in  FIG. 53 , threshold values Thres_LoD[0], Thres_LoD[1], and Thres_LoD[2] of respective LoDs are set. 
     In addition, the three-dimensional data encoding device may add the information indicating the threshold value of each LoD to, for example, a header of a bitstream. For example, in the case of the example illustrated in  FIG. 53 , the three-dimensional data encoding device may add threshold values Thres_LoD[0], Thres_LoD[1], and Thres_LoD[2] of respective LoDs to a header. 
     Alternatively, the three-dimensional data encoding device may assign all three-dimensional points which have not yet been assigned to any LoD in the lowermost-layer LoD. In this case, the three-dimensional data encoding device is capable of reducing the code amount of the header by not assigning the threshold value of the lowermost-layer LoD to the header. For example, in the case of the example illustrated in  FIG. 53 , the three-dimensional data encoding device assigns threshold values Thres_LoD[0] and Thres_LoD[1] to the header, and does not assign Thres_LoD[2] to the header. In this case, the three-dimensional data encoding device may estimate value 0 of Thres_LoD[2]. In addition, the three-dimensional data encoding device may add the number of LoDs to a header. In this way, the three-dimensional data encoding device is capable of determining the lowermost-layer LoD using the number of LoDs. 
     In addition, setting threshold values for the respective layers LoDs in such a manner that a larger threshold value is set to a higher layer makes a higher layer (layer closer to LoD0) to have a sparse point cloud (sparse) in which three-dimensional points are more distant and makes a lower layer to have a dense point cloud (dense) in which three-dimensional points are closer. It is to be noted that, in an example illustrated in  FIG. 53 , LoD0 is the uppermost layer. 
     In addition, the method of selecting an initial three-dimensional point at the time of setting each LoD may depend on an encoding order at the time of geometry information encoding. For example, the three-dimensional data encoding device configures LoD0 by selecting the three-dimensional point encoded first at the time of the geometry information encoding as initial point a0 of LoD0, and selecting point a1 and point a2 from initial point a0 as the origin. The three-dimensional data encoding device then may select the three-dimensional point whose geometry information has been encoded at the earliest time among three-dimensional points which do not belong to LoD0, as initial point b0 of LoD1. In other words, the three-dimensional data encoding device may select the three-dimensional point whose geometry information has been encoded at the earliest time among three-dimensional points which do not belong to layers (LoD0 to LoDn−1) above LoDn, as initial point n0 of LoDn. In this way, the three-dimensional data encoding device is capable of configuring the same LoD as in encoding by using, in decoding, the initial point selecting method similar to the one used in the encoding, which enables appropriate decoding of a bitstream. More specifically, the three-dimensional data encoding device selects the three-dimensional point whose geometry information has been decoded at the earliest time among three-dimensional points which do not belong to layers above LoDn, as initial point n0 of LoDn. 
     Hereinafter, a description is given of a method of generating the predicted value of the attribute information of each three-dimensional point using information of LoDs. For example, when encoding three-dimensional points starting with the three-dimensional points included in LoD0, the three-dimensional data encoding device generates current three-dimensional points which are included in LoD1 using encoded and decoded (hereinafter also simply referred to as “encoded”) attribute information included in LoD0 and LoD1. In this way, the three-dimensional data encoding device generates a predicted value of attribute information of each three-dimensional point included in LoDn using encoded attribute information included in LoDn′ (n′≤n). In other words, the three-dimensional data encoding device does not use attribute information of each of three-dimensional points included in any layer below LoDn to calculate a predicted value of attribute information of each of the three-dimensional points included in LoDn. 
     For example, the three-dimensional data encoding device calculates an average of attribute information of N or less three-dimensional points among encoded three-dimensional points surrounding a current three-dimensional point to be encoded, to generate a predicted value of attribute information of the current three-dimensional point. In addition, the three-dimensional data encoding device may add value N to, for example, a header of a bitstream. It is to be noted that the three-dimensional data encoding device may change value N for each three-dimensional point, and may add value N for each three-dimensional point. This enables selection of appropriate N for each three-dimensional point, which makes it possible to increase the accuracy of the predicted value. Accordingly, it is possible to reduce the prediction residual. Alternatively, the three-dimensional data encoding device may add value N to a header of a bitstream, and may fix the value indicating N in the bitstream. This eliminates the need to encode or decode value N for each three-dimensional point, which makes it possible to reduce the processing amount. In addition, the three-dimensional data encoding device may encode the values of N separately for each LoD. In this way, it is possible to increase the coding efficiency by selecting appropriate N for each LoD. 
     Alternatively, the three-dimensional data encoding device may calculate a predicted value of attribute information of three-dimensional point based on weighted average values of attribute information of encoded N neighbor three-dimensional points. For example, the three-dimensional data encoding device calculates weights using distance information between a current three-dimensional point and each of N neighbor three-dimensional points. 
     When encoding value N for each LoD, for example, the three-dimensional data encoding device sets larger value N to a higher layer LoD, and sets smaller value N to a lower layer LoD. The distance between three-dimensional points belonging to a higher layer LoD is large, there is a possibility that it is possible to increase the prediction accuracy by setting large value N, selecting a plurality of neighbor three-dimensional points, and averaging the values. Furthermore, the distance between three-dimensional points belonging to a lower layer LoD is small, it is possible to perform efficient prediction while reducing the processing amount of averaging by setting smaller value N. 
       FIG. 54  is a diagram illustrating an example of attribute information to be used for predicted values. As described above, the predicted value of point P included in LoDN is generated using encoded neighbor point P′ included in LoDN′ (N′≤N). Here, neighbor point P′ is selected based on the distance from point P. For example, the predicted value of attribute information of point b2 illustrated in  FIG. 54  is generated using attribute information of each of points a0, a1, b0, and b1. 
     Neighbor points to be selected vary depending on the values of N described above. For example, in the case of N=5, a0, a1, a2, b0, and b1 are selected as neighbor points. In the case of N=4, a0, a1, a2, and b1 are selected based on distance information. 
     The predicted value is calculated by distance-dependent weighted averaging. For example, in the example illustrated in  FIG. 54 , predicted value a2p of point a2 is calculated by weighted averaging of attribute information of each of point a0 and a1, as represented by (Equation A2) and (Equation A3). It is to be noted that A i  is an attribute information value of ai. 
     
       
         
           
             
               
                 
                   [ 
                   
                     Math 
                     . 
                     
                         
                     
                     ⁢ 
                     2 
                   
                   ] 
                 
               
               
                 
                     
                 
               
             
             
               
                 
                   
                     a 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     2 
                     ⁢ 
                     p 
                   
                   = 
                   
                     
                       ∑ 
                       
                         i 
                         = 
                         0 
                       
                       1 
                     
                     ⁢ 
                     
                       
                         w 
                         i 
                       
                       × 
                       
                         A 
                         i 
                       
                     
                   
                 
               
               
                 
                   ( 
                   
                     Equation 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     A2 
                   
                   ) 
                 
               
             
             
               
                 
                   
                     w 
                     i 
                   
                   = 
                   
                     
                       1 
                       
                         d 
                         ⁡ 
                         
                           ( 
                           
                             
                               a 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               2 
                             
                             , 
                             ai 
                           
                           ) 
                         
                       
                     
                     
                       
                         ∑ 
                         
                           j 
                           = 
                           0 
                         
                         1 
                       
                       ⁢ 
                       
                         1 
                         
                           d 
                           ⁡ 
                           
                             ( 
                             
                               
                                 a 
                                 ⁢ 
                                 
                                     
                                 
                                 ⁢ 
                                 2 
                               
                               , 
                               aj 
                             
                             ) 
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   
                     Equation 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     A3 
                   
                   ) 
                 
               
             
           
         
       
     
     In addition, predicted value b2p of point b2 is calculated by weighted averaging of attribute information of each of point a0, a1, a2, b0, and b1, as represented by (Equation A4) and (Equation A6). It is to be noted that B i  is an attribute information value of bi. 
     
       
         
           
             
               
                 
                   [ 
                   
                     Math 
                     . 
                     
                         
                     
                     ⁢ 
                     3 
                   
                   ] 
                 
               
               
                 
                     
                 
               
             
             
               
                 
                   
                     b 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     2 
                     ⁢ 
                     p 
                   
                   = 
                   
                     
                       
                         ∑ 
                         
                           i 
                           = 
                           0 
                         
                         2 
                       
                       ⁢ 
                       
                         
                           wa 
                           i 
                         
                         × 
                         
                           A 
                           i 
                         
                       
                     
                     + 
                     
                       
                         ∑ 
                         
                           i 
                           = 
                           0 
                         
                         1 
                       
                       ⁢ 
                       
                         
                           wb 
                           i 
                         
                         × 
                         
                           B 
                           i 
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   
                     Equation 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     A4 
                   
                   ) 
                 
               
             
             
               
                 
                   
                     wa 
                     i 
                   
                   = 
                   
                     
                       1 
                       
                         d 
                         ⁡ 
                         
                           ( 
                           
                             
                               b 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               2 
                             
                             , 
                             ai 
                           
                           ) 
                         
                       
                     
                     
                       
                         
                           ∑ 
                           
                             j 
                             = 
                             0 
                           
                           2 
                         
                         ⁢ 
                         
                           1 
                           
                             d 
                             ⁡ 
                             
                               ( 
                               
                                 
                                   a 
                                   ⁢ 
                                   
                                       
                                   
                                   ⁢ 
                                   2 
                                 
                                 , 
                                 aj 
                               
                               ) 
                             
                           
                         
                       
                       + 
                       
                         
                           ∑ 
                           
                             j 
                             = 
                             0 
                           
                           1 
                         
                         ⁢ 
                         
                           1 
                           
                             d 
                             ⁡ 
                             
                               ( 
                               
                                 
                                   b 
                                   ⁢ 
                                   
                                       
                                   
                                   ⁢ 
                                   2 
                                 
                                 , 
                                 bj 
                               
                               ) 
                             
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   
                     Equation 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     A5 
                   
                   ) 
                 
               
             
             
               
                 
                   
                     wb 
                     i 
                   
                   = 
                   
                     
                       1 
                       
                         d 
                         ⁡ 
                         
                           ( 
                           
                             
                               b 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               2 
                             
                             , 
                             bi 
                           
                           ) 
                         
                       
                     
                     
                       
                         
                           ∑ 
                           
                             j 
                             = 
                             0 
                           
                           2 
                         
                         ⁢ 
                         
                           1 
                           
                             d 
                             ⁡ 
                             
                               ( 
                               
                                 
                                   b 
                                   ⁢ 
                                   
                                       
                                   
                                   ⁢ 
                                   2 
                                 
                                 , 
                                 aj 
                               
                               ) 
                             
                           
                         
                       
                       + 
                       
                         
                           ∑ 
                           
                             j 
                             = 
                             0 
                           
                           1 
                         
                         ⁢ 
                         
                           1 
                           
                             d 
                             ⁡ 
                             
                               ( 
                               
                                 
                                   b 
                                   ⁢ 
                                   
                                       
                                   
                                   ⁢ 
                                   2 
                                 
                                 , 
                                 bj 
                               
                               ) 
                             
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   
                     Equation 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     A6 
                   
                   ) 
                 
               
             
           
         
       
     
     In addition, the three-dimensional data encoding device may calculate a difference value (prediction residual) generated from the value of attribute information of a three-dimensional point and neighbor points, and may quantize the calculated prediction residual. For example, the three-dimensional data encoding device performs quantization by dividing the prediction residual by a quantization scale (also referred to as a quantization step). In this case, an error (quantization error) which may be generated by quantization reduces as the quantization scale is smaller. In the other case where the quantization scale is larger, the resulting quantization error is larger. 
     It is to be noted that the three-dimensional data encoding device may change the quantization scale to be used for each LoD. For example, the three-dimensional data encoding device reduces the quantization scale more for a higher layer, and increases the quantization scale more for a lower layer. The value of attribute information of a three-dimensional point belonging to a higher layer may be used as a predicted value of attribute information of a three-dimensional point belonging to a lower layer. Thus, it is possible to increase the coding efficiency by reducing the quantization scale for the higher layer to reduce the quantization error that can be generated in the higher layer and to increase the prediction accuracy of the predicted value. It is to be noted that the three-dimensional data encoding device may add the quantization scale to be used for each LoD to, for example, a header. In this way, the three-dimensional data encoding device can decode the quantization scale correctly, thereby appropriately decoding the bitstream. 
     In addition, the three-dimensional data encoding device may convert a signed integer value (signed quantized value) which is a quantized prediction residual into an unsigned integer value (unsigned quantized value). This eliminates the need to consider occurrence of a negative integer when entropy encoding the prediction residual. It is to be noted that the three-dimensional data encoding device does not always need to convert a signed integer value into an unsigned integer value, and, for example, that the three-dimensional data encoding device may entropy encode a sign bit separately. 
     The prediction residual is calculated by subtracting a prediction value from the original value. For example, as represented by (Equation A7), prediction residual a2r of point a2 is calculated by subtracting predicted value a2p of point a2 from value A 2  of attribute information of point a2. As represented by (Equation A8), prediction residual b2r of point b2 is calculated by subtracting predicted value b2p of point b2 from value B 2  of attribute information of point b2. 
         a 2 r=A   2   −a 2 p   (Equation A7)
 
         b 2 r=B   2   −b 2 p   (Equation A8)
 
     In addition, the prediction residual is quantized by being divided by a Quantization Step (QS). For example, quantized value a2q of point a2 is calculated according to (Equation A9). Quantized value b2q of point b2 is calculated according to (Equation A10). Here, QS_LoD0 is a QS for LoD0, and QS_LoD1 is a QS for LoD1. In other words, a QS may be changed according to an LoD. 
         a 2 q=a 2 r/QS _ LoD 0  (Equation A9)
 
         b 2 q=b 2 r/QS _ LoD 1  (Equation A10)
 
     In addition, the three-dimensional data encoding device converts signed integer values which are quantized values as indicated below into unsigned integer values as indicated below. When signed integer value a2q is smaller than 0, the three-dimensional data encoding device sets unsigned integer value a2u to −1−(2×a2q). When signed integer value a2q is 0 or more, the three-dimensional data encoding device sets unsigned integer value a2u to 2×a2q. 
     Likewise, when signed integer value b2q is smaller than 0, the three-dimensional data encoding device sets unsigned integer value b2u to −1−(2× b2q). When signed integer value b2q is 0 or more, the three-dimensional data encoding device sets unsigned integer value b2u to 2×b2q. 
     In addition, the three-dimensional data encoding device may encode the quantized prediction residual (unsigned integer value) by entropy encoding. For example, the three-dimensional data encoding device may binarize the unsigned integer value and then apply binary arithmetic encoding to the binary value. 
     It is to be noted that, in this case, the three-dimensional data encoding device may switch binarization methods according to the value of a prediction residual. For example, when prediction residual pu is smaller than threshold value R_TH, the three-dimensional data encoding device binarizes prediction residual pu using a fixed bit count required for representing threshold value R_TH. In addition, when prediction residual pu is larger than or equal to threshold value R_TH, the three-dimensional data encoding device binarizes the binary data of threshold value R_TH and the value of (pu−R_TH), using exponential-Golomb coding, or the like. 
     For example, when threshold value R_TH is 63 and prediction residual pu is smaller than 63, the three-dimensional data encoding device binarizes prediction residual pu using 6 bits. When prediction residual pu is larger than or equal to 63, the three-dimensional data encoding device performs arithmetic encoding by binarizing the binary data (111111) of threshold value R_TH and (pu−63) using exponential-Golomb coding. 
     In a more specific example, when prediction residual pu is 32, the three-dimensional data encoding device generates 6-bit binary data (100000), and arithmetic encodes the bit sequence. In addition, when prediction residual pu is 66, the three-dimensional data encoding device generates binary data (111111) of threshold value R_TH and a bit sequence (00100) representing value 3 (66-63) using exponential-Golomb coding, and arithmetic encodes the bit sequence (111111+00100). 
     In this way, the three-dimensional data encoding device can perform encoding while preventing a binary bit count from increasing abruptly in the case where a prediction residual becomes large by switching binarization methods according to the magnitude of the prediction residual. It is to be noted that the three-dimensional data encoding device may add threshold value R_TH to, for example, a header of a bitstream. 
     For example, in the case where encoding is performed at a high bit rate, that is, when a quantization scale is small, a small quantization error and a high prediction accuracy are obtained. As a result, a prediction residual may not be large. Thus, in this case, the three-dimensional data encoding device sets large threshold value R_TH. This reduces the possibility that the binary data of threshold value R_TH is encoded, which increases the coding efficiency. In the opposite case where encoding is performed at a low bit rate, that is, when a quantization scale is large, a large quantization error and a low prediction accuracy are obtained. As a result, a prediction residual may be large. Thus, in this case, the three-dimensional data encoding device sets small threshold value R_TH. In this way, it is possible to prevent abrupt increase in bit length of binary data. 
     In addition, the three-dimensional data encoding device may switch threshold value R_TH for each LoD, and may add threshold value R_TH for each LoD to, for example, a header. In other words, the three-dimensional data encoding device may switch binarization methods for each LoD. For example, since distances between three-dimensional points are large in a higher layer, a prediction accuracy is low, which may increase a prediction residual. Thus, the three-dimensional data encoding device prevents abrupt increase in bit length of binary data by setting small threshold value R_TH to the higher layer. In addition, since distances between three-dimensional points are small in a lower layer, a prediction accuracy is high, which may reduce a prediction residual. Thus, the three-dimensional data encoding device increases the coding efficiency by setting large threshold value R_TH to the lower layer. 
       FIG. 55  is a diagram indicating examples of exponential-Golomb codes. The diagram indicates the relationships between pre-binarization values (non-binary values) and post-binarization bits (codes). It is to be noted that 0 and 1 indicated in  FIG. 55  may be inverted. 
     The three-dimensional data encoding device applies arithmetic encoding to the binary data of prediction residuals. In this way, the coding efficiency can be increased. It is to be noted that, in the application of the arithmetic encoding, there is a possibility that occurrence probability tendencies of 0 and 1 in each bit vary, in binary data, between an n-bit code which is a part binarized by n bits and a remaining code which is a part binarized using exponential-Golomb coding. Thus, the three-dimensional data encoding device may switch methods of applying arithmetic encoding between the n-bit code and the remaining code. 
     For example, the three-dimensional data encoding device performs arithmetic encoding on the n-bit code using one or more coding tables (probability tables) different for each bit. At this time, the three-dimensional data encoding device may change the number of coding tables to be used for each bit. For example, the three-dimensional data encoding device performs arithmetic encoding using one coding table for first bit b0 in an n-bit code. The three-dimensional data encoding device uses two coding tables for the next bit b1. The three-dimensional data encoding device switches coding tables to be used for arithmetic encoding of bit b1 according to the value (0 or 1) of b0. Likewise, the three-dimensional data encoding device uses four coding tables for the next bit b2. The three-dimensional data encoding device switches coding tables to be used for arithmetic encoding of bit b2 according to the values (in a range from 0 to 3) of b0 and b1. 
     In this way, the three-dimensional data encoding device uses 2n −1  coding tables when arithmetic encoding each bit bn−1 in n-bit code. The three-dimensional data encoding device switches coding tables to be used according to the values (occurrence patterns) of bits before bn−1. In this way, the three-dimensional data encoding device can use coding tables appropriate for each bit, and thus can increase the coding efficiency. 
     It is to be noted that the three-dimensional data encoding device may reduce the number of coding tables to be used for each bit. For example, the three-dimensional data encoding device may switch 2 m  coding tables according to the values (occurrence patterns) of m bits (m&lt;n−1) before bn−1 when arithmetic encoding each bit bn−1. In this way, it is possible to increase the coding efficiency while reducing the number of coding tables to be used for each bit. It is to be noted that the three-dimensional data encoding device may update the occurrence probabilities of 0 and 1 in each coding table according to the values of binary data occurred actually. In addition, the three-dimensional data encoding device may fix the occurrence probabilities of 0 and 1 in coding tables for some bit(s). In this way, it is possible to reduce the number of updates of occurrence probabilities, and thus to reduce the processing amount. 
     For example, when an n-bit code is b0, b1, b2, . . . , bn−1, the coding table for b0 is one table (CTb0). Coding tables for b1 are two tables (CTb10 and CTb11). Coding tables to be used are switched according to the value (0 or 1) of b0. Coding tables for b2 are four tables (CTb20, CTb21, CTb22, and CTb23). Coding tables to be used are switched according to the values (in the range from 0 to 3) of b0 and b1. Coding tables for bn−1 are 2 n−1  tables (CTbn0, CTbn1, . . . , CTbn (2 n−1 −1)). Coding tables to be used are switched according to the values (in a range from 0 to 2 n−1 −1) of b0, b1, . . . , bn−2. 
     It is to be noted that the three-dimensional data encoding device may apply, to an n-bit code, arithmetic encoding (m=2 n ) by m-ary that sets the value in the range from 0 to 2 n −1 without binarization. When the three-dimensional data encoding device arithmetic encodes an n-bit code by an m-ary, the three-dimensional data decoding device may reconstruct the n-bit code by arithmetic decoding the m-ary. 
       FIG. 56  is a diagram for illustrating processing in the case where remaining codes are exponential-Golomb codes. As indicated in  FIG. 56 , each remaining code which is a part binarized using exponential-Golomb coding includes a prefix and a suffix. For example, the three-dimensional data encoding device switches coding tables between the prefix and the suffix. In other words, the three-dimensional data encoding device arithmetic encodes each of bits included in the prefix using coding tables for the prefix, and arithmetic encodes each of bits included in the suffix using coding tables for the suffix. 
     It is to be noted that the three-dimensional data encoding device may update the occurrence probabilities of 0 and 1 in each coding table according to the values of binary data occurred actually. In addition, the three-dimensional data encoding device may fix the occurrence probabilities of 0 and 1 in one of coding tables. In this way, it is possible to reduce the number of updates of occurrence probabilities, and thus to reduce the processing amount. For example, the three-dimensional data encoding device may update the occurrence probabilities for the prefix, and may fix the occurrence probabilities for the suffix. 
     In addition, the three-dimensional data encoding device decodes a quantized prediction residual by inverse quantization and reconstruction, and uses a decoded value which is the decoded prediction residual for prediction of a current three-dimensional point to be encoded and the following three-dimensional point(s). More specifically, the three-dimensional data encoding device calculates an inverse quantized value by multiplying the quantized prediction residual (quantized value) with a quantization scale, and adds the inverse quantized value and a prediction value to obtain the decoded value (reconstructed value). 
     For example, quantized value a2iq of point a2 is calculated using quantized value a2q of point a2 according to (Equation A11). Inverse quantized value b2iq of point b2q is calculated using quantized value b2q of point b2 according to (Equation A12). Here, QS_LoD0 is a QS for LoD0, and QS_LoD1 is a QS for LoD1. In other words, a QS may be changed according to an LoD. 
         a 2 iq=a 2 q×QS _ LoD 0  (Equation A11)
 
         b 2 iq=b 2 q×QS _ LoD 1  (Equation A12)
 
     For example, as represented by (Equation A13), decoded value a2rec of point a2 is calculated by adding inverse quantization value a2iq of point a2 to predicted value a2p of point a2. As represented by (Equation A14), decoded value b2rec of point b2 is calculated by adding inverse quantized value b2iq of point b2 to predicted value b2p of point b2. 
         a 2 rec=a 2 iq+a 2 p   (Equation A13)
 
         b 2 rec=b 2 iq+b 2 p   (Equation A14)
 
     Hereinafter, a syntax example of a bitstream according to the present embodiment is described.  FIG. 57  is a diagram indicating the syntax example of an attribute header (attribute_header) according to the present embodiment. The attribute header is header information of attribute information. As indicated in  FIG. 57 , the attribute header includes the number of layers information (NumLoD), the number of three-dimensional points information (NumOfPoint[i]), a layer threshold value (Thres_LoD[i]), the number of neighbor points information (NumNeighborPoint[i]), a prediction threshold value (THd[i]), a quantization scale (QS[i]), and a binarization threshold value (R_TH[i]). 
     The number of layers information (NumLoD) indicates the number of LoDs to be used. 
     The number of three-dimensional points information (NumOfPoint[i]) indicates the number of three-dimensional points belonging to layer i. It is to be noted that the three-dimensional data encoding device may add, to another header, the number of three-dimensional points information indicating the total number of three-dimensional points. In this case, the three-dimensional data encoding device does not need to add, to a header, NumOfPoint [NumLoD−1] indicating the number of three-dimensional points belonging to the lowermost layer. In this case, the three-dimensional data decoding device is capable of calculating NumOfPoint [NumLoD−1] according to (Equation A15). In this case, it is possible to reduce the code amount of the header. 
     
       
         
           
             
               
                 
                   
                       
                   
                   ⁢ 
                   
                     [ 
                     
                       Math 
                       . 
                       
                           
                       
                       ⁢ 
                       4 
                     
                     ] 
                   
                 
               
               
                 
                     
                 
               
             
             
               
                 
                   
                     NumOfPoint 
                     ⁡ 
                     
                       [ 
                       
                         NumLoD 
                         - 
                         1 
                       
                       ] 
                     
                   
                   = 
                   
                     AllNumOfPoint 
                     - 
                     
                       
                         ∑ 
                         
                           j 
                           = 
                           0 
                         
                         
                           NumLoD 
                           - 
                           2 
                         
                       
                       ⁢ 
                       
                         NumOfPoint 
                         ⁡ 
                         
                           [ 
                           j 
                           ] 
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   
                     Equation 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     A15 
                   
                   ) 
                 
               
             
           
         
       
     
     The layer threshold value (Thres_LoD[i]) is a threshold value to be used to set layer i. The three-dimensional data encoding device and the three-dimensional data decoding device configure LoDi in such a manner that the distance between points in LoDi becomes larger than threshold value Thres_LoD[i]. The three-dimensional data encoding device does not need to add the value of Thres_LoD [NumLoD−1] (lowermost layer) to a header. In this case, the three-dimensional data decoding device may estimate 0 as the value of Thres_LoD [NumLoD−1]. In this case, it is possible to reduce the code amount of the header. 
     The number of neighbor points information (NumNeighborPoint[i]) indicates the upper limit value of the number of neighbor points to be used to generate a predicted value of a three-dimensional point belonging to layer i. The three-dimensional data encoding device may calculate a predicted value using the number of neighbor points M when the number of neighbor points M is smaller than NumNeighborPoint[i] (M&lt;NumNeighborPoint[i]). Furthermore, when there is no need to differentiate the values of NumNeighborPoint[i] for respective LoDs, the three-dimensional data encoding device may add a piece of the number of neighbor points information (NumNeighborPoint) to be used in all LoDs to a header. 
     The prediction threshold value (THd[i]) indicates the upper limit value of the distance between a current three-dimensional point to be encoded or decoded in layer i and each of neighbor three-dimensional points to be used to predict the current three-dimensional point. The three-dimensional data encoding device and the three-dimensional data decoding device do not use, for prediction, any three-dimensional point distant from the current three-dimensional point over THd[i]. It is to be noted that, when there is no need to differentiate the values of THd[i] for respective LoDs, the three-dimensional data encoding device may add a single prediction threshold value (THd) to be used in all LoDs to a header. 
     The quantization scale (QS[i]) indicates a quantization scale to be used for quantization and inverse quantization in layer i. 
     The binarization threshold value (R_TH[i]) is a threshold value for switching binarization methods of prediction residuals of three-dimensional points belonging to layer i. For example, the three-dimensional data encoding device binarizes prediction residual pu using a fixed bit count when a prediction residual is smaller than threshold value R_TH, and binarizes the binary data of threshold value R_TH and the value of (pu−R_TH) using exponential-Golomb coding when a prediction residual is larger than or equal to threshold value R_TH. It is to be noted that, when there is no need to switch the values of R_TH[i] between LoDs, the three-dimensional data encoding device may add a single binarization threshold value (R_TH) to be used in all LoDs to a header. 
     It is to be noted that R_TH[i] may be the maximum value which can be represented by n bits. For example, R_TH is 63 in the case of 6 bits, and R_TH is 255 in the case of 8 bits. Alternatively, the three-dimensional data encoding device may encode a bit count instead of encoding the maximum value which can be represented by n bits as a binarization threshold value. For example, the three-dimensional data encoding device may add value 6 in the case of R_TH[i]=63 to a header, and may add value 8 in the case of R_TH[i]=255 to a header. Alternatively, the three-dimensional data encoding device may define the minimum value (minimum bit count) representing R_TH[i], and add a relative bit count from the minimum value to a header. For example, the three-dimensional data encoding device may add value 0 to a header when R_TH[i]=63 is satisfied and the minimum bit count is 6, and may add value 2 to a header when R_TH[i]=255 is satisfied and the minimum bit count is 6. 
     Alternatively, the three-dimensional data encoding device may entropy encode at least one of NumLoD, Thres_LoD[i], NumNeighborPoint[i], THd[i], QS[i], and R_TH[i], and add the entropy encoded one to a header. For example, the three-dimensional data encoding device may binarize each value and perform arithmetic encoding on the binary value. In addition, the three-dimensional data encoding device may encode each value using a fixed length in order to reduce the processing amount. 
     Alternatively, the three-dimensional data encoding device does not always need to add at least one of NumLoD, Thres_LoD[i], NumNeighborPoint[i], THd[i], QS[i], and R_TH[i] to a header. For example, at least one of these values may be defined by a profile or a level in a standard, or the like. In this way, it is possible to reduce the bit amount of the header. 
       FIG. 58  is a diagram indicating the syntax example of attribute data (attribute_data) according to the present embodiment. The attribute data includes encoded data of the attribute information of a plurality of three-dimensional points. As indicated in  FIG. 58 , the attribute data includes an n-bit code and a remaining code. 
     The n-bit code is encoded data of a prediction residual of a value of attribute information or a part of the encoded data. The bit length of the n-bit code depends on value R_TH[i]. For example, the bit length of the n-bit code is 6 bits when the value indicated by R_TH[i] is 63, the bit length of the n-bit code is 8 bits when the value indicated by R_TH[i] is 255. 
     The remaining code is encoded data encoded using exponential-Golomb coding among encoded data of the prediction residual of the value of the attribute information. The remaining code is encoded or decoded when the value of the n-bit code is equal to R_TH[i]. The three-dimensional data decoding device decodes the prediction residual by adding the value of the n-bit code and the value of the remaining code. It is to be noted that the remaining code does not always need to be encoded or decoded when the value of the n-bit code is not equal to R_TH[i]. 
     Hereinafter, a description is given of a flow of processing in the three-dimensional data encoding device.  FIG. 59  is a flowchart of a three-dimensional data encoding process performed by the three-dimensional data encoding device. 
     First, the three-dimensional data encoding device encodes geometry information (geometry) (S 3001 ). For example, the three-dimensional data encoding is performed using octree representation. 
     When the positions of three-dimensional points changed by quantization, etc, after the encoding of the geometry information, the three-dimensional data encoding device re-assigns attribute information of the original three-dimensional points to the post-change three-dimensional points (S 3002 ). For example, the three-dimensional data encoding device interpolates values of attribute information according to the amounts of change in position to re-assign the attribute information. For example, the three-dimensional data encoding device detects pre-change N three-dimensional points closer to the post-change three-dimensional positions, and performs weighted averaging of the values of attribute information of the N three-dimensional points. For example, the three-dimensional data encoding device determines weights based on distances from the post-change three-dimensional positions to the respective N three-dimensional positions in weighted averaging. The three-dimensional data encoding device then determines the values obtained through the weighted averaging to be the values of the attribute information of the post-change three-dimensional points. When two or more of the three-dimensional points are changed to the same three-dimensional position through quantization, etc., the three-dimensional data encoding device may assign the average value of the attribute information of the pre-change two or more three-dimensional points as the values of the attribute information of the post-change three-dimensional points. 
     Next, the three-dimensional data encoding device encodes the attribute information (attribute) re-assigned (S 3003 ). For example, when encoding a plurality of kinds of attribute information, the three-dimensional data encoding device may encode the plurality of kinds of attribute information in order. For example, when encoding colors and reflectances as attribute information, the three-dimensional data encoding device may generate a bitstream added with the color encoding results and the reflectance encoding results after the color encoding results. It is to be noted that the order of the plurality of encoding results of attribute information to be added to a bitstream is not limited to the order, and may be any order. 
     Alternatively, the three-dimensional data encoding device may add, to a header for example, information indicating the start location of encoded data of each attribute information in a bitstream. In this way, the three-dimensional data decoding device is capable of selectively decoding attribute information required to be decoded, and thus is capable of skipping the decoding process of the attribute information not required to be decoded. Accordingly, it is possible to reduce the amount of processing by the three-dimensional data decoding device. Alternatively, the three-dimensional data encoding device may encode a plurality of kinds of attribute information in parallel, and may integrate the encoding results into a single bitstream. In this way, the three-dimensional data encoding device is capable of encoding the plurality of kinds of attribute information at high speed. 
       FIG. 60  is a flowchart of an attribute information encoding process (S 3003 ). First, the three-dimensional data encoding device sets LoDs (S 3011 ). In other words, the three-dimensional data encoding device assigns each of three-dimensional points to any one of the plurality of LoDs. 
     Next, the three-dimensional data encoding device starts a loop for each LoD (S 3012 ). In other words, the three-dimensional data encoding device iteratively performs the processes of Steps from S 3013  to S 3021  for each LoD. 
     Next, the three-dimensional data encoding device starts a loop for each three-dimensional point (S 3013 ). In other words, the three-dimensional data encoding device iteratively performs the processes of Steps from S 3014  to S 3020  for each three-dimensional point. 
     First, the three-dimensional data encoding device searches a plurality of neighbor points which are three-dimensional points present in the neighborhood of a current three-dimensional point to be processed and are to be used to calculate a predicted value of the current three-dimensional point (S 3014 ). Next, the three-dimensional data encoding device calculates the weighted average of the values of attribute information of the plurality of neighbor points, and sets the resulting value to predicted value P (S 3015 ). Next, the three-dimensional data encoding device calculates a prediction residual which is the difference between the attribute information of the current three-dimensional point and the predicted value (S 3016 ). Next, the three-dimensional data encoding device quantizes the prediction residual to calculate a quantized value (S 3017 ). Next, the three-dimensional data encoding device arithmetic encodes the quantized value (S 3018 ). 
     Next, the three-dimensional data encoding device inverse quantizes the quantized value to calculate an inverse quantized value (S 3019 ). Next, the three-dimensional data encoding device adds a prediction value to the inverse quantized value to generate a decoded value (S 3020 ). Next, the three-dimensional data encoding device ends the loop for each three-dimensional point (S 3021 ). Next, the three-dimensional data encoding device ends the loop for each LoD (S 3022 ). 
     Hereinafter, a description is given of a three-dimensional data decoding process in the three-dimensional data decoding device which decodes a bitstream generated by the three-dimensional data encoding device. 
     The three-dimensional data decoding device generates decoded binary data by arithmetic decoding the binary data of the attribute information in the bitstream generated by the three-dimensional data encoding device, according to the method similar to the one performed by the three-dimensional data encoding device. It is to be noted that when methods of applying arithmetic encoding are switched between the part (n-bit code) binarized using n bits and the part (remaining code) binarized using exponential-Golomb coding in the three-dimensional data encoding device, the three-dimensional data decoding device performs decoding in conformity with the arithmetic encoding, when applying arithmetic decoding. 
     For example, the three-dimensional data decoding device performs arithmetic decoding using coding tables (decoding tables) different for each bit in the arithmetic decoding of the n-bit code. At this time, the three-dimensional data decoding device may change the number of coding tables to be used for each bit. For example, the three-dimensional data decoding device performs arithmetic decoding using one coding table for first bit b0 in the n-bit code. The three-dimensional data decoding device uses two coding tables for the next bit b1. The three-dimensional data decoding device switches coding tables to be used for arithmetic decoding of bit b1 according to the value (0 or 1) of b0. Likewise, the three-dimensional data decoding device uses four coding tables for the next bit b2. The three-dimensional data decoding device switches coding tables to be used for arithmetic decoding of bit b2 according to the values (in the range from 0 to 3) of b0 and b1. 
     In this way, the three-dimensional data decoding device uses 2 n−1  coding tables when arithmetic decoding each bit bn−1 in the n-bit code. The three-dimensional data decoding device switches coding tables to be used according to the values (occurrence patterns) of bits before bn−1. In this way, the three-dimensional data decoding device is capable of appropriately decoding a bitstream encoded at an increased coding efficiency using the coding tables appropriate for each bit. 
     It is to be noted that the three-dimensional data decoding device may reduce the number of coding tables to be used for each bit. For example, the three-dimensional data decoding device may switch 2 m  coding tables according to the values (occurrence patterns) of m bits (m&lt;n−1) before bn−1 when arithmetic decoding each bit bn−1. In this way, the three-dimensional data decoding device is capable of appropriately decoding the bitstream encoded at the increased coding efficiency while reducing the number of coding tables to be used for each bit. It is to be noted that the three-dimensional data decoding device may update the occurrence probabilities of 0 and 1 in each coding table according to the values of binary data occurred actually. In addition, the three-dimensional data decoding device may fix the occurrence probabilities of 0 and 1 in coding tables for some bit(s). In this way, it is possible to reduce the number of updates of occurrence probabilities, and thus to reduce the processing amount. 
     For example, when an n-bit code is b0, b1, b2, . . . , bn−1, the coding table for b0 is one (CTb0). Coding tables for b1 are two tables (CTb10 and CTb11). Coding tables to be used are switched according to the value (0 or 1) of b0. Coding tables for b2 are four tables (CTb20, CTb21, CTb22, and CTb23). Coding tables to be used according to the values (in the range from 0 to 3) of b0 and b1. Coding tables for bn−1 are 2 n−1  tables (CTbn0, CTbn1, . . . , CTbn (2 n−1 −1)). Coding tables to be used are switched according to the values (in the range from 0 to 2 n−1 −1) of b0, b1, . . . , bn−2. 
       FIG. 61  is a diagram for illustrating processing in the case where remaining codes are exponential-Golomb codes. As indicated in  FIG. 61 , the part (remaining part) binarized and encoded by the three-dimensional data encoding device using exponential-Golomb coding includes a prefix and a suffix. For example, the three-dimensional data decoding device switches coding tables between the prefix and the suffix. In other words, the three-dimensional data decoding device arithmetic decodes each of bits included in the prefix using coding tables for the prefix, and arithmetic decodes each of bits included in the suffix using coding tables for the suffix. 
     It is to be noted that the three-dimensional data decoding device may update the occurrence probabilities of 0 and 1 in each coding table according to the values of binary data occurred at the time of decoding. In addition, the three-dimensional data decoding device may fix the occurrence probabilities of 0 and 1 in one of coding tables. In this way, it is possible to reduce the number of updates of occurrence probabilities, and thus to reduce the processing amount. For example, the three-dimensional data decoding device may update the occurrence probabilities for the prefix, and may fix the occurrence probabilities for the suffix. 
     Furthermore, the three-dimensional data decoding device decodes the quantized prediction residual (unsigned integer value) by debinarizing the binary data of the prediction residual arithmetic decoded according to a method in conformity with the encoding method used by the three-dimensional data encoding device. The three-dimensional data decoding device first arithmetic decodes the binary data of an n-bit code to calculate a value of the n-bit code. Next, the three-dimensional data decoding device compares the value of the n-bit code with threshold value R_TH. 
     In the case where the value of the n-bit code and threshold value R_TH match, the three-dimensional data decoding device determines that a bit encoded using exponential-Golomb coding is present next, and arithmetic decodes the remaining code which is the binary data encoded using exponential-Golomb coding. The three-dimensional data decoding device then calculates, from the decoded remaining code, a value of the remaining code using a reverse lookup table indicating the relationship between the remaining code and the value.  FIG. 62  is a diagram indicating an example of a reverse lookup table indicating relationships between remaining codes and the values thereof. Next, the three-dimensional data decoding device adds the obtained value of the remaining code to R_TH, thereby obtaining a debinarized quantized prediction residual. 
     In the opposite case where the value of the n-bit code and threshold value R_TH do not match (the value of the n-bit code is smaller than value R_TH), the three-dimensional data decoding device determines the value of the n-bit code to be the debinarized quantized prediction residual as it is. In this way, the three-dimensional data decoding device is capable of appropriately decoding the bitstream generated while switching the binarization methods according to the values of the prediction residuals by the three-dimensional data encoding device. 
     It is to be noted that, when threshold value R_TH is added to, for example, a header of a bitstream, the three-dimensional data decoding device may decode threshold value R_TH from the header, and may switch decoding methods using decoded threshold value R_TH. When threshold value R_TH is added to, for example, a header for each LoD, the three-dimensional data decoding device switch decoding methods using threshold value R_TH decoded for each LoD. 
     For example, when threshold value R_TH is 63 and the value of the decoded n-bit code is 63, the three-dimensional data decoding device decodes the remaining code using exponential-Golomb coding, thereby obtaining the value of the remaining code. For example, in the example indicated in  FIG. 62 , the remaining code is 00100, and 3 is obtained as the value of the remaining code. Next, the three-dimensional data decoding device adds 63 that is threshold value R_TH and 3 that is the value of the remaining code, thereby obtaining 66 that is the value of the prediction residual. 
     In addition, when the value of the decoded n-bit code is 32, the three-dimensional data decoding device sets 32 that is the value of the n-bit code to the value of the prediction residual. 
     In addition, the three-dimensional data decoding device converts the decoded quantized prediction residual, for example, from an unsigned integer value to a signed integer value, through processing inverse to the processing in the three-dimensional data encoding device. In this way, when entropy decoding the prediction residual, the three-dimensional data decoding device is capable of appropriately decoding the bitstream generated without considering occurrence of a negative integer. It is to be noted that the three-dimensional data decoding device does not always need to convert an unsigned integer value to a signed integer value, and that, for example, the three-dimensional data decoding device may decode a sign bit when decoding a bitstream generated by separately entropy encoding the sign bit. 
     The three-dimensional data decoding device performs decoding by inverse quantizing and reconstructing the quantized prediction residual after being converted to the signed integer value, to obtain a decoded value. The three-dimensional data decoding device uses the generated decoded value for prediction of a current three-dimensional point to be decoded and the following three-dimensional point(s). More specifically, the three-dimensional data decoding device multiplies the quantized prediction residual by a decoded quantization scale to calculate an inverse quantized value and adds the inverse quantized value and the predicted value to obtain the decoded value. 
     The decoded unsigned integer value (unsigned quantized value) is converted into a signed integer value through the processing indicated below. When the least significant bit (LSB) of decoded unsigned integer value a2u is 1, the three-dimensional data decoding device sets signed integer value a2q to −((a2u+1)&gt;&gt;1). When the LSB of unsigned integer value a2u is not 1, the three-dimensional data decoding device sets signed integer value a2q to ((a2u&gt;&gt;1). 
     Likewise, when an LSB of decoded unsigned integer value b2u is 1, the three-dimensional data decoding device sets signed integer value b2q to −((b2u+1)&gt;&gt;1). When the LSB of decoded unsigned integer value n2u is not 1, the three-dimensional data decoding device sets signed integer value b2q to ((b2u&gt;&gt;1). 
     Details of the inverse quantization and reconstruction processing by the three-dimensional data decoding device are similar to the inverse quantization and reconstruction processing in the three-dimensional data encoding device. 
     Hereinafter, a description is given of a flow of processing in the three-dimensional data decoding device.  FIG. 63  is a flowchart of a three-dimensional data decoding process performed by the three-dimensional data decoding device. First, the three-dimensional data decoding device decodes geometry information (geometry) from a bitstream (S 3031 ). For example, the three-dimensional data decoding device performs decoding using octree representation. 
     Next, the three-dimensional data decoding device decodes attribute information (attribute) from the bitstream (S 3032 ). For example, when decoding a plurality of kinds of attribute information, the three-dimensional data decoding device may decode the plurality of kinds of attribute information in order. For example, when decoding colors and reflectances as attribute information, the three-dimensional data decoding device decodes the color encoding results and the reflectance encoding results in order of assignment in the bitstream. For example, when the reflectance encoding results are added after the color encoding results in a bitstream, the three-dimensional data decoding device decodes the color encoding results, and then decodes the reflectance encoding results. It is to be noted that the three-dimensional data decoding device may decode, in any order, the encoding results of the attribute information added to the bitstream. 
     Alternatively, the three-dimensional data encoding device may add, to a header for example, information indicating the start location of encoded data of each attribute information in a bitstream. In this way, the three-dimensional data decoding device is capable of selectively decoding attribute information required to be decoded, and thus is capable of skipping the decoding process of the attribute information not required to be decoded. Accordingly, it is possible to reduce the amount of processing by the three-dimensional data decoding device. In addition, the three-dimensional data decoding device may decode a plurality of kinds of attribute information in parallel, and may integrate the decoding results into a single three-dimensional point cloud. In this way, the three-dimensional data decoding device is capable of decoding the plurality of kinds of attribute information at high speed. 
       FIG. 64  is a flowchart of an attribute information decoding process (S 3032 ). First, the three-dimensional data decoding device sets LoDs (S 3041 ). In other words, the three-dimensional data decoding device assigns each of three-dimensional points having the decoded geometry information to any one of the plurality of LoDs. For example, this assignment method is the same as the assignment method used in the three-dimensional data encoding device. 
     Next, the three-dimensional data decoding device starts a loop for each LoD (S 3042 ). In other words, the three-dimensional data decoding device iteratively performs the processes of Steps from S 3043  to S 3049  for each LoD. 
     Next, the three-dimensional data decoding device starts a loop for each three-dimensional point (S 3043 ). In other words, the three-dimensional data decoding device iteratively performs the processes of Steps from S 3044  to S 3048  for each three-dimensional point. 
     First, the three-dimensional data decoding device searches a plurality of neighbor points which are three-dimensional points present in the neighborhood of a current three-dimensional point to be processed and are to be used to calculate a predicted value of the current three-dimensional point to be processed (S 3044 ). Next, the three-dimensional data decoding device calculates the weighted average of the values of attribute information of the plurality of neighbor points, and sets the resulting value to predicted value P (S 3045 ). It is to be noted that these processes are similar to the processes in the three-dimensional data encoding device. 
     Next, the three-dimensional data decoding device arithmetic decodes the quantized value from the bitstream (S 3046 ). The three-dimensional data decoding device inverse quantizes the decoded quantized value to calculate an inverse quantized value (S 3047 ). Next, the three-dimensional data decoding device adds a predicted value to the inverse quantized value to generate a decoded value (S 3048 ). Next, the three-dimensional data decoding device ends the loop for each three-dimensional point (S 3049 ). Next, the three-dimensional data encoding device ends the loop for each LoD (S 3050 ). 
     The following describes configurations of the three-dimensional data encoding device and three-dimensional data decoding device according to the present embodiment.  FIG. 65  is a block diagram illustrating a configuration of three-dimensional data encoding device  3000  according to the present embodiment. Three-dimensional data encoding device  3000  includes geometry information encoder  3001 , attribute information re-assigner  3002 , and attribute information encoder  3003 . 
     Attribute information encoder  3003  encodes geometry information (geometry) of a plurality of three-dimensional points included in an input point cloud. Attribute information re-assigner  3002  re-assigns the values of attribute information of the plurality of three-dimensional points included in the input point cloud, using the encoding and decoding results of the geometry information. Attribute information encoder  3003  encodes the re-assigned attribute information (attribute). Furthermore, three-dimensional data encoding device  3000  generates a bitstream including the encoded geometry information and the encoded attribute information. 
       FIG. 66  is a block diagram illustrating a configuration of three-dimensional data decoding device  3010  according to the present embodiment. Three-dimensional data decoding device  3010  includes geometry information decoder  3011  and attribute information decoder  3012 . 
     Geometry information decoder  3011  decodes the geometry information (geometry) of a plurality of three-dimensional points from a bitstream. Attribute information decoder  3012  decodes the attribute information (attribute) of the plurality of three-dimensional points from the bitstream. Furthermore, three-dimensional data decoding device  3010  integrates the decoded geometry information and the decoded attribute information to generate an output point cloud. 
     Embodiment 5 
     Hereinafter, a three-dimensional point to be encoded is referred to as a first three-dimensional point, and one or more three-dimensional points in the vicinity of the first three-dimensional point is referred to as one or more second three-dimensional points in some cases. 
     For example, in generating of a predicted value of an attribute information item (attribute information) of a three-dimensional point, an attribute value as it is of a closest three-dimensional point among encoded and decoded three-dimensional points in the vicinity of a three-dimensional point to be encoded may be generated as a predicted value. In the generating of the predicted value, prediction mode information (PredMode) may be appended for each three-dimensional point, and one predicted value may be selected from a plurality of predicted values to allow generation of a predicted value. Specifically, for example, it is conceivable that, for total number M of prediction modes, an average value is assigned to prediction mode 0, an attribute value of three-dimensional point A is assigned to prediction mode 1, . . . , and an attribute value of three-dimensional point Z is assigned to prediction mode M−1, and the prediction mode used for prediction is appended to a bitstream for each three-dimensional point. As such, a first prediction mode value indicating a first prediction mode for calculating, as a predicted value, an average of attribute information items of the surrounding three-dimensional points may be smaller than a second prediction mode value indicating a second prediction mode for calculating, as a predicted value, an attribute information item as it is of a surrounding three-dimensional point. Here, the “average value” as the predicted value calculated in prediction mode 0 is an average value of the attribute values of the three-dimensional points in the vicinity of the three-dimensional point to be encoded. 
       FIG. 67  is a diagram showing a first example of a table representing predicted values calculated in the prediction modes according to Embodiment 5.  FIG. 68  is a diagram showing examples of attribute information items used as the predicted values according to Embodiment 5.  FIG. 69  is a diagram showing a second example of a table representing predicted values calculated in the prediction modes according to Embodiment 5. 
     Number M of prediction modes may be appended to a bitstream. Number M of prediction modes may be defined by a profile or a level of standards rather than appended to the bitstream. Number M of prediction modes may be also calculated from number N of three-dimensional points used for prediction. For example, number M of prediction modes may be calculated by M=N+1. 
     The table in  FIG. 67  is an example of a case with number N of three-dimensional points used for prediction being 4 and number M of prediction modes being 5. A predicted value of an attribute information item of point b2 can be generated by using attribute information items of points a0, a1, a2, b1. In selecting one prediction mode from a plurality of prediction modes, a prediction mode for generating, as a predicted value, an attribute value of each of points a0, a1, a2, b1 may be selected in accordance with distance information from point b2 to each of points a0, a1, a2, b1. The prediction mode is appended for each three-dimensional point to be encoded. The predicted value is calculated in accordance with a value corresponding to the appended prediction mode. 
     The table in  FIG. 69  is, as in  FIG. 67 , an example of a case with number N of three-dimensional points used for prediction being 4 and number M of prediction modes being 5. A predicted value of an attribute information item of point a2 can be generated by using attribute information items of points a0, a1. In selecting one prediction mode from a plurality of prediction modes, a prediction mode for generating, as a predicted value, an attribute value of each of points a0 and a1 may be selected in accordance with distance information from point a2 to each of points a0, a1. The prediction mode is appended for each three-dimensional point to be encoded. The predicted value is calculated in accordance with a value corresponding to the appended prediction mode. 
     When the number of neighboring points, that is, number N of surrounding three-dimensional points is smaller than four such as at point a2 above, a prediction mode to which a predicted value is not assigned may be written as “not available” in the table. 
     Assignment of values of the prediction modes may be determined in accordance with the distance from the three-dimensional point to be encoded. For example, prediction mode values indicating a plurality of prediction modes decrease with decreasing distance from the three-dimensional point to be encoded to the surrounding three-dimensional points having the attribute information items used as the predicted values. The example in  FIG. 67  shows that points b1, a2, a1, a0 are sequentially located closer to point b2 as the three-dimensional point to be encoded. For example, in the calculating of the predicted value, the attribute information item of point b1 is calculated as the predicted value in a prediction mode indicated by a prediction mode value of “1” among two or more prediction modes, and the attribute information item of point a2 is calculated as the predicted value in a prediction mode indicated by a prediction mode value of “2”. As such, the prediction mode value indicating the prediction mode for calculating, as the predicted value, the attribute information item of point b1 is smaller than the prediction mode value indicating the prediction mode for calculating, as the predicted value, the attribute information item of point a2 farther from point b2 than point b1. 
     Thus, a small prediction mode value can be assigned to a point that is more likely to be predicted and selected due to a short distance, thereby reducing a bit number for encoding the prediction mode value. Also, a small prediction mode value may be preferentially assigned to a three-dimensional point belonging to the same LoD as the three-dimensional point to be encoded. 
       FIG. 70  is a diagram showing a third example of a table representing predicted values calculated in the prediction modes according to Embodiment 5. Specifically, the third example is an example of a case where an attribute information item used as a predicted value is a value of color information (YUV) of a surrounding three-dimensional point. As such, the attribute information item used as the predicted value may be color information indicating a color of the three-dimensional point. 
     As shown in  FIG. 70 , a predicted value calculated in a prediction mode indicated by a prediction mode value of “0” is an average of Y, U, and V components defining a YUV color space. Specifically, the predicted value includes a weighted average Yave of Y component values Yb1, Ya2, Ya1, Ya0 corresponding to points b1, a2, a1, a0, respectively, a weighted average Uave of U component values Uh1, Ua2, Ua1, Ua0 corresponding to points b1, a2, a1, a0, respectively, and a weighted average Vave of V component values Vb1, Va2, Va1, Va0 corresponding to points b1, a2, a1, a0, respectively. Predicted values calculated in prediction modes indicated by prediction mode values of “1” to “4” include color information of the surrounding three-dimensional points b1, a2, a1, a0. The color information is indicated by combinations of the Y, U, and V component values. 
     In  FIG. 70 , the color information is indicated by a value defined by the YUV color space, but not limited to the YUV color space. The color information may be indicated by a value defined by an RGB color space or a value defined by any other color space. 
     As such, in the calculating of the predicted value, two or more averages or two or more attribute information items may be calculated as the predicted values of the prediction modes. The two or more averages or the two or more attribute information items may indicate two or more component values each defining a color space. 
     For example, when a prediction mode indicated by a prediction mode value of “2” in the table in  FIG. 70  is selected, a Y component, a U component, and a V component as attribute values of the three-dimensional point to be encoded may be encoded as predicted values Ya2, Ua2, Va2. In this case, the prediction mode value of “2” is appended to the bitstream. 
       FIG. 71  is a diagram showing a fourth example of a table representing predicted values calculated in the prediction modes according to Embodiment 5. Specifically, the fourth example is an example of a case where an attribute information item used as a predicted value is a value of reflectance information of a surrounding three-dimensional point. The reflectance information is, for example, information indicating reflectance R. 
     As shown in  FIG. 71 , a predicted value calculated in a prediction mode indicated by a prediction mode value of “0” is weighted average Rave of reflectances Rb1, Ra2, Ra1, Ra0 corresponding to points b1, a2, a1, a0, respectively. Predicted values calculated in prediction modes indicated by prediction mode values of “1” to “4” are reflectances Rb1, Ra2, Ra1, Ra0 of surrounding three-dimensional points b1, a2, a1, a0, respectively. 
     For example, when a prediction mode indicated by a prediction mode value of “3” in the table in  FIG. 71  is selected, a reflectance as an attribute value of a three-dimensional point to be encoded may be encoded as predicted value Ra1. In this case, the prediction mode value of “3” is appended to the bitstream. 
     As shown in  FIGS. 52 and 53 , the attribute information item may include a first attribute information item and a second attribute information item different from the first attribute information item. The first attribute information item is, for example, color information. The second attribute information item is, for example, reflectance information. In the calculating of the predicted value, a first predicted value may be calculated by using the first attribute information item, and a second predicted value may be calculated by using the second attribute information item. 
     When the attribute information item includes a plurality of components like color information such as a YUV color space or an RGB color space, predicted values may be calculated in different prediction modes for the respective components. For example, for the YUV space, predicted values using a Y component, a U component, and a V component may be calculated in prediction modes selected for the respective components. For example, prediction mode values may be selected in prediction mode Y for calculating the predicted value using the Y component, prediction mode U for calculating the predicted value using the U component, and prediction mode V for calculating the predicted value using the V component. In this case, values in tables in  FIGS. 54 to 56  described later may be used as the prediction mode values indicating the prediction modes of the components, and the prediction mode values may be appended to the bitstream. The YUV color space has been described above, but the same applies to the RGB color space. 
     Predicted values including two or more components among a plurality of components of an attribute information item may be calculated in a common prediction mode. For example, for the YUV color space, prediction mode values may be selected in prediction mode Y for calculating the predicted value using the Y component and prediction mode UV for calculating the predicted value using the UV components. In this case, values in tables in  FIGS. 54 and 57  described later may be used as the prediction mode values indicating the prediction modes of the components, and the prediction mode values may be appended to the bitstream. 
       FIG. 72  is a diagram showing a fifth example of a table representing predicted values calculated in the prediction modes according to Embodiment 5. Specifically, the fifth example is an example of a case where an attribute information item used as a predicted value is a Y component value of color information of a surrounding three-dimensional point. 
     As shown in  FIG. 72 , a predicted value calculated in prediction mode Y indicated by a prediction mode value of “0” is weighted average Yave of Y component values Yb1, Ya2, Ya1, Ya0 corresponding to points b1, a2, a1, a0, respectively. Predicted values calculated in prediction modes indicated by prediction mode values of “1” to “4” are Y component values Yb1, Ya2, Ya1, Ya0 of surrounding three-dimensional points b1, a2, a1, a0, respectively. 
     For example, when prediction mode Y indicated by a prediction mode value of “2” in the table in  FIG. 72  is selected, a Y component as an attribute value of a three-dimensional point to be encoded may be used as predicted value Ya2 and encoded. In this case, the prediction mode value of “2” is appended to the bitstream. 
       FIG. 73  is a diagram showing a sixth example of a table representing predicted values calculated in the prediction modes according to Embodiment 5. Specifically, the sixth example is an example of a case where an attribute information item used as a predicted value is a U component value of color information of a surrounding three-dimensional point. 
     As shown in  FIG. 73 , a predicted value calculated in prediction mode U indicated by a prediction mode value of “0” is weighted average Uave of U component values Ub1, Ua2, Ua1, Ua0 corresponding to points b1, a2, a1, a0, respectively. Predicted values calculated in prediction modes indicated by prediction mode values of “1” to “4” are U component values Ub1, Ua2, Ua1, Ua0 of surrounding three-dimensional points b1, a2, a1, a0, respectively. 
     For example, when prediction mode U indicated by a prediction mode value of “1” in the table in  FIG. 73  is selected, a U component as an attribute value of a three-dimensional point to be encoded may be encoded as predicted value Ub1. In this case, the prediction mode value of “1” is appended to the bitstream. 
       FIG. 74  is a diagram showing a seventh example of a table representing predicted values calculated in the prediction modes according to Embodiment 5. Specifically, the seventh example is an example of a case where an attribute information item used as a predicted value is a V component value of color information of a surrounding three-dimensional point. 
     As shown in  FIG. 74 , a predicted value calculated in prediction mode V indicated by a prediction mode value of “0” is weighted average Vave of V component values Vb1, Va2, Va1, Va0 corresponding to points b1, a2, a1, a0, respectively. Predicted values calculated in prediction modes indicated by prediction mode values of “1” to “4” are V component values Vb1, Va2, Va1, Va0 of surrounding three-dimensional points b1, a2, a1, a0, respectively. 
     For example, when prediction mode V indicated by a prediction mode value of “4” in the table in  FIG. 74  is selected, a V component as an attribute value of a three-dimensional point to be encoded may be used as predicted value Va0 and encoded. In this case, the prediction mode value of “4” is appended to the bitstream. 
       FIG. 75  is a diagram showing an eighth example of a table representing predicted values calculated in the prediction modes according to Embodiment 5. Specifically, the eighth example is an example of a case where attribute information items used as predicted values are a U component value and a V component value of color information of a surrounding three-dimensional point. 
     As shown in  FIG. 75 , a predicted value calculated in prediction mode U indicated by a prediction mode value of “0” includes weighted average Uave of U component values Ub1, Ub2, Ua1, Ua0 corresponding to points b1, a2, a1, a0, respectively and weighted average Vave of V component values Vb1, Va2, Va1, Va0 corresponding to points b1, a2, a1, a0, respectively. Predicted values calculated in prediction modes indicated by prediction mode values of “1” to “4” include U component values and V component values of surrounding three-dimensional points b1, a2, a1, a0, respectively. 
     For example, when prediction mode UV indicated by a prediction mode value of “1” in the table in  FIG. 75  is selected, a U component and a V component as attribute values of a three-dimensional point to be encoded may be used as predicted values Ub1, Vb1 and encoded. In this case, the prediction mode value of “1” is appended to the bitstream. 
     A prediction mode in encoding may be selected by RD optimization. For example, it is conceivable that cost cost(P) when certain prediction mode P is selected is calculated, and prediction mode P with minimum cost(P) is selected. Cost cost(P) may be calculated by Equation D1 using, for example, prediction residual residual(P) when a predicted value of prediction mode P is used, bit number bit(P) required for encoding prediction mode P, and adjustment parameter value λ. 
       cost( P )=abs(residual( P ))+λ×bit( P )  (Equation D1)
 
     where abs(x) denotes an absolute value of x. 
     A square value of x may be used instead of abs(x). 
     Using Equation D1 above allows selection of a prediction mode considering balance between a size of a prediction residual and a bit number required for encoding the prediction mode. Different adjustment parameter values X, may be set in accordance with values of a quantization scale. For example, at a small quantization scale (at a high bit rate), value λ, may be set smaller to select a prediction mode with smaller prediction residual residual(P) to increase prediction accuracy as much as possible. At a large quantization scale (at a low bit rate), value λ, may be set larger to select an appropriate prediction mode while considering bit number bit(P) required for encoding prediction mode P. 
     “At a small quantization scale” is, for example, when the quantization scale is smaller than a first quantization scale. “At a large quantization scale” is, for example, when the quantization scale is larger than a second quantization scale equal to or greater than the first quantization scale. Values λ, may be set smaller at smaller quantization scales. 
     Prediction residual residual(P) is calculated by subtracting a predicted value of prediction mode P from an attribute value of a three-dimensional point to be encoded. Instead of prediction residual residual(P) in calculating of cost, prediction residual residual(P) may be quantized or inverse quantized and added to the predicted value to obtain a decoded value, and a difference (encoding error) from a decoded value when an attribute value of an original three-dimensional point and prediction mode P are used may be reflected in the cost value. This allows selection of a prediction mode with a small encoding error. 
     In binarizing and encoding a prediction mode, for example, a binarized bit number may be used as bit number bit(P) required for encoding prediction mode P. For example, with number M of prediction modes being 5, as in  FIG. 76 , a prediction mode value indicating the prediction mode may be binarized by a truncated unary code in accordance with number M of prediction modes with a maximum value of 5. In this case, 1 bit for a prediction mode value of “0”, 2 bits for a prediction mode value of “1”, 3 bits for a prediction mode value of “2”, and 4 bits for prediction mode values of “4” and “5” are used as bit numbers bit(P) required for encoding the prediction mode values. By using the truncated unary code, the bit number is set smaller for smaller prediction mode values. This can reduce an encoding amount of a prediction mode value indicating a prediction mode for calculating a predicted value that is more likely to be selected, for example, that is more likely to minimize cost(P), such as an average value calculated as a predicted value when the prediction mode value is “0”, or an attribute information item of a three-dimensional point calculated as a predicted value when the prediction mode value is “1”, that is, an attribute information item of a three-dimensional point close to the three-dimensional point to be encoded. 
     When a maximum value of the number of prediction modes is not determined, as in  FIG. 77 , a prediction mode value indicating a prediction mode may be binarized by a unary code. When a probability of appearance of each prediction mode is close, as shown in  FIG. 78 , the prediction mode value indicating the prediction mode may be binarized by a fixed code to reduce an encoding amount. 
     As bit number bit(P) required for encoding the prediction mode value indicating prediction mode P, binarized data of the prediction mode value indicating prediction mode P may be arithmetic-encoded, and an encoding amount after the arithmetic-encoding may be used as a value of bit(P). This allows calculation of cost using more accurate required bit number bit(P), thereby allowing selection of a more appropriate prediction mode. 
       FIG. 76  is a diagram showing a first example of a binarization table in binarizing and encoding the prediction mode values according to Embodiment 5. Specifically, the first example is an example of binarizing the prediction mode values with a truncated unary code with number M of prediction modes being 5. 
       FIG. 77  is a diagram showing a second example of a binarization table in binarizing and encoding the prediction mode values according to Embodiment 5. Specifically, the second example is an example of binarizing the prediction mode values with a unary code with number M of prediction modes being 5. 
       FIG. 78  is a diagram showing a third example of a binarization table in binarizing and encoding the prediction mode values according to Embodiment 5. Specifically, the third example is an example of binarizing the prediction mode values with a fixed code with number M of prediction modes being 5. 
     A prediction mode value indicating a prediction mode (PredMode) may be arithmetic-encoded after binarized, and appended to the bitstream. As described above, the prediction mode value may be binarized, for example, by the truncated unary code in accordance with number M of prediction modes. In this case, a maximum bit number after binarization of the prediction mode value is M−1. 
     The binary data after binarization may be arithmetic-encoded with reference to an encoding table. In this case, for example, encoding tables may be switched for encoding for each bit of the binary data, thereby improving an encoding efficiency. Also, to reduce the number of encoding tables, among the binary data, the beginning bit one bit may be encoded with reference to encoding table A for one bit, and each of remaining bits may be encoded with reference to encoding table B for remaining bits. For example, in encoding binarized data “1110” with a prediction mode value of “3” in  FIG. 79 , the beginning bit one bit “1” may be encoded with reference to encoding table A, and each of remaining bits “110” may be encoded with reference to encoding table B. 
       FIG. 79  is a diagram for describing an example of encoding binary data in the binarization table in binarizing and encoding the prediction modes according to Embodiment 5. The binarization table in  FIG. 79  is an example of binarizing the prediction mode values with a truncated unary code with number M of prediction modes being 5. 
     Thus, an encoding efficiency can be improved by switching the encoding tables in accordance with a bit position of the binary data while reducing the number of encoding tables. Further, in encoding the remaining bits, arithmetic-encoding may be performed by switching the encoding tables for each bit, or decoding may be performed by switching the encoding tables in accordance with a result of the arithmetic-encoding. 
     In binarizing and encoding the prediction mode value with the truncated unary code using number M of prediction modes, number M of prediction modes used in the truncated unary code may be appended to a header and the like of the bitstream so that the prediction mode can be specified from binary data decoded on a decoding side. Also, value MaxM that may be a value of the number of prediction modes may be defined by standards or the like, and value MaxM−M (M≤MaxM) may be appended to the header. Number M of prediction modes may be defined by a profile or a level of standards rather than appended to the stream. 
     It is considered that the prediction mode value binarized by the truncated unary code is arithmetic-encoded by switching the encoding tables between one bit part and a remaining part as described above. The probability of appearance of 0 and 1 in each encoding table may be updated in accordance with actually generated binary data. Also, the probability of appearance of 0 and 1 in either of the encoding tables may be fixed. Thus, an update frequency of the probability of appearance may be reduced to reduce a processing amount. For example, the probability of appearance of the one bit part may be updated, and the probability of appearance of the remaining bit part may be fixed. 
       FIG. 80  is a flowchart of an example of encoding a prediction mode value according to Embodiment 5.  FIG. 81  is a flowchart of an example of decoding a prediction mode value according to Embodiment 5. 
     As shown in  FIG. 80 , in encoding the prediction mode value, first, the prediction mode value is binarized by a truncated unary code in accordance with number M of prediction modes (S 3401 ). 
     Then, binary data of the truncated unary code is arithmetic-encoded (S 3402 ). Thus, the binary data is included as a prediction mode in the bitstream. 
     Also, as shown in  FIG. 81 , in decoding the prediction mode value, first, the bitstream is arithmetic-decoded by using number M of prediction modes to generate binary data of the truncated unary code (S 3403 ). 
     Then, the prediction mode value is calculated from the binary data of the truncated unary code (S 3404 ). 
     As a method of binarizing the prediction mode value indicating the prediction mode (PredMode), the example of binarizing with the truncated unary code using number M of prediction modes has been described, but not limited to this. For example, the prediction mode value may be binarized by a truncated unary code in accordance with number L (L≤M) of prediction modes assigned with predicted values. For example, with number M of prediction modes being 5, when two surrounding three-dimensional points are available for prediction of a certain three-dimensional point to be encoded, as shown in  FIG. 82 , three prediction modes are available and the remaining two prediction modes are not available in some cases. For example, as shown in  FIG. 82 , with number M of prediction modes being 5, two three-dimensional points in the vicinity of the three-dimensional point to be encoded are available for prediction, and predicted values are not assigned to prediction modes indicated by prediction mode values of “3” and “4” in some cases. 
     In this case, as shown in  FIG. 83 , the prediction mode value is binarized by a truncated unary code in accordance with number L of prediction modes assigned with predicted values as a maximum value. This may reduce the bit number after binarization as compared to when the prediction mode value is binarized by the truncated unary code in accordance with number M of prediction modes. For example, in this case, L is 3, and the prediction mode value can be binarized by a truncated unary code in accordance with a maximum value of 3 to reduce the bit number. As such, binarization by the truncated unary code in accordance with number L of prediction modes assigned with predicted values as a maximum value may reduce the bit number after binarization of the prediction mode value. 
     The binary data after binarization may be arithmetic-encoded with reference to an encoding table. In this case, for example, encoding tables may be switched for encoding for each bit of the binary data, thereby improving an encoding efficiency. Also, to reduce the number of encoding tables, among binarized data, the beginning bit one bit may be encoded with reference to encoding table A for one bit, and each of remaining bits may be encoded with reference to encoding table B for remaining bits. For example, in encoding binarized data “11” with a prediction mode value of “2” in  FIG. 83 , the beginning bit one bit “1” may be encoded with reference to encoding table A, and remaining bit “1” may be encoded with reference to encoding table B. 
       FIG. 83  is a diagram for describing an example of encoding binary data in the binarization table in binarizing and encoding the prediction modes according to Embodiment 5. The binarization table in  FIG. 83  is an example of binarizing the prediction mode values with a truncated unary code with number L of prediction modes assigned with predicted values being 3. 
     Thus, an encoding efficiency can be improved by switching the encoding tables in accordance with a bit position of the binary data while reducing the number of encoding tables. Further, in encoding the remaining bits, arithmetic-encoding may be performed by switching the encoding tables for each bit, or decoding may be performed by switching the encoding tables in accordance with a result of the arithmetic-encoding. 
     In binarizing and encoding the prediction mode value with the truncated unary code using number L of prediction modes assigned with predicted values, a predicted value may be assigned to a prediction mode to calculate number L in the same manner as in encoding and the prediction mode may be decoded by using calculated number L so that the prediction mode can be specified from binary data decoded on a decoding side. 
     It is considered that the prediction mode value binarized by the truncated unary code is arithmetic-encoded by switching the encoding tables between one bit part and a remaining part as described above. The probability of appearance of 0 and 1 in each encoding table may be updated in accordance with actually generated binary data. Also, the probability of appearance of 0 and 1 in either of the encoding tables may be fixed. Thus, an update frequency of the probability of appearance may be reduced to reduce a processing amount. For example, the probability of appearance of the one bit part may be updated, and the probability of appearance of the remaining bit part may be fixed. 
       FIG. 84  is flowchart of another example of encoding a prediction mode value according to Embodiment 5.  FIG. 85  is a flowchart of another example of decoding a prediction mode value according to Embodiment 5. 
     As shown in  FIG. 84 , in encoding the prediction mode value, first, number L of prediction modes assigned with predicted values is calculated (S 3411 ). 
     Then, the prediction mode value is binarized by a truncated unary code in accordance with number L (S 3412 ). 
     Then, binary data of the truncated unary code is arithmetic-encoded (S 3413 ). 
     Also, as shown in  FIG. 85 , in decoding the prediction mode value, first, number L of prediction modes assigned with predicted values is calculated (S 3414 ). 
     Then, the bitstream is arithmetic-decoded by using number L to generate binary data of the truncated unary code (S 3415 ). 
     Then, the prediction mode value is calculated from the binary data of the truncated unary code (S 3416 ). 
     The prediction mode value needs not be appended for all attribute values. For example, if a certain condition is satisfied, the prediction mode may be fixed so that the prediction mode value is not appended to the bitstream, and if the certain condition is not satisfied, the prediction mode may be selected to append the prediction mode value to the bitstream. For example, if condition A is satisfied, the prediction mode value may be fixed at “0” and a predicted value may be calculated from an average value of surrounding three-dimensional points. If condition A is not satisfied, one prediction mode may be selected from a plurality of prediction modes and a prediction mode value indicating the selected prediction mode may be append to the bitstream. 
     Certain condition A is, for example, that calculated maximum absolute differential value maxdiff of attribute values (a[0] to a[N−1]) of N (encoded and decoded) three-dimensional points in the vicinity of a three-dimensional point to be encoded is smaller than threshold Thfix. When the maximum absolute differential value of the attribute values of the surrounding three-dimensional points is smaller than threshold Thfix, it is determined that there is a small difference between the attribute values of the three-dimensional points and selecting a prediction mode causes no difference in the predicted value. Then, the prediction mode value is fixed at “0” and the prediction mode value is not encoded, thereby allowing generation of an appropriate predicted value while reducing an encoding amount for encoding the prediction mode. 
     Threshold Thfix may be appended to the header and the like of the bitstream, and the encoder may perform encoding while changing threshold Thfix. For example, in encoding at a high bit rate, the encoder may set threshold Thfix smaller than that at a low bit rate and append threshold Thfix to the header and increase the case of encoding by selecting a prediction mode, and thus perform encoding so that the prediction residual is as small as possible. Also, in encoding at the low bit rate, the encoder sets threshold Thfix larger than that at the high bit rate and appends threshold Thfix to the header, and performs encoding in a fixed prediction mode. As such, increasing the case of encoding in the fixed prediction mode at the low bit rate can improve an encoding efficiency while reducing a bit amount for encoding the prediction mode. Threshold Thfix may be defined by a profile or a level of standards rather than appended to the bitstream. 
     The N three-dimensional points in the vicinity of the three-dimensional point to be encoded, which are used for prediction, are N encoded and decoded three-dimensional points with a distance from the three-dimensional point to be encoded being smaller than threshold THd. A maximum value of N may be appended as NumNeighborPoint to the bitstream. The value of N needs not always match NumNeighborPoint as in the case where the number of surrounding encoded and decoded three-dimensional points is smaller than NumNeighborPoint. 
     The example has been given in which the prediction mode value is fixed at “0” if maximum absolute differential value maxdiff of the attribute values of the three-dimensional points in the vicinity of the three-dimensional point to be encoded, which are used for prediction, is smaller than threshold Thfix[i]. However, not limited to this, the prediction mode value may be fixed at any of “0” to “M−1”. The prediction mode value to be fixed may be appended to the bitstream. 
       FIG. 86  is a flowchart of an example of a process of determining whether or not a prediction mode value is fixed under condition A in encoding according to Embodiment 5.  FIG. 87  is a flowchart of an example of a process of determining whether the prediction mode value is fixed or decoded under condition A in decoding according to Embodiment 5. 
     As shown in  FIG. 86 , first, the three-dimensional data encoding device calculates maximum absolute differential value maxdiff of attribute values of N three-dimensional points in the vicinity of a three-dimensional point to be encoded (S 3421 ). 
     Then, the three-dimensional data encoding device determines whether or not maximum absolute differential value maxdiff is smaller than threshold Thfix (S 3422 ). Threshold Thfix may be encoded and appended to the header and the like of the stream. 
     When maximum absolute differential value maxdiff is smaller than threshold Thfix (Yes in S 3422 ), the three-dimensional data encoding device sets the prediction mode value to “0” (S 3423 ). 
     When maximum absolute differential value maxdiff is equal to or greater than threshold Thfix (No in S 3422 ), the three-dimensional data encoding device selects one prediction mode from a plurality of prediction modes (S 3424 ). A process of selecting the prediction mode will be described later in detail with reference to  FIG. 94 . 
     Then, the three-dimensional data encoding device arithmetic-encodes a prediction mode value indicating the selected prediction mode (S 3425 ). Specifically, the three-dimensional data encoding device performs steps S 3401  and S 3402  described with reference to  FIG. 80  to arithmetic-encode the prediction mode value. The three-dimensional data encoding device may perform arithmetic-encoding by binarizing prediction mode PredMode with a truncated unary code using the number of prediction modes assigned with predicted values. Specifically, the three-dimensional data encoding device may perform steps S 3411  to S 3413  described with reference to  FIG. 84  to arithmetic-encode the prediction mode value. 
     The three-dimensional data encoding device calculates a predicted value of the prediction mode set in step S 3423  or the prediction mode selected in step S 3425  to output the calculated predicted value (S 3426 ). When using the prediction mode value set in step S 3423 , the three-dimensional data encoding device calculates an average of attribute values of N surrounding three-dimensional points as a predicted value of a prediction mode indicated by the prediction mode value of “0”. 
     Also, as shown in  FIG. 87 , first, the three-dimensional data decoding device calculates maximum absolute differential value maxdiff of attribute values of N three-dimensional points in the vicinity of a three-dimensional point to be decoded (S 3431 ). Maximum absolute differential value maxdiff may be calculated as shown in  FIG. 88 . Maximum absolute differential value maxdiff is, for example, a maximum value of a plurality of calculated absolute values of differences between all possible pairs when any two of the N surrounding three-dimensional points are paired. 
     Then, the three-dimensional data decoding device determines whether or not maximum absolute differential value maxdiff is smaller than threshold Thfix (S 3432 ). Threshold Thfix may be set by decoding the header and the like of the stream. 
     When maximum absolute differential value maxdiff is smaller than threshold Thfix (Yes in S 3432 ), the three-dimensional data decoding device sets the prediction mode value to “0” (S 3433 ). 
     When maximum absolute differential value maxdiff is equal to or greater than threshold Thfix (No in S 3432 ), the three-dimensional data decoding device decodes the prediction mode value from the bitstream (S 3434 ). 
     The three-dimensional data decoding device calculates a predicted value of a prediction mode indicated by the prediction mode value set in step S 3433  or the prediction mode value decoded in step S 3434  to output the calculated predicted value (S 3435 ). When using the prediction mode value set in step S 3433 , the three-dimensional data decoding device calculates an average of attribute values of N surrounding three-dimensional points as a predicted value of a prediction mode indicated by the prediction mode value of “0”. 
       FIG. 89  is a diagram showing an example of a syntax according to Embodiment 5. NumLoD, NumNeighborPoint[i], NumPredMode[i], Thfix[i], and NumOfPoint[i] in the syntax in  FIG. 89  will be sequentially described. 
     NumLoD indicates the number of LoDs. 
     NumNeighborPoint[i] indicates an upper limit value of the number of surrounding points used for generating a predicted value of a three-dimensional point belonging to level i. When number M of surrounding points is smaller than NumNeighborPoint[i] (M&lt;NumNeighborPoint[i]), the predicted value may be calculated by using number M of surrounding points. When a value of NumNeighborPoint[i] needs not be divided among LoDs, one NumNeighborPoint may be appended to the header. 
     NumPredMode[i] is a total number (M) of prediction modes used for predicting an attribute value of level i. Possible value MaxM of the number of prediction modes may be defined by standards or the like, and value MaxM−M (0&lt;M≤MaxM) may be appended to the header as NumPredMode[i] and binarized by a truncated unary code in accordance with maximum value MaxM−1 and encoded. Number of prediction modes NumPredMode[i] may be defined by a profile or a level of standards rather than appended to the stream. The number of prediction modes may be defined by NumNeighborPoint[i]+NumPredMode[i]. When the value of NumPredMode[i] needs not be divided among LoDs, one NumPredMode may be appended to the header. 
     Thfix[i] indicates a threshold of a maximum absolute differential value for determining whether or not a prediction mode of level i is fixed. If the maximum absolute differential value of attribute values of surrounding three-dimensional points used for prediction is smaller than Thfix[i], the prediction mode is fixed at 0. Thfix[i] may be defined by a profile or a level of standards rather than appended to the stream. When the value of Thfix[i] needs not be divided among LoDs, one Thfix may be appended to the header. 
     NumOfPoint[i] indicates the number of three-dimensional points belonging to level i. When total number AllNumOfPoint of three-dimensional points is appended to another header, NumOfPoint[NumLoD-1] (the number of three-dimensional points belonging to the lowest level) may be calculated by the following equation: 
       [Math. 5] 
       AllNumOfPoint−Σ j=0   NumLoD−2 NumOfPoint[ j ]   (Equation D2)
 
     rather than appended to the header. This can reduce an encoding amount of the header. 
     As a setting example of NumPredMode[i], the value of NumPredMode[i] may be set larger for a higher level at which prediction is more difficult due to a longer distance between three-dimensional points belonging to the level, thereby increasing the number of selectable prediction modes. Also, the value NumPredMode[i] may be set smaller for a lower level at which prediction is easy, thereby reducing a bit amount required for encoding the prediction mode. Such setting can increase the number of selectable prediction modes to reduce a prediction residual at the upper level, and reduce an encoding amount of a prediction mode at the lower level, thereby improving an encoding efficiency. 
     As a setting example of Thfix[i], the value of Thfix[i] may be set smaller for a higher level at which prediction is difficult due to a long distance from the three-dimensional point belonging to LoD, thereby increasing the case of selecting the prediction mode. Also, the value of Thfix[i] may be set larger value for a lower level at which prediction is easy, and the prediction mode may be fixed to reduce a bit amount required for encoding the prediction mode. Such setting can increase the case of selecting the prediction mode to reduce a prediction residual at the upper level, and fix the prediction mode to reduce an encoding amount of the prediction mode at the lower level, thereby improving an encoding efficiency. 
     NumLoD, NumNeighborPoint[i], NumPredMode[i], Thfix[i], or NumOfPoint[i] described above may be entropy encoded and appended to the header. For example, the values may be binarized and arithmetic-encoded. The values may be encoded at a fixed length to reduce a processing amount. 
       FIG. 90  is a diagram showing an example of a syntax according to Embodiment 5. PredMode, n-bit code, and remaining code in the syntax in  FIG. 90  will be sequentially described. 
     PredMode indicates a prediction mode for encoding and decoding an attribute value of a j-th three-dimensional point in level i. PredMode is “0” to “M−1” (M is a total number of prediction modes). When PredMode is not in the bitstream (maxdiff≥Thfix[i] &amp;&amp; NumPredMode[i]&gt;1 as a condition is not satisfied), the value of PredMode may be estimated as 0. The value of PredMode may be estimated as any of “0” to “M−1”, not limited to “0”. An estimated value when PredMode is not in the bitstream may be separately appended to the header and the like. PredMode may be binarized by a truncated unary code in accordance with the number of prediction modes assigned with predicted values and arithmetic-encoded. 
     The n-bit code indicates encoded data of a prediction residual of a value of an attribute information item. A bit length of the n-bit code depends on a value of R_TH[i]. The bit length of the n-bit code is, for example, 6 bits when the value of R_TH[i] is 63, and 8 bits when the value of R_TH[i] is 255. 
     The remaining code indicates encoded data encoded by Exponential-Golomb among encoded data of the prediction residual of the attribute information item. The remaining code is decoded when the n-bit code is equal to R_TH[i], and the value of the n-bit code is added to the value of the remaining code to decode the prediction residual. When the n-bit code is not equal to R_TH[i], the remaining code needs not be decoded. 
     Now, a flow of a process of the three-dimensional data encoding device will be described.  FIG. 91  is a flowchart of a three-dimensional data encoding process by the three-dimensional data encoding device according to Embodiment 5. 
     First, the three-dimensional data encoding device encodes geometry information (geometry) (S 3441 ). For example, three-dimensional data encoding is encoding by using an octree representation. 
     When a position of a three-dimensional point is changed by quantization or the like after encoding of geometry information, the three-dimensional data encoding device reassigns an attribute information item of an original three-dimensional point to the three-dimensional point after change (S 3442 ). For example, the three-dimensional data encoding device performs reassignment by interpolating a value of the attribute information item in accordance with a change amount of the position. For example, the three-dimensional data encoding device detects N three-dimensional points before change close to the three-dimensional position after change, and performs weighted averaging of values of attribute information items of the N three-dimensional points. For example, the three-dimensional data encoding device determines, in the weighted averaging, a weight based on a distance from the three-dimensional position after change to each of the N three-dimensional points. Then, the three-dimensional data encoding device sets the value obtained by the weighted averaging to a value of an attribute information item of the three-dimensional point after change. When two or more three-dimensional points are changed to the same three-dimensional position by quantization or the like, the three-dimensional data encoding device may assign an average value of attribute information items of two or more three-dimensional points before change as a value of an attribute information item of a three-dimensional point after change. 
     Then, the three-dimensional data encoding device encodes the attribute information item (Attribute) after reassignment (S 3443 ). For example, when encoding multiple types of attribute information items, the three-dimensional data encoding device may sequentially encode the multiple types of attribute information items. For example, when encoding a color and a reflectance as attribute information items, the three-dimensional data encoding device may generate a bitstream appended with a color encoding result followed by a reflectance encoding result. The plurality of encoding results of the attribute information items may be appended to the bitstream in any order, not limited to this. 
     The three-dimensional data encoding device may append information indicating an encoded data start location of each attribute information item in the bitstream to the header and the like. Thus, the three-dimensional data decoding device can selectively decode an attribute information item that requires decoding, thereby omitting a decoding process of an attribute information item that does not require decoding. This can reduce a processing amount of the three-dimensional data decoding device. The three-dimensional data encoding device may concurrently encode multiple types of attribute information items, and combine encoding results into one bitstream. Thus, the three-dimensional data encoding device can quickly encode the multiple types of attribute information items. 
       FIG. 92  is a flowchart of an attribute information item encoding process (S 3443 ) according to Embodiment 5. First, the three-dimensional data encoding device sets LoD (S 3451 ). Specifically, the three-dimensional data encoding device assigns each three-dimensional point to any of a plurality of LoDs. 
     Then, the three-dimensional data encoding device starts a loop for each LoD (S 3452 ). Specifically, the three-dimensional data encoding device repeats processes in steps S 3453  to S 3461  for each LoD. 
     Then, the three-dimensional data encoding device starts a loop for each three-dimensional point (S 3453 ). Specifically, the three-dimensional data encoding device repeats processes in steps S 3454  to S 3460  for each three-dimensional point. 
     First, the three-dimensional data encoding device searches a plurality of surrounding points that are three-dimensional points in the vicinity of a target three-dimensional point to be processed and used for calculating a predicted value of the target three-dimensional point (S 3454 ). 
     Then, the three-dimensional data encoding device calculates predicted value P of the target three-dimensional point (S 3455 ). A specific example of a calculation process of predicted value P will be described later with reference to  FIG. 93 . 
     Then, the three-dimensional data encoding device calculates, as a prediction residual, a difference between an attribute information item of the target three-dimensional point and the predicted value (S 3456 ). 
     Then, the three-dimensional data encoding device quantizes the prediction residual to calculate a quantized value (S 3457 ). 
     Then, the three-dimensional data encoding device arithmetic-encodes the quantized value (S 3458 ). 
     The three-dimensional data encoding device inverse quantizes the quantized value to calculate an inverse quantized value (S 3459 ). 
     Then, the three-dimensional data encoding device adds the predicted value to the inverse quantized value to generate a decoded value (S 3460 ). 
     Then, the three-dimensional data encoding device finishes the loop for each three-dimensional point (S 3461 ). 
     The three-dimensional data encoding device also finishes the loop for each LoD (S 3462 ). 
       FIG. 93  is a flowchart of a predicted value calculation process (S 3455 ) by the three-dimensional data encoding device according to Embodiment 5. 
     First, the three-dimensional data encoding device calculates a weighted average of attribute values of the N three-dimensional points in the vicinity of the target three-dimensional point to be processed, which can be used for predicting a predicted value of the target three-dimensional point, and assigns the calculated weighted average to a prediction mode indicated by a prediction mode value of “0” (S 3420 ). 
     Then, the three-dimensional data encoding device performs steps S 3421  to S 3426  described with reference to  FIG. 86  to output a predicted value of the target three-dimensional point. 
       FIG. 94  is a flowchart of a prediction mode selection process (S 3424 ) according to Embodiment 5. 
     First, the three-dimensional data encoding device assigns attribute information items of the N three-dimensional points in the vicinity of the target three-dimensional point to prediction mode values of “1” to “N” in one increment sequentially from a three-dimensional point closer to the target three-dimensional point (S 3427 ). The prediction mode values of “0” to “N” are assigned, and thus a total of N+1 prediction modes are generated. When N+1 is larger than maximum number M of prediction modes (NumPredMode) appended to the bitstream, the three-dimensional data encoding device may generate up to M prediction modes. 
     Then, the three-dimensional data encoding device calculates cost of each prediction mode, and selects a prediction mode with minimum cost (S 3428 ). 
       FIG. 95  is a flowchart of a prediction mode selection process (S 3428 ) that minimizes cost according to Embodiment 5. 
     First, the three-dimensional data encoding device sets i=0 and mincost=∞ as initial values (S 3471 ). The set initial values of i and mincost are stored in a memory of the three-dimensional data encoding device. 
     Then, the three-dimensional data encoding device calculates cost cost[i] of i-th prediction mode PredMode[i] using, for example, Equation D1 (S 3472 ). 
     Then, the three-dimensional data encoding device determines whether or not calculated cost cost[i] is smaller than mincost stored in the memory (S 3473 ). 
     Then, when calculated cost cost[i] is smaller than mincost stored in the memory (Yes in S 3473 ), the three-dimensional data encoding device sets mincost=cost[i], sets the prediction mode to predmode[i] (S 3474 ), and goes to step S 3475 . Specifically, the value of mincost stored in the memory is updated to the value of cost[i], and predmode[i] is stored as a prediction mode in the memory. 
     When, calculated cost cost[i] is equal to or greater than mincost stored in the memory (No in S 3473 ), the three-dimensional data encoding device goes to step S 3475 . 
     Then, the three-dimensional data encoding device increments the value of i by one (S 3475 ). 
     Then, the three-dimensional data encoding device determines whether or not i is smaller than the number of prediction modes (S 3476 ). 
     When i is smaller than the number of prediction modes (Yes in S 3476 ), the three-dimensional data encoding device returns to step S 3472 , and when not (No in S 3476 ), the three-dimensional data encoding device finishes the process of selecting the prediction mode that minimizes cost. 
     Now, a flow of a process of the three-dimensional data decoding device will be described.  FIG. 96  is a flowchart of a three-dimensional data decoding process by the three-dimensional data decoding device according to Embodiment 5. First, the three-dimensional data decoding device decodes the geometry information (geometry) from the bitstream (S 3444 ). For example, the three-dimensional data decoding device performs decoding by using an octree representation. 
     Then, the three-dimensional data decoding device decodes an attribute information item (Attribute) from the bitstream (S 3445 ). For example, when decoding multiple types of attribute information items, the three-dimensional data decoding device may sequentially decode the multiple types of attribute information items. For example, when decoding a color and a reflectance as attribute information items, the three-dimensional data decoding device decodes a color encoding result and a reflectance encoding result in the order of appending to the bitstream. For example, when the bitstream is appended with the color encoding result followed by the reflectance encoding result, the three-dimensional data decoding device decodes the color encoding result and then decodes the reflectance encoding result. The three-dimensional data decoding device may decode encoding results of the attribute information items appended to the bitstream in any order. 
     The three-dimensional data decoding device may obtain information indicating an encoded data start location of each attribute information item in the bitstream by decoding the header and the like. Thus, the three-dimensional data decoding device can selectively decode an attribute information item that requires decoding, thereby omitting a decoding process of an attribute information item that does not require decoding. This can reduce a processing amount of the three-dimensional data decoding device. The three-dimensional data decoding device may concurrently decode multiple types of attribute information items, and combine decoding results into one three-dimensional point cloud. Thus, the three-dimensional data decoding device can quickly decode the multiple types of attribute information items. 
       FIG. 97  is a flowchart of an attribute information item decoding process (S 3445 ) according to Embodiment 5. First, the three-dimensional data decoding device sets LoD (S 3481 ). Specifically, the three-dimensional data decoding device assigns each of a plurality of three-dimensional points having decoded geometry information to any of a plurality of LoDs. For example, this assignment method is the same as that used by the three-dimensional data encoding device. 
     Then, the three-dimensional data decoding device starts a loop for each LoD (S 3482 ). Specifically, the three-dimensional data decoding device repeats processes in steps S 3483  to S 3489  for each LoD. 
     Then, the three-dimensional data decoding device starts a loop for each three-dimensional point (S 3483 ). Specifically, the three-dimensional data decoding device repeats processes in steps S 3484  to S 3488  for each three-dimensional point. 
     First, the three-dimensional data decoding device searches a plurality of surrounding points that are three-dimensional points in the vicinity of a target three-dimensional point to be processed and used for calculating a predicted value of the target three-dimensional point (S 3484 ). This process is the same as that by the three-dimensional data encoding device. 
     Then, the three-dimensional data decoding device calculates predicted value P of the target three-dimensional point (S 3485 ). 
     Then, the three-dimensional data decoding device arithmetic-decodes a quantized value from the bitstream (S 3486 ). 
     The three-dimensional data decoding device also inverse quantizes the decoded quantized value to calculate an inverse quantized value (S 3487 ). 
     Then, the three-dimensional data decoding device adds the predicted value to the inverse quantized value to generate a decoded value (S 3488 ). 
     Then, the three-dimensional data decoding device finishes the loop for each three-dimensional point (S 3489 ). 
     The three-dimensional data decoding device also finishes the loop for each LoD (S 3490 ). 
       FIG. 98  is a flowchart of a predicted value calculation process (S 3485 ) by the three-dimensional data decoding device according to Embodiment 5. 
     First, the three-dimensional data decoding device calculates a weighted average of attribute values of the N three-dimensional points in the vicinity of the target three-dimensional point to be processed, which can be used for predicting a predicted value of the target three-dimensional point, and assigns the calculated weighted average to a prediction mode indicated by a prediction mode value of “0” (S 3430 ). 
     Then, the three-dimensional data decoding device performs steps S 3431  to S 3435  described with reference to  FIG. 87  to output a predicted value of the target three-dimensional point. 
     Instead of performing step S 3430 , after it is determined Yes in step S 3432  or when the prediction mode value decoded in step S 3434  is “0”, the weighted average of the attribute values of the N three-dimensional points in the vicinity of the target three-dimensional point to be processed, which can be used for predicting a predicted value of the target three-dimensional point, may be calculated as a predicted value. This eliminates the need to calculate the average value in prediction modes other than the prediction mode indicated by the prediction mode value of “0”, thereby reducing a processing amount. 
       FIG. 99  is a flowchart of a prediction mode decoding process (S 3434 ) according to Embodiment 5. 
     First, the three-dimensional data decoding device assigns attribute information items of the N three-dimensional points in the vicinity of the target three-dimensional point to prediction mode values of “1” to “N” in one increment sequentially from a three-dimensional point closer to the target three-dimensional point (S 3491 ). The prediction mode values of “0” to “N” are assigned, and thus a total of N+1 prediction modes are generated. When N+1 is larger than maximum number M of prediction modes (NumPredMode) appended to the bitstream, the three-dimensional data decoding device may generate up to M prediction modes. 
     Then, the three-dimensional data decoding device arithmetic-decodes the prediction mode by using the number of prediction modes (S 3492 ). Specifically, the three-dimensional data decoding device may perform steps S 3403  and S 3404  described with reference to  FIG. 81  to arithmetic-decode the prediction mode. The three-dimensional data decoding device may also perform steps S 3414  to S 3416  described with reference to  FIG. 85  to arithmetic-decode the prediction mode. 
       FIG. 100  is a block diagram showing a configuration of attribute information encoder  3100  included in the three-dimensional data encoding device according to Embodiment 5.  FIG. 100  shows an attribute information encoder in detail among a geometry information encoder, an attribute information item reassigner, and the attribute information encoder included in the three-dimensional data encoding device. 
     Attribute information encoder  3400  includes LoD generator  3401 , surrounding searcher  3402 , predictor  3403 , prediction residual calculator  3404 , quantizer  3405 , arithmetic encoder  3406 , inverse quantizer  3407 , decoded value generator  3408 , and memory  3409 . 
     LoD generator  3401  generates LoD by using geometry information (geometry) of a three-dimensional point. 
     Surrounding searcher  3402  searches a neighboring three-dimensional point adjacent to each three-dimensional point by using an LoD generation result by LoD generator  3401  and distance information indicating a distance between three-dimensional points. 
     Predictor  3403  generates a predicted value of an attribute information item of a target three-dimensional point to be encoded. Specifically, predictor  3403  assigns predicted values to prediction modes indicated by prediction mode values of “0” to “M−1”, and selects a prediction mode. Predictor  3403  outputs the selected prediction mode, specifically, the prediction mode value indicating the prediction mode to the arithmetic encoder. Predictor  3403  performs, for example, the process in step S 3455 . 
     Prediction residual calculator  3404  calculates (generates) a prediction residual of the predicted value of the attribute information item generated by predictor  3403 . Prediction residual calculator  3404  performs the process in step S 3456 . 
     Quantizer  3405  quantizes the prediction residual of the attribute information item calculated by prediction residual calculator  3404 . 
     Arithmetic encoder  3106  arithmetic-encodes the prediction residual quantized by quantizer  3105 . Arithmetic encoder  3406  outputs a bitstream including the arithmetic-encoded prediction residual, for example, to the three-dimensional data decoding device. 
     The prediction residual may be binarized, for example, by quantizer  3405  before arithmetic-encoded by arithmetic encoder  3406 . Arithmetic encoder  3406  may generate and encode various header information items (header information). Arithmetic encoder  3406  may also obtain a prediction mode used for encoding from Prediction block, and arithmetic-encode and append the prediction mode to the bitstream. 
     Inverse quantizer  3407  inverse quantizes the prediction residual quantized by quantizer  3405 . Inverse quantizer  3407  performs the process in step S 3459 . 
     Decoded value generator  3408  adds the predicted value of the attribute information item generated by predictor  3403  to the prediction residual inverse quantized by inverse quantizer  3407  to generate a decoded value. 
     Memory  3409  stores a decoded value of an attribute information item of each three-dimensional point decoded by decoded value generator  3408 . For example, when generating a predicted value of a three-dimensional point having been not yet encoded, predictor  3403  generates a predicted value by using the decoded value of the attribute information item of each three-dimensional point stored in memory  3409 . 
       FIG. 101  is a block diagram of a configuration of attribute information decoder  3410  included in the three-dimensional data decoding device according to Embodiment 5.  FIG. 101  shows an attribute information decoder in detail among a geometry information decoder and the attribute information decoder included in the three-dimensional data decoding device. 
     Attribute information decoder  3410  includes LoD generator  3411 , surrounding searcher  3412 , predictor  3413 , arithmetic decoder  3414 , inverse quantizer  3415 , decoded value generator  3416 , and memory  3417 . 
     LoD generator  3411  generates LoD by using geometry information (geometry information) of a three-dimensional point decoded by a geometry information decoder (not shown). 
     Surrounding searcher  3412  searches a neighboring three-dimensional point adjacent to each three-dimensional point by using an LoD generation result by LoD generator  3411  and distance information indicating a distance between three-dimensional points. 
     Predictor  3413  generates a predicted value of an attribute information item of a target three-dimensional point to be decoded. Predictor  3413  performs, for example, the process in step S 3485 . 
     Arithmetic decoder  3414  arithmetic-decodes the prediction residual in the bitstream obtained by attribute information encoder  3400 . Arithmetic decoder  3414  may decode various header information items. Arithmetic decoder  3414  may also output an arithmetic-decoded prediction mode to predictor  3413 . In this case, predictor  3413  may calculate a predicted value by using the prediction mode obtained by arithmetic decoding by arithmetic decoder  3414 . 
     Inverse quantizer  3415  inverse quantizes the prediction residual arithmetic-decoded by arithmetic decoder  3414 . 
     Decoded value generator  3416  adds the predicted value generated by predictor  3413  and the prediction residual inverse quantized by inverse quantizer  3415  to generate a decoded value. Decoded value generator  3416  outputs decoded attribute information data to any other device. 
     Memory  3417  stores a decoded value of an attribute information item of each three-dimensional point decoded by decoded value generator  3416 . For example, when generating a predicted value of a three-dimensional point having been not yet decoded, predictor  3413  generates a predicted value by using the decoded value of the attribute information item of each three-dimensional point stored in memory  3417 ; 
     Embodiment 6 
     As described above, the three-dimensional data encoding device calculates a maximum absolute differential value of attribute values of N three-dimensional points (surrounding three-dimensional points) in the vicinity of a target three-dimensional point to be encoded, which can be used for prediction by the three-dimensional data encoding device and the three-dimensional data decoding device (that is, a maximum absolute value of a difference between attribute values of any two three-dimensional points among the N three-dimensional points). The three-dimensional data encoding device also switches between fixing a prediction mode in accordance with the calculated maximum absolute differential value, that is, using an arbitrarily predetermined prediction mode, and selecting and appending a prediction mode to the bitstream. 
     However, the three-dimensional data encoding device needs not switch between fixing a prediction mode in accordance with the maximum absolute differential value, and selecting and appending a prediction mode to the bitstream. For example, the three-dimensional data encoding device may select whether to fix the prediction mode under the condition described above or select the prediction mode, and append the result as a prediction mode fixing flag to the bitstream. 
     Thus, the three-dimensional data decoding device can decode the prediction mode fixing flag appended to the bitstream to determine whether the three-dimensional data encoding device has fixed the prediction mode or has selected and encoded the prediction mode. 
     When the three-dimensional data encoding device has fixed the prediction mode, the three-dimensional data decoding device can determine that the prediction mode is not encoded in the bitstream. When the three-dimensional data encoding device has selected the prediction mode, the three-dimensional data decoding device can determine that the prediction mode in the bitstream requires decoding. Thus, the three-dimensional data decoding device can correctly decode the encoded prediction mode included in the bitstream. 
     Also, the three-dimensional data decoding device can arithmetic-decode the prediction mode without calculating a maximum absolute differential value of attribute values of N three-dimensional points in the vicinity of a target three-dimensional point to be encoded, which can be used for prediction. Thus, the three-dimensional data decoding device can concurrently perform arithmetic-decoding of the bitstream and LoD generation and the like. As a result, the three-dimensional data decoding device can increase throughput of the entire process. 
     The three-dimensional data encoding device may append a prediction mode fixing flag for each three-dimensional point. 
     Thus, the three-dimensional data decoding device can switch between fixing the prediction mode and selecting the prediction mode for each three-dimensional point in accordance with the prediction mode fixing flag. Thus, the three-dimensional data encoding device can improve an encoding efficiency. 
     The three-dimensional data encoding device may set a prediction mode fixing flag for each LoD. For example, the three-dimensional data encoding device sets the prediction mode fixing flag to 0 to select a prediction mode for an upper level, among LoDs, at which prediction is difficult, and sets the prediction mode fixing flag to 1 to fix the prediction mode for a lower level at which prediction is easy. Thus, the three-dimensional data encoding device can reduce an encoding amount for appending the prediction mode. 
       FIG. 102  is a flowchart of a prediction mode determination process performed by the three-dimensional data encoding device according to this embodiment. 
     First, the three-dimensional data encoding device calculates maximum absolute differential value maxdiff of attribute values of N three-dimensional points in the vicinity of a target three-dimensional point to be encoded (S 3501 ). 
       FIG. 103  is a diagram showing an example of a syntax of the prediction mode determination process performed by the three-dimensional data encoding device according to this embodiment. Specifically,  FIG. 103  shows an example of a syntax in step S 3501  shown in  FIG. 102 . 
     In  FIG. 103 , the attribute values of the N three-dimensional points in the vicinity of the target three-dimensional point to be encoded are denoted by a[0] to a[N−1], and the maximum absolute differential value is denoted by maxdiff. The attribute values of the N three-dimensional points in the vicinity of the target three-dimensional point to be encoded are attribute values encoded by the three-dimensional data encoding device and decoded by the three-dimensional data decoding device. 
     The three-dimensional data encoding device calculates maximum absolute differential value maxdiff, for example, by the example of the syntax shown in  FIG. 103 . 
     The N three-dimensional points in the vicinity of the target three-dimensional point to be encoded, which are used for prediction by the three-dimensional data encoding device, are N encoded and decoded three-dimensional points with a distance from the target three-dimensional point to be encoded shorter than threshold THd. 
     Here, as described above, the three-dimensional data encoding device may append a maximum value of N as NumNeighborPoint to the bitstream. The value of N needs not match NumNeighborPoint as in the case where the number of encoded and decoded three-dimensional points in attribute information items (pieces of attribute information) of the three-dimensional points in the vicinity of the target three-dimensional point to be encoded is smaller than NumNeighborPoint. 
     Again with reference to  FIG. 102 , the three-dimensional data encoding device then determines whether or not maxdiff&lt;Thfix is satisfied (S 3502 ). Thfix is an arbitrarily predetermined constant. 
     When determining that maxdiff&lt;Thfix is satisfied (Yes in S 3502 ), the three-dimensional data encoding device performs arithmetic-encoding with a prediction mode fixing flag (fixedPredMode) being 1 (S 3503 ). 
     Then, the three-dimensional data encoding device sets a prediction mode value (PredMode/hereinafter also simply referred to as a prediction mode) to 0 (S 3504 ). 
     When determining that maxdiff&lt;Thfix is not satisfied (No in S 3502 ), the three-dimensional data encoding device performs arithmetic-encoding with the prediction mode fixing flag being 0 (S 3505 ). 
     Then, the three-dimensional data encoding device selects a prediction mode (S 3506 ). 
     Then, the three-dimensional data encoding device arithmetic-encodes the selected prediction mode (S 3507 ). 
     The example has been given above in which the three-dimensional data encoding device fixes the prediction mode at 0 if the maximum absolute differential value of the attribute values of the three-dimensional points in the vicinity of the target three-dimensional point to be encoded, which are used for prediction, is smaller than Thfix[i], but not limited to this. For example, the three-dimensional data encoding device may fix the prediction mode at any of 0 to M−1. 
     The three-dimensional data encoding device may append a value of a fixed prediction mode (also referred to as PredMode or mode number) to the bitstream. 
       FIG. 104  is a flowchart of a prediction mode determination process performed by the three-dimensional data decoding device according to this embodiment. 
     First, the three-dimensional data decoding device arithmetic-decodes an encoded prediction mode fixing flag included in the bitstream (S 3511 ). 
     Then, the three-dimensional data decoding device determines whether or not the prediction mode fixing flag==1 is satisfied (S 3512 ). 
     When determining that the prediction mode fixing flag==1 is satisfied (Yes in S 3512 ), the three-dimensional data decoding device sets the prediction mode value to 0 (S 3513 ). 
     When determining that the prediction mode fixing flag==1 is not satisfied (No in S 3512 ), the three-dimensional data decoding device decodes the prediction mode value from the bitstream and determines the prediction mode value (S 3514 ). 
     The three-dimensional data decoding device determines a predicted value in accordance with the determined prediction mode. 
     The prediction mode fixing flag may be provided in any position. 
       FIG. 105  is a diagram showing an example of a syntax of attribute data when a prediction mode fixing flag is provided for each three-dimensional point. 
     fixedPredMode is a flag indicating if the three-dimensional data encoding device fixes a prediction mode. For example, when a value of fixedPredMode is 1, the three-dimensional data encoding device may fix a prediction mode, and when the value of fixedPredMode is 0, the three-dimensional data encoding device may select a prediction mode. 
     fixedPredMode may be also set for each LoD as in  FIG. 106 . 
       FIG. 106  is a diagram showing an example of a syntax of attribute data when a prediction mode fixing flag is provided for each LoD. 
     fixedPredMode[i] is a flag indicating if a prediction mode of level i of LoD is fixed. 
     PredMode is a value indicating a prediction mode for encoding and decoding an attribute value of a j-th three-dimensional point at level i. PredMode takes any of 0 to M−1 (M is a total number of prediction modes). When PredMode is not in the bitstream (specifically, when !fixedPredMode&amp;&amp;NumPredMode[i]&gt;1 is not satisfied), the three-dimensional data decoding device may estimate PredMode as 0. 
     When PredMode is not in the bitstream, the three-dimensional data decoding device needs not set PredMode to 0, and may use any of 0 to M−1 as an estimated value. 
     The three-dimensional data encoding device may separately append, to a header and the like, the estimated value when PredMode is not in the bitstream. 
     As described above, the three-dimensional data encoding device may binarize PredMode by truncated unary coding using total number M of prediction modes, and arithmetic-encode the binarized value. 
     The truncated unary coding is one method of binarization. By using the truncated unary coding, for a multivalued signal taking a value other than a maximum value, a signal is generated including the same number of is as indicated by the multivalued signal, with 0 at the end. For a multivalued signal taking a maximum value, the maximum value is previously set, and a signal is generated including the same number of is as indicated by the multivalued signal (without 0 at the end). For example, as described above, when the number of prediction modes is 5, and the three-dimensional data encoding device binarizes each of the prediction modes by using the truncated unary coding, prediction modes 0 to 4 are sequentially represented by 0, 10, 110, 1110, 1111. As such, the three-dimensional data encoding device binarizes the prediction mode by the truncated unary coding using the number of prediction modes (that is, in accordance with the number of prediction modes). 
     By using the truncated unary coding, for a multivalued signal taking a value other than the maximum value, a signal may be generated including the same number of 0s as indicated by the multivalued signal, with 1 at the end. Specifically, 0(s) and 1(s) described above may be inverted. 
     The three-dimensional data encoding device may arithmetic-encode, as NumPredMode, the value of total number M of prediction modes, and append NumPredMode to the header. 
     NumPredMode is a value indicating the total number of prediction modes. 
     Thus, the three-dimensional data decoding device can decode NumPredMode in the header to calculate total number M of prediction modes, and decode PredMode in accordance with total number M of prediction modes. Thus, the three-dimensional data decoding device can set (generate) LoD, calculate three-dimensional points in the vicinity of a target three-dimensional point to be decoded, which can be used for prediction, and perform arithmetic-decoding of the bitstream without waiting for calculation of the number of prediction modes assigned with predicted values. As a result, the three-dimensional data decoding device can concurrently perform arithmetic-decoding of the bitstream and LoD generation and the like, thereby increasing throughput of the entire process. 
     An n-bit code is encoded data of a prediction residual of a value of an attribute information item (attribute information). A bit length of the n-bit code depends on a value of R_TH[i]. For example, the bit length is 6 bits when the value of R_TH[i] is 63, and 8 bits when the value of R_TH[i] is 255. Any value of R_TH may be previously set. 
     A remaining code is encoded data encoded by an Exponential-Golomb code among encoded data of the prediction residual of the value of the attribute information item. The three-dimensional data decoding device decodes the remaining code when the n-bit code is equal to R_TH[i], and adds the value of the n-bit code to the value of the remaining code to decode the prediction residual. 
     When the n-bit code is not equal to R_TH[i], the three-dimensional data decoding device needs not decode the remaining code. 
       FIG. 107  is a flowchart of an example of a prediction mode encoding process by the three-dimensional data encoding device. 
     First, the three-dimensional data encoding device binarizes the prediction mode by the truncated unary coding using total number M of prediction modes (S 3521 ). 
     Then, the three-dimensional data encoding device arithmetic-encodes binary data of the truncated unary coding (S 3522 ). 
     Then, the three-dimensional data encoding device appends total number M of prediction modes as NumPredMode to the header and encodes NumPredMode (S 3523 ). 
     The three-dimensional data encoding device transmits a bitstream including, for example, encoded NumPredMode to the three-dimensional data decoding device. 
       FIG. 108  is a flowchart of an example of a prediction mode decoding process by the three-dimensional data decoding device. 
     First, the three-dimensional data decoding device decodes encoded NumPredMode included in the bitstream to set total number M of prediction modes (S 3524 ). 
     Then, the three-dimensional data decoding device arithmetic-decodes encoded PredMode in accordance with decoded total number M of prediction modes, and generates binary data of the truncated unary coding (S 3525 ). 
     Then, the three-dimensional data decoding device calculates a prediction mode from the binary data of the truncated unary coding (S 3526 ). 
     The three-dimensional data encoding device may arithmetic-encode fixedPredMode descried above with reference to an encoding table. The three-dimensional data encoding device may update the probability of appearance of 0 and 1 in the encoding table in accordance with a value of actually generated fixedPredMode. The three-dimensional data encoding device may fix the probability of appearance of 0 and 1 in either of encoding tables. Thus, the three-dimensional data encoding device can reduce an update frequency of the probability of appearance of 0 and 1 in the encoding table to reduce a processing amount. 
       FIG. 109  is a flowchart of a three-dimensional data encoding process by the three-dimensional data encoding device according to this embodiment. 
     First, the three-dimensional data encoding device encodes geometry information (geometry) (S 3531 ). For example, the three-dimensional data encoding device may perform encoding by using an octree representation. 
     Then, when a position of a three-dimensional point is changed by quantization or the like after encoding of the geometry information, the three-dimensional data encoding device reassigns an attribute information item of an original three-dimensional point to the three-dimensional point after change (S 3532 ). 
     The three-dimensional data encoding device may perform reassignment by interpolating a value of the attribute information item in accordance with a change amount of the position. For example, the three-dimensional data encoding device may detect N three-dimensional points before change in the vicinity of a target three-dimensional point to be encoded, which are close to the three-dimensional position after change. Then, the three-dimensional data encoding device may perform weighted averaging of values of attribute information items of the detected N three-dimensional points in accordance with a distance from the target three-dimensional position to be encoded after change to each of the N three-dimensional points, and set the weighted average value as a value of an attribute information item of the three-dimensional point after change. When two or more three-dimensional points are changed to the same three-dimensional position by quantization or the like, the three-dimensional data encoding device may assign an average value of attribute information items of two or more three-dimensional points before change as a value of an attribute information item of a three-dimensional point after change. 
     Then, the three-dimensional data encoding device encodes the attribute information item (Attribute) after reassignment (S 3533 ). For example, the three-dimensional data encoding device may sequentially encode a plurality of attribute information items. 
     Also, for example, when encoding a color and a reflectance as attribute information items, the three-dimensional data encoding device may generate a bitstream appended with a color encoding result followed by a reflectance encoding result. 
     The three-dimensional data encoding device may append the encoding results of the attribute information items to the bitstream in any order. The three-dimensional data encoding device may append, to the header and the like, an encoded data start location of each attribute information item in the bitstream. 
     Thus, the three-dimensional data decoding device can decode an attribute information item that requires decoding. As a result, the three-dimensional data decoding device can omit a decoding process of an attribute information item that does not require decoding, thereby reducing a processing amount. 
     The three-dimensional data encoding device may concurrently encode a plurality of attribute information items, and combine encoding results into one bitstream. 
     Thus, the three-dimensional data encoding device can quickly encode the plurality of attribute information items. 
       FIG. 110  is a flowchart of an attribute information item encoding process (S 3533 ) shown in  FIG. 109 . 
     First, the three-dimensional data encoding device sets LoD (S 35331 ). Specifically, the three-dimensional data encoding device assigns each three-dimensional point to any of a plurality of LoDs. 
     Then, the three-dimensional data encoding device starts a loop for each LoD (S 35332 ). Specifically, the three-dimensional data encoding device repeats processes in steps S 35333  to S 35341  for each LoD. 
     Then, the three-dimensional data encoding device starts a loop for each three-dimensional point (S 35333 ). Specifically, the three-dimensional data encoding device repeats processes in steps S 35334  to S 35340  for each three-dimensional point at a certain LoD.  FIG. 110  shows encoding of target three-dimensional point P to be encoded. 
     Then, the three-dimensional data encoding device searches a plurality of surrounding points that are three-dimensional points in the vicinity of target three-dimensional point P to be processed and used for calculating a predicted value of target three-dimensional point P (S 35334 ). 
     Then, the three-dimensional data encoding device calculates a predicted value of target three-dimensional point P (S 35335 ). 
     Then, the three-dimensional data encoding device calculates, as a prediction residual, a difference between an attribute information item of target three-dimensional point P and the predicted value (S 35336 ). 
     Then, the three-dimensional data encoding device quantizes the prediction residual to calculate a quantized value (S 35337 ). 
     Then, the three-dimensional data encoding device arithmetic-encodes the quantized value (S 35338 ). 
     Then, the three-dimensional data encoding device inverse quantizes the quantized value to calculate an inverse quantized value (S 35339 ). 
     Then, the three-dimensional data encoding device adds the predicted value to the inverse quantized value to generate a decoded value (S 35340 ). 
     Then, the three-dimensional data encoding device finishes the loop for each three-dimensional point (S 35341 ). 
     The three-dimensional data encoding device also finishes the loop for each LoD (S 35342 ). 
       FIG. 111  is a flowchart of a predicted-value calculation process (S 35335 ) shown in  FIG. 110 . 
     First, the three-dimensional data encoding device calculates a weighted average value of attribute values of the N three-dimensional points in the vicinity of the target three-dimensional point to be encoded, which can be used for prediction, and assigns the calculated weighted average value to prediction mode 0 (S 353351 ). 
     Then, the three-dimensional data encoding device calculates maximum absolute differential value maxdiff of the attribute values of the N three-dimensional points in the vicinity of the target three-dimensional point to be encoded (S 353352 ). 
     Then, the three-dimensional data encoding device determines whether or not maximum absolute differential value maxdiff&lt;Thfix is satisfied (S 353353 ). 
     When determining that maximum absolute differential value maxdiff&lt;Thfix is satisfied (Yes in S 353353 ), the three-dimensional data encoding device performs arithmetic-encoding with a prediction mode fixing flag being 1 (S 353354 ). 
     Then, the three-dimensional data encoding device sets the prediction mode to 0 (prediction mode for indicating the weighted average value as a predicted value) (S 353355 ). 
     Then, the three-dimensional data encoding device arithmetic-encodes the predicted value of the set prediction mode, and outputs the predicted value to, for example, the three-dimensional data decoding device (S 353356 ). 
     When determining that maximum absolute differential value maxdiff&lt;Thfix is not satisfied (No in S 353353 ), the three-dimensional data encoding device performs arithmetic-encoding with the prediction mode fixing flag being 0 (S 353357 ). 
     Then, the three-dimensional data encoding device selects and determines a prediction mode (S 353358 ). 
     Then, the three-dimensional data encoding device arithmetic-encodes the selected and determined prediction mode (S 353359 ). 
     As described above, the three-dimensional data encoding device may binarize prediction mode PredMode by truncated unary coding using total number M of prediction modes and arithmetic-encode PredMode. The three-dimensional data encoding device may encode total number M of prediction modes as NumPredMode and append NumPredMode to the header. 
     Thus, the three-dimensional data decoding device can decode NumPredMode in the header, thereby correctly decoding prediction mode PredMode. 
     When NumPredMode is 1, the three-dimensional data encoding device needs not encode PredMode. Thus, the three-dimensional data encoding device can reduce an encoding amount when NumPredMode is 1. 
       FIG. 112  is a flowchart of a prediction mode selection process (S 353358 ) shown in  FIG. 111 . 
     First, the three-dimensional data encoding device assigns attribute information items of the N three-dimensional points in the vicinity of the target three-dimensional point to be encoded to prediction modes 1 to N sequentially from a three-dimensional point closer to the target three-dimensional point (S 3541 ). For example, the three-dimensional data encoding device generates N+1 prediction modes. When N+1 is larger than total number M of prediction modes (NumPredMode) appended to the bitstream, the three-dimensional data encoding device may generate up to M prediction modes. 
     Then, the three-dimensional data encoding device calculates cost of each prediction mode, and selects a prediction mode with minimum cost (S 3542 ). 
       FIG. 113  is a flowchart of a specific example of the prediction mode selection process (S 3542 ) shown in  FIG. 112 . 
     First, the three-dimensional data encoding device sets i=0 and mincost=∞ (S 35421 ). 
     Then, the three-dimensional data encoding device calculates cost (cost[i]) of i-th prediction mode PredMode[i] (S 35422 ). 
     Then, the three-dimensional data encoding device determines whether or not cost[i]&lt;mincost is satisfied (S 35423 ). 
     Then, when determining that cost[i]&lt;mincost is satisfied (Yes in S 35423 ), the three-dimensional data encoding device sets mincost=cost[i], and sets the prediction mode to PredMode[i] (S 35424 ). 
     Following step S 35424  or when determining that cost[i]&lt;mincost is not satisfied (No in S 35423 ), the three-dimensional data encoding device sets i=i+1 (S 35425 ). 
     Then, the three-dimensional data encoding device determines whether or not i&lt;the number of prediction modes (total number of prediction modes) is satisfied (S 35426 ). 
     When determining that i&lt;the number of prediction modes is not satisfied (No in S 35426 ), the three-dimensional data encoding device finishes the selection process. When determining that i&lt;the number of prediction modes is satisfied (Yes in S 35426 ), the three-dimensional data encoding device returns the process to step S 35422 . 
       FIG. 114  is a flowchart of a three-dimensional data decoding process by the three-dimensional data decoding device according to this embodiment. 
     The three-dimensional data decoding device decodes geometry information (geometry) of an encoded three-dimensional point (S 3551 ). For example, the three-dimensional data decoding device may decode the geometry information by using an octree representation. 
     Then, the three-dimensional data decoding device decodes an attribute information item of the encoded three-dimensional point (S 3552 ). 
     The three-dimensional data decoding device may sequentially decode a plurality of attribute information items. For example, when decoding a color and a reflectance as attribute information items, the three-dimensional data decoding device may decode a bitstream appended with a color encoding result followed by a reflectance encoding result in this order. 
     The three-dimensional data decoding device may decode the encoding results of the attribute information items appended to the bitstream in any order. 
     The three-dimensional data decoding device may obtain an encoded data start location of each attribute information item in the bitstream by decoding the header and the like. 
     Thus, the three-dimensional data decoding device can decode an attribute information item that requires decoding. As a result, the three-dimensional data decoding device can omit a decoding process of an attribute information item that does not require decoding, thereby reducing a processing amount. 
     The three-dimensional data decoding device may concurrently decode a plurality of attribute information items, and combine decoding results into one three-dimensional point cloud. 
     Thus, the three-dimensional data decoding device can quickly decode the plurality of attribute information items. 
       FIG. 115  is a flowchart of a calculation process of a predicted value of P (S 3552 ) shown in  FIG. 114 . 
     First, the three-dimensional data decoding device obtains decoded geometry information of a three-dimensional point included in the bitstream (S 35520 ). Specifically, the three-dimensional data decoding device decodes encoded geometry information of a three-dimensional point included in the bitstream transmitted from the three-dimensional data encoding device, and thus obtains the decoded geometry information. 
     Then, the three-dimensional data decoding device sets LoD (S 35521 ). Specifically, the three-dimensional data decoding device assigns each three-dimensional point to any of a plurality of LoDs. 
     Then, the three-dimensional data decoding device starts a loop for each LoD (S 35522 ). Specifically, the three-dimensional data decoding device repeats processes in steps S 35523  to S 35528  for each LoD. 
     The three-dimensional data decoding device obtains an attribute information item included in the bitstream concurrently with, for example, the processes in step S 35520  and thereafter (S 355201 ). 
     The three-dimensional data decoding device decodes PredMode and a quantized value of P (S 355211 ). 
     For example, in steps in the dashed-line encircled portion (more specifically, steps S 35521  and step S 355211 ) in  FIG. 115 , the three-dimensional data decoding device can append the number of three-dimensional points NumOfPoint for each LoD to the header and the like, and thus independently perform a decoding process of PredMode in the bitstream and a process of calculating three-dimensional points in the vicinity of a target three-dimensional point to be decoded, which can be used for prediction after LoD generation. Thus, the three-dimensional data decoding device can independently perform LoD generation and searching of a neighboring point of P, and an arithmetic-decoding process of PredMode, an n-bit code, and a remaining code (decoding of PredMode and quantized value of P). Thus, the three-dimensional data decoding device may concurrently perform the processes. 
     Thus, the three-dimensional data decoding device can reduce time for the entire process. 
     Then, the three-dimensional data decoding device starts a loop for each three-dimensional point (S 35523 ). Specifically, the three-dimensional data decoding device repeats processes in steps S 35524  to S 35527  for each three-dimensional point at a certain LoD.  FIG. 115  shows decoding of target three-dimensional point P to be decoded. 
     Then, the three-dimensional data decoding device searches a plurality of surrounding points that are three-dimensional points in the vicinity of target three-dimensional point P to be processed and used for calculating a predicted value of target three-dimensional point P (S 35524 ). 
     Then, the three-dimensional data decoding device calculates a predicted value of target three-dimensional point P in accordance with PredMode (that is, a prediction mode value) decoded in step S 355211  (S 35525 ). 
     Then, the three-dimensional data decoding device inverse quantizes a quantized value in accordance with a quantized value of P decoded in step S 355211  to calculate an inverse quantized value (S 35526 ). 
     Then, the three-dimensional data decoding device adds the predicted value to the inverse quantized value to generate a decoded value (S 35527 ). 
     Then, the three-dimensional data decoding device finishes the loop for each three-dimensional point (S 35528 ). 
     The three-dimensional data decoding device also finishes the loop for each LoD (S 35529 ). 
       FIG. 116  is a flowchart of details of the calculation process of the predicted value of P (S 35525 ) shown in  FIG. 115 . 
     First, the three-dimensional data decoding device calculates a weighted average value of attribute values of the N three-dimensional points in the vicinity of the target three-dimensional point to be decoded, which can be used for prediction, and assigns the calculated weighted average value to prediction mode 0 (S 355251 ). 
     Then, the three-dimensional data decoding device assigns attribute information items of the N three-dimensional points to prediction modes 1 to N sequentially from a three-dimensional point closer to the target three-dimensional point to be decoded (S 355252 ). 
     Then, the three-dimensional data decoding device outputs the predicted value of the prediction mode decoded in step S 355211  shown in  FIG. 115  (S 355253 ). 
     The three-dimensional data encoding device may calculate a weighted average value of attribute values of the N three-dimensional points in the vicinity of the target three-dimensional point to be encoded after setting the prediction mode to 0, that is, when maxdiff&lt;Thfix is true or the decoded prediction mode is 0. 
     Thus, when the prediction mode is other than 0, the three-dimensional data decoding device needs not calculate a weighted average value. Thus, the three-dimensional data decoding device can reduce a processing amount. 
       FIG. 117  is a flowchart of a calculation process of a prediction mode and a quantized value of P (S 355211 ) shown in  FIG. 116 . 
     First, the three-dimensional data decoding device arithmetic-decodes a prediction mode fixing flag (S 3561 ). 
     Then, the three-dimensional data decoding device determines whether or not the arithmetic-decoded prediction mode fixing flag==1 is satisfied (S 3562 ). 
     Then, when determining that the prediction mode fixing flag==1 is satisfied (Yes in S 3562 ), the three-dimensional data decoding device fixes the prediction mode at 0 (weighted average value) (S 3563 ). 
     When determining that the prediction mode fixing flag==1 is not satisfied (No in S 3562 ), the three-dimensional data decoding device decodes the prediction mode from the bitstream (S 3564 ). 
     As described above, the three-dimensional data decoding device may arithmetic-decode prediction mode PredMode in accordance with total number M of prediction modes obtained by decoding the header of the bitstream. 
     When total number M of prediction modes is 1, the three-dimensional data decoding device may estimate PredMode as 0 without decoding PredMode. 
     Then, the three-dimensional data decoding device determines whether or not a value of an n-bit code==R_TH[LoDN] is satisfied (S 3565 ). 
     When determining that the value of the n-bit code==R_TH[LoDN] is satisfied (Yes in S 3565 ), the three-dimensional data decoding device arithmetic-decodes a remaining code (S 3566 ). 
     Then, the three-dimensional data decoding device calculates a value of the remaining code with reference to a table for an Exponential-Golomb code (S 3567 ). 
     Then, the three-dimensional data decoding device sets (R_TH[LoDN]+value of remaining code) as a prediction residual (S 3568 ). 
     Then, the three-dimensional data decoding device transforms the decoded prediction residual from an unsigned integer value to a signed integer value (S 3569 ). 
     When determining that the value of the n-bit code==R_TH[LoDN] is not satisfied (No in S 3565 ), the three-dimensional data decoding device decodes the prediction mode from the bitstream (S 3570 ), and performs step S 3569 . 
     As described above, the three-dimensional data encoding device calculates a maximum absolute differential value of attribute values of N three-dimensional points in the vicinity of a target three-dimensional point to be encoded, which can be used for prediction by the three-dimensional data encoding device and the three-dimensional data decoding device. The three-dimensional data encoding device also switches between fixing a prediction mode in accordance with the calculated maximum absolute differential value and selecting and appending a prediction mode to the bitstream. 
     However, the three-dimensional data encoding device needs not switch between fixing a prediction mode in accordance with the maximum absolute differential value, and selecting and appending a prediction mode to the bitstream. For example, the three-dimensional data encoding device may always select a prediction mode and append the prediction mode to the bitstream. 
     Thus, the three-dimensional data decoding device can always decode the prediction mode appended to the bitstream, thereby correctly decoding the bitstream. 
     Also, the three-dimensional data decoding device can arithmetic-decode the prediction mode without calculating a maximum absolute differential value of attribute values of N three-dimensional points in the vicinity of a target three-dimensional point to be decoded, which can be used for prediction. Thus, the three-dimensional data decoding device can concurrently perform arithmetic-decoding of the bitstream and LoD generation and the like. As a result, the three-dimensional data decoding device can increase throughput of the entire process. 
     When total number M of prediction modes is 1, the three-dimensional data decoding device can estimate the prediction mode value as 0 without reference to the value. Thus, when total number M of prediction modes is 1, the three-dimensional data encoding device needs not append the prediction mode to the bitstream. 
     Thus, the three-dimensional data encoding device can reduce an encoding amount when total number M of prediction modes is 1. 
       FIG. 118  is a flowchart of a process when the three-dimensional data encoding device does not fix a prediction mode according to this embodiment. 
     First, the three-dimensional data encoding device selects a prediction mode (S 3571 ). 
     Then, the three-dimensional data encoding device arithmetic-encodes the selected prediction mode (S 3572 ). 
       FIG. 119  is a flowchart of a process when the three-dimensional data decoding device does not fix a prediction mode according to this embodiment. 
     The three-dimensional data decoding device decodes the prediction mode from the bitstream (S 3573 ). 
     The three-dimensional data encoding device may always select a prediction mode by any method. For example, Thfix[i]=0 in the example of the syntax may be used. Thus, the three-dimensional data encoding device can always append PredMode to the bitstream because a minimum value of maxdiff is 0. 
     For the three-dimensional data encoding device to always append PredMode to the bitstream, Thfix[i] may be any value as long as maxdiff≥Thfix[i] is true. 
       FIG. 120  is a diagram showing another example of a syntax of attribute data according to this embodiment. 
     PredMode is a value indicating a prediction mode for encoding and decoding an attribute value of a j-th three-dimensional point at level i of LoD. PredMode takes any of 0 to M−1 (M is a total number of prediction modes). 
     When PredMode is not in the bitstream (specifically, NumPredMode[i]&gt;1 is not satisfied), the three-dimensional data decoding device may estimate PredMode as 0. 
     When PredMode is not in the bitstream, the three-dimensional data decoding device needs not set PredMode to 0, and may use any of 0 to M−1 as an estimated value. 
     The three-dimensional data encoding device may separately append, to the header and the like, the estimated value when PredMode is not in the bitstream. 
     As described above, the three-dimensional data encoding device may binarize PredMode by truncated unary coding using total number M of prediction modes, and arithmetic-encode the binarized value. 
     The three-dimensional data encoding device may encode, as NumPredMode, the value of total number M of prediction modes, and append NumPredMode to the header of the bitstream. 
     Thus, the three-dimensional data decoding device can decode NumPredMode in the header to calculate total number M of prediction modes, and decode PredMode in accordance with total number M of prediction modes. As a result, the three-dimensional data decoding device can generate LoD, calculate three-dimensional points in the vicinity of a target three-dimensional point to be decoded, which can be used for prediction, and perform arithmetic-decoding of the bitstream without waiting for calculation of the number of prediction modes assigned with predicted values. 
     Thus, the three-dimensional data decoding device can concurrently perform arithmetic-decoding of the bitstream and LoD generation and the like. As a result, the three-dimensional data decoding device can increase throughput of the entire process. 
     An n-bit code is encoded data of a prediction residual of a value of an attribute information item. A bit length of the n-bit code depends on a value of R_TH[i]. For example, the bit length is 6 bits when the value of R_TH[i] is 63, and 8 bits when the value of R_TH[i] is 255. 
     A remaining code is encoded data encoded by an Exponential-Golomb code among encoded data of the prediction residual of the value of the attribute information item. The three-dimensional data decoding device decodes the remaining code when the n-bit code is equal to R_TH[i], and adds the value of the n-bit code to the value of the remaining code to decode the prediction residual. 
     When the n-bit code is not equal to R_TH[i], the three-dimensional data decoding device needs not decode the remaining code. 
       FIG. 121  is a flowchart of an example of a prediction mode encoding process by the three-dimensional data encoding device according to this embodiment. 
     First, the three-dimensional data encoding device binarizes the prediction mode by the truncated unary coding using total number M of prediction modes (S 3574 ). 
     Then, the three-dimensional data encoding device arithmetic-encodes binary data of the truncated unary coding (S 3575 ). 
     Then, the three-dimensional data encoding device appends total number M of prediction modes as NumPredMode to the header and encodes NumPredMode (S 3576 ). 
       FIG. 122  is a flowchart of an example of a prediction mode decoding process by the three-dimensional data decoding device according to this embodiment. 
     First, the three-dimensional data decoding device decodes encoded NumPredMode included in the bitstream to set total number M of prediction modes (S 3577 ). 
     Then, the three-dimensional data decoding device arithmetic-decodes encoded PredMode in accordance with decoded total number M of prediction modes, and generates binary data of the truncated unary coding (S 3578 ). 
     Then, the three-dimensional data decoding device calculates a prediction mode from the binary data of the truncated unary coding (S 3579 ). 
       FIG. 123  is a flowchart of another example of the predicted-value calculation process (step S 35335 ) shown in  FIG. 110 . 
     First, the three-dimensional data encoding device calculates a weighted average value of attribute values of the N three-dimensional points in the vicinity of the target three-dimensional point to be encoded, which can be used for prediction, and assigns the calculated weighted average value to prediction mode 0 (S 3581 ). 
     Then, the three-dimensional data encoding device selects and determines a prediction mode (S 3582 ). 
     Then, the three-dimensional data encoding device arithmetic-encodes the selected and determined prediction mode (S 3583 ). 
     The three-dimensional data encoding device outputs a predicted value of the determined prediction mode (S 3584 ). 
     As described above, the three-dimensional data encoding device may binarize prediction mode PredMode in accordance with total number M of prediction modes and arithmetic-encodes PredMode. The three-dimensional data encoding device may encode total number M of prediction modes as NumPredMode and append NumPredMode to the header. 
     Thus, the three-dimensional data decoding device can decode NumPredMode in the header, thereby correctly decoding prediction mode PredMode. 
     When NumPredMode is 1, the three-dimensional data encoding device needs not encode PredMode. 
     Thus, the three-dimensional data encoding device can reduce an encoding amount when NumPredMode is 1. 
       FIG. 124  is a flowchart of a prediction mode selection process (S 3582 ) shown in  FIG. 123 . 
     First, the three-dimensional data encoding device assigns attribute information items of the N three-dimensional points in the vicinity of the target three-dimensional point to be encoded to prediction modes 1 to N sequentially from a three-dimensional point closer to the target three-dimensional point (S 35821 ). For example, the three-dimensional data encoding device generates N+1 prediction modes. When N+1 is larger than total number M of prediction modes (NumPredMode) appended to the bitstream, the three-dimensional data encoding device may generate up to M prediction modes. 
     Then, the three-dimensional data encoding device calculates cost of each prediction mode, and selects a prediction mode with minimum cost (S 35822 ). 
       FIG. 125  is a flowchart of a specific example of a prediction mode selection process (S 35822 ) shown in  FIG. 124 . 
     First, the three-dimensional data encoding device sets i=0 and mincost=∞ (S 358221 ). 
     Then, the three-dimensional data encoding device calculates cost[i] of i-th prediction mode PredMode[i] (S 358222 ). 
     Then, the three-dimensional data encoding device determines whether or not cost[i]&lt;mincost is satisfied (S 358223 ). 
     Then, when determining that cost[i]&lt;mincost is satisfied (Yes in S 358223 ), the three-dimensional data encoding device sets mincost=cost[i], and sets the prediction mode to PredMode[i] (S 358224 ). 
     Following step S 358224  or when determining that cost[i]&lt;mincost is not satisfied (No in S 358223 ), the three-dimensional data encoding device sets i=i+1 (S 358225 ). 
     Then, the three-dimensional data encoding device determines whether or not i&lt;the number of prediction modes is satisfied (S 358226 ). 
     When determining that i&lt;the number of prediction modes is not satisfied (No in S 358226 ), the three-dimensional data encoding device finishes the selection process. When determining that i&lt;the number of prediction modes is satisfied (Yes in S 358226 ), the three-dimensional data encoding device returns the process to step S 358222 . 
     When the number of three-dimensional points in the vicinity of the target three-dimensional point to be encoded is N, the three-dimensional data encoding device generates N+1 prediction modes. When N+1 is larger than total number M of prediction modes (NumPredMode) appended to the bitstream, the three-dimensional data encoding device may generate up to M prediction modes. 
       FIG. 126  is a flowchart of another example of the calculation process of a prediction mode and a quantized value of P (S 355211 ) shown in  FIG. 115 . 
     First, the three-dimensional data decoding device decodes the prediction mode from the bitstream (S 3552111 ). 
     As described above, the three-dimensional data decoding device may arithmetic-decode prediction mode PredMode in accordance with total number M of prediction modes obtained by decoding the header. 
     When total number M of prediction modes is 1, the three-dimensional data decoding device may estimate PredMode as 0 without decoding PredMode. 
     Then, the three-dimensional data decoding device arithmetic-decodes an n-bit code (S 3552112 ). 
     Then, the three-dimensional data decoding device determines whether or not a value of the n-bit code==R_TH[LoDN] is satisfied (S 3552113 ). 
     When determining that the value of the n-bit code==R_TH[LoDN] is satisfied (Yes in S 3552113 ), the three-dimensional data decoding device arithmetic-decodes a remaining code (S 3552114 ). 
     Then, the three-dimensional data decoding device calculates a value of the remaining code with reference to a table for an Exponential-Golomb code (S 3552115 ). 
     Then, the three-dimensional data decoding device sets (R_TH[LoDN]+value of remaining code) as a prediction residual (S 3552116 ). 
     Then, the three-dimensional data decoding device transforms the decoded prediction residual from an unsigned integer value to a signed integer value (S 3552117 ). 
     When determining that the value of the n-bit code==R_TH[LoDN] is not satisfied (No in S 3552113 ), the three-dimensional data decoding device decodes the prediction mode from the bitstream (S 3552118 ), and performs step S 3552117 . 
       FIG. 127  is a diagram showing an example of attribute information used in calculating a predicted value. 
     For example, a predicted value of attribute information on point a2 shown in  FIG. 127  is generated using attribute information on points a0 and a1. Furthermore, for example, a predicted value of attribute information on point a5 shown in  FIG. 127  is generated using attribute information on points a0, a1, a2, a3, and a4. 
     Note that the peripheral points selected varies with the value of N described above. For example, in the case of N=5, points a0, a1, a2, a3, and a4 are selected as peripheral points of point a5. In the case of N=4, points a0, a1, a2, and a4 are selected based on distance information. 
     The three-dimensional data encoding device may generate LoDs in descending order of level (beginning with LoD0, for example). Alternatively, the three-dimensional data encoding device may generate LoDs in ascending order of level (beginning with LoD2, for example). 
     The predicted value is calculated from an attribute value based on weighted averaging for neighboring points. 
     For example, in the example shown in  FIG. 127 , predicted value a2p of point a2 is calculated by weighted averaging of attribute values of points a0 and a1, as shown by the following equations (Equation F1), (Equation F2), and (Equation F3). 
     
       
         
           
             
               
                 
                   [ 
                   
                     Math 
                     . 
                     
                         
                     
                     ⁢ 
                     6 
                   
                   ] 
                 
               
               
                 
                     
                 
               
             
             
               
                 
                   
                     a 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     2 
                     ⁢ 
                     p 
                   
                   = 
                   
                     
                       ∑ 
                       
                         i 
                         = 
                         0 
                       
                       1 
                     
                     ⁢ 
                     
                       
                         w 
                         i 
                       
                       × 
                       
                         A 
                         i 
                       
                     
                   
                 
               
               
                 
                   ( 
                   
                     Equation 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     F1 
                   
                   ) 
                 
               
             
             
               
                 
                   
                     w 
                     i 
                   
                   = 
                   
                     
                       1 
                       
                          
                         
                           ai 
                           - 
                           ave 
                         
                          
                       
                     
                     
                       
                         ∑ 
                         
                           j 
                           = 
                           0 
                         
                         1 
                       
                       ⁢ 
                       
                         1 
                         
                            
                           
                             aj 
                             - 
                             ave 
                           
                            
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   
                     Equation 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     F2 
                   
                   ) 
                 
               
             
             
               
                 
                   ave 
                   = 
                   
                     
                       
                         ∑ 
                         
                           i 
                           = 
                           1 
                         
                         1 
                       
                       ⁢ 
                       
                         A 
                         i 
                       
                     
                     2 
                   
                 
               
               
                 
                   ( 
                   
                     Equation 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     F3 
                   
                   ) 
                 
               
             
           
         
       
     
     Note that A i  is a value of attribute information on point ai. ave denotes an average value of A i . 
     Note that a median of A i  may be used instead of the average value. Furthermore, (ai−ave) 2  and (aj−ave) 2  may be used instead of |ai−ave| and |aj−ave|. 
     For example, predicted value a5p of point a5 is calculated by weighted averaging of attribute information on points a0, a1, a2, a3, and a4, as shown by the following equations (Equation F4), (Equation F5), and (Equation F6). 
     
       
         
           
             
               
                 
                   [ 
                   
                     Math 
                     . 
                     
                         
                     
                     ⁢ 
                     7 
                   
                   ] 
                 
               
               
                 
                     
                 
               
             
             
               
                 
                   
                     a 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     5 
                     ⁢ 
                     p 
                   
                   = 
                   
                     
                       ∑ 
                       
                         i 
                         = 
                         0 
                       
                       4 
                     
                     ⁢ 
                     
                       
                         w 
                         i 
                       
                       × 
                       
                         A 
                         i 
                       
                     
                   
                 
               
               
                 
                   ( 
                   
                     Equation 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     F4 
                   
                   ) 
                 
               
             
             
               
                 
                   
                     w 
                     i 
                   
                   = 
                   
                     
                       1 
                       
                          
                         
                           ai 
                           - 
                           ave 
                         
                          
                       
                     
                     
                       
                         ∑ 
                         
                           j 
                           = 
                           0 
                         
                         4 
                       
                       ⁢ 
                       
                         1 
                         
                            
                           
                             aj 
                             - 
                             ave 
                           
                            
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   
                     Equation 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     F5 
                   
                   ) 
                 
               
             
             
               
                 
                   ave 
                   = 
                   
                     
                       
                         ∑ 
                         
                           i 
                           = 
                           1 
                         
                         5 
                       
                       ⁢ 
                       
                         A 
                         i 
                       
                     
                     5 
                   
                 
               
               
                 
                   ( 
                   
                     Equation 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     F6 
                   
                   ) 
                 
               
             
           
         
       
     
     Here, if the value of ai and the value of ave are the same, |ai−ave| is 0, and it is difficult to appropriately calculate the value of w i . To cope with this, when|ai−ave| is 0, for example, the three-dimensional data encoding device performs the calculation by setting |ai−ave| at 1. 
     In this way, the three-dimensional data encoding device can calculate the value of w i . 
     If the value of aj and the value of ave are the same, |aj−ave| is 0, and it is difficult to appropriately calculate the value of w i . To cope with this, when|aj−ave| is 0, for example, the three-dimensional data encoding device performs the calculation by setting |aj−ave| at 1. 
     In this way, the three-dimensional data encoding device can calculate the value of w i . 
     Predicted value aNp of point aN is calculated by weighted averaging of attribute information on points N−4, N−3, N−2, and N−1, as shown by the following equations (Equation F7), (Equation F8), and (Equation F9). Note that N denotes a positive integer equal to or greater than 5. 
     
       
         
           
             
               
                 
                   [ 
                   
                     Math 
                     . 
                     
                         
                     
                     ⁢ 
                     8 
                   
                   ] 
                 
               
               
                 
                     
                 
               
             
             
               
                 
                   aNp 
                   = 
                   
                     
                       ∑ 
                       
                         i 
                         = 
                         
                           N 
                           - 
                           4 
                         
                       
                       
                         N 
                         - 
                         1 
                       
                     
                     ⁢ 
                     
                       
                         w 
                         i 
                       
                       × 
                       
                         A 
                         i 
                       
                     
                   
                 
               
               
                 
                   ( 
                   
                     Equation 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     F7 
                   
                   ) 
                 
               
             
             
               
                 
                   
                     w 
                     i 
                   
                   = 
                   
                     
                       1 
                       
                          
                         
                           ai 
                           - 
                           ave 
                         
                          
                       
                     
                     
                       
                         ∑ 
                         
                           j 
                           = 
                           
                             N 
                             - 
                             4 
                           
                         
                         
                           N 
                           - 
                           1 
                         
                       
                       ⁢ 
                       
                         1 
                         
                            
                           
                             aj 
                             - 
                             ave 
                           
                            
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   
                     Equation 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     F8 
                   
                   ) 
                 
               
             
             
               
                 
                   ave 
                   = 
                   
                     
                       
                         ∑ 
                         
                           i 
                           = 
                           
                             N 
                             - 
                             4 
                           
                         
                         
                           N 
                           - 
                           1 
                         
                       
                       ⁢ 
                       
                         A 
                         i 
                       
                     
                     4 
                   
                 
               
               
                 
                   ( 
                   
                     Equation 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     F9 
                   
                   ) 
                 
               
             
           
         
       
     
     For example, the three-dimensional data encoding device performs the calculation by setting |ai−ave| at 1 in the case of |ai−ave|==0, and performs the calculation by setting |ai−ave| at |ai−ave| otherwise. 
     For example, the three-dimensional data encoding device performs the calculation by setting |aj−ave| at 1 in the case of |aj−ave|==0, and performs the calculation by setting |aj−ave| at |aj−ave| otherwise. 
     Embodiment 7 
     As another example of encoding the attribute information of a three-dimensional point by using the information on the LoDs, a method will be described that encodes a plurality of three-dimensional points in order from the three-dimensional points included in the bottom layer of the LoDs. For example, when encoding a plurality of three-dimensional points in order from the three-dimensional points included in the bottom layer LoDn of the LoDs, the three-dimensional data encoding device may calculate the predicted values of the three-dimensional points included in the LoDn by using the attribute information of the three-dimensional points included in a layer higher than the LoDn of the LoDs. 
       FIG. 128  is a diagram showing an example of the reference relationship. For example, in the case of the example shown in  FIG. 128 , the three-dimensional data encoding device calculates the predicted values of the three-dimensional points included in the LoD2 by using the attribute information of the three-dimensional points included in the LoD0 or the LoD1. Additionally, the three-dimensional data encoding device calculates the predicted values of the three-dimensional points included in the LoD1 by using the attribute information of the three-dimensional points included in the LoD0. In this case, the LoD0 or the LoD1 need not necessarily be the attribute information that has been encoded and decoded. In this case, the three-dimensional data encoding device may use, for example, the value before encoding. 
     In this manner, the three-dimensional data encoding device may generate the predicted values of the attribute information of the three-dimensional points included in the LoDn by using the attribute information included in the LoDn′ (n′&lt;n). Accordingly, since the plurality of three-dimensional points included in the LoDn do not refer to each other, the three-dimensional data encoding device can calculate in parallel the predicted values of the plurality of three-dimensional points included in the LoDn. 
     For example, the three-dimensional data encoding device generates the predicted value of the attribute information of a three-dimensional point by calculating the average of the attribute values of N or less three-dimensional points among the three-dimensional points around a current three-dimensional point to be encoded. Additionally, the three-dimensional data encoding device may add the value of N to the header of a bitstream or the like. Note that the three-dimensional data encoding device may change the value of N for each three-dimensional point, and may add the value of N for each three-dimensional point. Accordingly, since an appropriate N can be selected for each three-dimensional point, the accuracy of the predicted value can be improved. Therefore, the predicted residual can be reduced. Additionally, the three-dimensional data encoding device may add the value of N to the header of a bitstream, and may fix the value of N within the bitstream. Accordingly, since it becomes unnecessary to encode or decode the value of N for each three-dimensional point, the processing amount can be reduced. Additionally, the three-dimensional data encoding device may separately encode the value of N for each LoD. Accordingly, the coding efficiency can be improved by selecting an appropriate N for each LoD. 
     Alternatively, the three-dimensional data encoding device may calculate the predicted value of the attribute information of a three-dimensional point with the weighted average value of the attribute information of N peripheral three-dimensional points. For example, the three-dimensional data encoding device calculates the weight by using respective pieces of distance information of a current three-dimensional point and N peripheral three-dimensional points. 
     When separately encoding the value of N for each LoD, the three-dimensional data encoding device sets, for example, the value of N to be larger for the higher layers in the LoDs, and the value of N to be smaller for the lower layers. The distance between three-dimensional points belonging to the higher layers in the LoDs is larger than the distance between three-dimensional points belonging to the higher layer in the LoDs. Therefore, in the higher layers, there is a possibility that the prediction accuracy can be improved by averaging more peripheral three-dimensional points by setting the value of N to be large. Additionally, the distance between three-dimensional points belonging to the lower layers in the LoDs is short. Therefore, in the lower layers, it becomes possible to perform efficient prediction while suppressing the processing amount of averaging, by setting the value of N to be small. 
     As described above, the predicted value of the point P included in the LoDN is generated by using the encoded surrounding point P′ included in the LoDN′ (N′&lt;=N). Here, the surrounding point P′ is selected based on the distance from the point P. For example, the predicted value of the attribute information of the point b2 shown in  FIG. 128  is generated by using the attribute information of the points a0, a1, and a2. 
     The peripheral points to be selected are changed according to the above-described value of N. For example, when N=3, the points a0, a1, and a2 are selected as the surrounding points of the point b2. When N=2, the points a1 and a2 are selected based on the distance information. 
     The predicted value is calculated by the distance-dependent weighted averaging. For example, in the example shown in  FIG. 128 , a predicted value b2p of the point b2 is calculated by the weighted average of the attribute information of the point a0 and the point a1, as shown in (Equation J1) and (Equation J2). Note that A i  is the value of the attribute information of a point ai. Additionally, d (p, q) is, for example, the Euclid distance between the three-dimensional point p and the three-dimensional point q. 
     
       
         
           
             
               
                 
                   [ 
                   
                     Math 
                     . 
                     
                         
                     
                     ⁢ 
                     9 
                   
                   ] 
                 
               
               
                 
                     
                 
               
             
             
               
                 
                   
                     b 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     2 
                     ⁢ 
                     p 
                   
                   = 
                   
                     
                       ∑ 
                       
                         i 
                         = 
                         0 
                       
                       2 
                     
                     ⁢ 
                     
                       
                         w 
                         i 
                       
                       × 
                       
                         A 
                         i 
                       
                     
                   
                 
               
               
                 
                   ( 
                   
                     Equation 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     J1 
                   
                   ) 
                 
               
             
             
               
                 
                   
                     w 
                     i 
                   
                   = 
                   
                     
                       1 
                       
                         d 
                         ⁡ 
                         
                           ( 
                           
                             
                               b 
                               ⁢ 
                               2 
                             
                             , 
                             ai 
                           
                           ) 
                         
                       
                     
                     
                       
                         ∑ 
                         
                           j 
                           = 
                           0 
                         
                         2 
                       
                       ⁢ 
                       
                         1 
                         
                           d 
                           ⁡ 
                           
                             ( 
                             
                               
                                 b 
                                 ⁢ 
                                 2 
                               
                               , 
                               aj 
                             
                             ) 
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   
                     Equation 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     J2 
                   
                   ) 
                 
               
             
           
         
       
     
     Additionally, as shown in (Equation J3) and (Equation J4), a predicted value aNp of a point aN is calculated by the weighted average of the attribute information of points aN−4, aN−3, aN−2, and aN−1. 
     
       
         
           
             
               
                 
                   [ 
                   
                     Math 
                     . 
                     
                         
                     
                     ⁢ 
                     10 
                   
                   ] 
                 
               
               
                 
                     
                 
               
             
             
               
                 
                   aNp 
                   = 
                   
                     
                       ∑ 
                       
                         i 
                         = 
                         
                           N 
                           - 
                           4 
                         
                       
                       
                         N 
                         - 
                         1 
                       
                     
                     ⁢ 
                     
                       
                         w 
                         i 
                       
                       × 
                       
                         A 
                         i 
                       
                     
                   
                 
               
               
                 
                   ( 
                   
                     Equation 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     J3 
                   
                   ) 
                 
               
             
             
               
                 
                   
                     w 
                     i 
                   
                   = 
                   
                     
                       1 
                       
                          
                         
                           aN 
                           - 
                           ai 
                         
                          
                       
                     
                     
                       
                         ∑ 
                         
                           j 
                           = 
                           
                             N 
                             - 
                             4 
                           
                         
                         
                           N 
                           - 
                           1 
                         
                       
                       ⁢ 
                       
                         1 
                         
                            
                           
                             aN 
                             - 
                             aj 
                           
                            
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   
                     Equation 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     J4 
                   
                   ) 
                 
               
             
           
         
       
     
     Additionally, the three-dimensional data encoding device may calculate the difference value (predicted residual) between the value of the attribute information of a three-dimensional point, and the predicted value generated from the surrounding points, and may quantize the calculated predicted residual. For example, the three-dimensional data encoding device performs quantization by dividing the predicted residual by a quantization scale (also called a quantization step). In this case, the smaller the quantization scale, the smaller the error (quantization error) that may occur due to quantization. Conversely, the larger the quantization scale, the larger the quantization error. 
     Note that the three-dimensional data encoding device may change the quantization scale to be used for each LoD. For example, the three-dimensional data encoding device makes the quantization scale smaller for the higher layers, and makes the quantization scale larger for the lower layers. Since the value of the attribute information of three-dimensional points belonging to the higher layers may be used as the predicted value of the attribute information of three-dimensional points belonging to the lower layers, the coding efficiency can be improved by suppressing the quantization error that may occur in the higher layers by making the quantization scale for the higher layers small to increase the accuracy of the predicted value. Note that the three-dimensional data encoding device may add the quantization scale used for each LoD to a header or the like. Accordingly, since the three-dimensional data decoding device can correctly decode the quantization scale, a bitstream can be appropriately decoded. 
     Additionally, the three-dimensional data encoding device may adaptively switch the quantization scale to be used according to the importance of a current three-dimensional point. For example, the three-dimensional data encoding device uses a small quantization scale for a three-dimensional point with high importance, and uses a large quantization scale for a three-dimensional point with low importance. Here, the importance may be calculated from, for example, the number of times that the current three-dimensional point has been referred to by the other three-dimensional points at the time of calculation of the predicted value, the weight at that time, or the like. For example, the value of the following QW (Quantization Weight) is used as the importance. The three-dimensional data encoding device sets the value of the QW of a three-dimensional point with high importance to be large, and makes the quantization scale small. Accordingly, since the quantization error of a three-dimensional point with high importance becomes small, the coding efficiency can be improved. 
       FIG. 129  is a diagram showing a calculation example of the QW. The QS (quantization step) may be changed according to the LoD. QS_LoD0 is the QS for the LoD0 and QS_LoD1 is the QS for LoD1. 
     The QW is the value representing the importance of a current three-dimensional point. For example, when the point b2 is used for calculation of the predicted value of the point c0, the value of the QW of the point c0 may be multiplied by a weight W b2 _c0 for the point b2 calculated at the time of generation of the predicted value of the point c0, and the obtained value may be added to the value of the QW of the point b2. Accordingly, the value of the QW of a three-dimensional point that has been used often for generating the predicted value becomes large, and the prediction efficiency can be improved by suppressing the quantization error of the three-dimensional point. 
     For example, the three-dimensional data encoding device may first initialize the values of the QWs of all three-dimensional points with 1, and may update the QW of each three-dimensional point according to a prediction structure. Alternatively, the three-dimensional data encoding device may change an initial value according to the layer of a LoD, without initializing the QWs of all three-dimensional points with the value 1. For example, the three-dimensional data encoding device may make the quantization scale for the higher layers smaller by setting the initial values of the QWs for the higher layers to be larger. Accordingly, since the prediction errors for the higher layers can be suppressed, the prediction accuracy for the lower layers can be increased, and the coding efficiency can be improved. 
     Additionally, the three-dimensional data encoding device may convert a signed integer value (signed quantized value), which is the predicted residual after quantization, into an unsigned integer value (unsigned quantized value). Accordingly, when entropy encoding the predicted residual, it becomes unnecessary to consider the occurrence of a negative integer. Note that the three-dimensional data encoding device need not necessarily convert a signed integer value into an unsigned integer value, and may, for example, separately entropy encode a sign bit. 
       FIG. 130  is a diagram showing a calculation example of a predicted residual. The predicted residual is calculated by subtracting a predicted value from an original value. For example, as shown in (Equation J5), the predicted residual b2r of the point b2 is calculated by subtracting the predicted value b2p of the point b2 from the value B 2  of the attribute information of the point b2. 
         b 2 r=B   2   −b 2 p   (Equation J5)
 
     Additionally, the predicted residual is quantized by being divided by the QS (Quantization Step). For example, the quantized value b2q of the point b2 is calculated by (Equation J6). Here, QS_LoD1 is the QS for the LoD1. That is, the QS may be changed according to the LoD. 
         b 2 q=b 2 r/QS _ LoD 1  (Equation J6)
 
     Additionally, when using the QW as described above, the quantized value b2q of the point b2 is calculated by (Equation J7) and (Equation J8). 
     
       
         
           
             
               
                 
                   [ 
                   
                     Math 
                     . 
                     
                         
                     
                     ⁢ 
                     11 
                   
                   ] 
                 
               
               
                 
                     
                 
               
             
             
               
                 
                   
                     b 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     2 
                     ⁢ 
                     q 
                   
                   = 
                   
                     
                       
                         
                           b 
                           ⁢ 
                           2 
                           ⁢ 
                           r 
                         
                         + 
                         
                           QS_LoD1 
                           2 
                         
                       
                       QS_LoD1 
                     
                     × 
                     QWb 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     2 
                   
                 
               
               
                 
                   ( 
                   
                     Equation 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     J7 
                   
                   ) 
                 
               
             
             
               
                 
                   
                     QWb 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     2 
                   
                   = 
                   
                     1 
                     + 
                     
                       
                         ∑ 
                         
                           i 
                           = 
                           0 
                         
                         2 
                       
                       ⁢ 
                       
                         
                           w 
                           
                             
                               b 
                               ⁢ 
                               2 
                             
                             - 
                           
                         
                         ⁢ 
                         ci 
                         × 
                         QWci 
                       
                     
                   
                 
               
               
                 
                   ( 
                   
                     Equation 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     J8 
                   
                   ) 
                 
               
             
           
         
       
     
     Additionally, the three-dimensional data encoding device converts the signed integer value, which is the above-described quantized value, to an unsigned integer value as follows. When the signed integer value b2q is smaller than 0, the three-dimensional data encoding device sets the unsigned integer value b2u to −1−(2×b2q). When the signed integer value b2q is 0 or more, the three-dimensional data encoding device sets the unsigned integer value b2u to 2×b2q. 
     Additionally, the three-dimensional data encoding device scans and encodes the predicted residual (unsigned integer value) after quantization according to a certain order. For example, the three-dimensional data encoding device encodes a plurality of three-dimensional points in order from three-dimensional points included in the higher layers of the LoDs toward the lower layers. 
     Embodiment 8 
     According to a three-dimensional data encoding device according to Embodiment 8, geometry information of a plurality of three-dimensional points is encoded using a prediction tree generated based on the geometry information. 
       FIG. 131  is a diagram illustrating an example of a prediction tree used in the three-dimensional data encoding method according to Embodiment 8.  FIG. 132  is a flowchart illustrating an example of the three-dimensional data encoding method according to Embodiment 8.  FIG. 133  is a flowchart illustrating an example of a three-dimensional data decoding method according to Embodiment 8. 
     As shown in  FIG. 131  and  FIG. 132 , in the three-dimensional data encoding method, a prediction tree is generated using a plurality of three-dimensional points, and node information included in each node in the prediction tree is then encoded. In this way, a bitstream including encoded node information is obtained. Each item of node information is information concerning one node of the prediction tree, for example. Each item of node information includes geometry information of one node, an index of the one node, the number of child nodes of the one node, a prediction mode used for encoding the geometry information of the one node, and a prediction residual. 
     As shown in  FIG. 131  and  FIG. 133 , in the three-dimensional data decoding device, each item of encoded node information included in the bitstream is decoded, and then the geometry information is decoded while generating the prediction tree. 
     Next, a method of generating a prediction tree will be described with reference to  FIG. 134 . 
       FIG. 134  is a diagram for describing a method of generating a prediction tree according to Embodiment 8. 
     In the method of generating a prediction tree, as shown in Part (a) of  FIG. 134 , the three-dimensional data encoding device first adds point 0 as an initial point of the prediction tree. Geometry information of point 0 is represented by coordinates including three elements (x0, y0, z0). The geometry information of point 0 may be represented by coordinates of the three-dimensional Cartesian coordinate system or coordinates of the polar coordinate system. 
     child_count is incremented by 1 each time one child node is added to the node for which the child_count is set. Once the generation of the prediction tree is completed, child_count of each node indicates the number of child nodes of the node, and is added to the bitstream. pred_mode indicates the prediction mode for predicting values of the geometry information of each node. Details of the prediction mode will be described later. 
     As shown in Part (b) of  FIG. 134 , the three-dimensional data encoding device then adds point 1 to the prediction tree. In this step, the three-dimensional data encoding device may search the point cloud already added to the prediction tree for a point nearest to point 1 and add point 1 as a child node of the nearest point. Geometry information of point 1 is represented by coordinates including three elements (x1, y1, z1). The geometry information of point 1 may be represented by coordinates of the three-dimensional Cartesian coordinate system or coordinates of the polar coordinate system. In the case of  FIG. 134 , point 0 is the nearest point of point 1, and point 1 is added as a child node of point 0. The three-dimensional data encoding device then increments by 1 the value indicated by child_count of point 0. 
     Note that the predicted value of the geometry information of each node may be calculated when adding the node to the prediction tree. For example, in the case of Part (b) of  FIG. 134 , the three-dimensional data encoding device may add point 1 as a child node of point 0 and calculate the geometry information of point 0 as a predicted value. In that case, pred_mode=1 may be set. pred_mode is prediction mode information (prediction mode value) indicating a prediction mode. After calculating the predicted value, the three-dimensional data encoding device may calculate residual value (prediction residual) of point 1. Here, residual_value is a difference value obtained by subtracting the predicted value calculated in the prediction mode indicated by pred_mode from the geometry information of the node. As described, according to the three-dimensional data encoding method, the difference value with respect to the predicted value, rather than the geometry information itself, is encoded, so that the encoding efficiency can be improved. 
     As shown in Part (c) of  FIG. 134 , the three-dimensional data encoding device then adds point 2 to the prediction tree. In this step, the three-dimensional data encoding device may search the point cloud already added to the prediction tree for a point nearest to point 2 and add point 2 as a child node of the nearest point. Geometry information of point 2 is represented by coordinates including three elements (x2, y2, z2). The geometry information of point 2 may be represented by coordinates of the three-dimensional Cartesian coordinate system or coordinates of the polar coordinate system. In the case of  FIG. 134 , point 1 is the nearest point of point 2, and point 2 is added as a child node of point 1. The three-dimensional data encoding device then increments by 1 the value indicated by child_count of point 1. 
     As shown in Part (d) of  FIG. 134 , the three-dimensional data encoding device then adds point 3 to the prediction tree. In this step, the three-dimensional data encoding device may search the point cloud already added to the prediction tree for a point nearest to point 3 and add point 3 as a child node of the nearest point. Geometry information of point 3 is represented by coordinates including three elements (x3, y3, z3). The geometry information of point 3 may be represented by coordinates of the three-dimensional Cartesian coordinate system or coordinates of the polar coordinate system. In the case of  FIG. 134 , point 0 is the nearest point of point 3, and point 3 is added as a child node of point 0. The three-dimensional data encoding device then increments by 1 the value indicated by child_count of point 0. 
     In this way, the three-dimensional data encoding device adds all points to the prediction tree and ends the generation of the prediction tree. When the generation of the prediction tree ends, any node having child_count=0 is a leaf of the prediction tree. After the generation of the prediction tree ends, the three-dimensional data encoding device encodes child_count, pred_mode, and residual_value of each node selected in the depth-first order from the root node. Selecting a node in the depth-first order means that the three-dimensional data encoding device selects, as a node subsequent to a node selected, a child node that has not been selected yet of the one or more child nodes of the selected node. When the selected node has no child node, the three-dimensional data encoding device selects a child node that has not been selected yet of the parent node of the selected node. 
     Note that the order of encoding is not limited to the depth-first order, but may be the width-first order, for example. When selecting a node in the width-first order, the three-dimensional data encoding device selects, as a node subsequent to a node selected, a node that has not been selected yet of the one or more nodes at the same depth (layer) as the selected node. When there is no node at the same depth as the selected node, the three-dimensional data encoding device selects a node that has not been selected yet of the one or more nodes at the subsequent depth. 
     Note that points 0 to 3 are examples of three-dimensional points. 
     Note that although child_count, pred_mode, and residual_value are calculated when adding each point to the prediction tree in the three-dimensional data encoding method described above, the present invention is not necessarily limited to this, and they may be calculated after the generation of the prediction tree ends. 
     The three-dimensional data encoding device to which a plurality of three-dimensional points are input may re-order the input three-dimensional points in ascending or descending Morton order and process the three-dimensional points in the latter order. This allows the three-dimensional data encoding device to efficiently search for the nearest point of the three-dimensional point to be processed and improve the encoding efficiency. The three-dimensional data encoding device need not re-order the three-dimensional points and may process the three-dimensional points in the order of input. For example, the three-dimensional data encoding device may generate a prediction tree without a branch in the order of input of a plurality of three-dimensional points. Specifically, the three-dimensional data encoding device may add an input three-dimensional point subsequent to a predetermined three-dimensional point in the order of input of a plurality of three-dimensional points as a child node of the predetermined three-dimensional point. 
     Next, a first example of prediction modes will be described with reference to  FIG. 135 .  FIG. 135  is a diagram for describing a first example of prediction modes according to Embodiment 8.  FIG. 135  is a diagram illustrating a part of a prediction tree. 
     As shown below, eight prediction modes may be set. As an example, a case where a predicted value for point c is calculated as shown in  FIG. 135  will be described. In the prediction tree, as shown, the parent node of point c is point p0, the grandparent node of point c is point p1, and the great grandparent node of point c is point p2. Note that point c, point p0, point p1, and point p2 are examples of three-dimensional points. 
     A prediction mode whose prediction mode value is 0 (referred to as prediction mode 0, hereinafter) may be set without prediction. That is, in prediction mode 0, the three-dimensional data encoding device may calculate geometry information of input point c as a predicted value of point c. 
     A prediction mode whose prediction mode value is 1 (referred to as prediction mode 1, hereinafter) may be set for a differential prediction with respect to point p0. That is, the three-dimensional data encoding device may calculate geometry information of point p0, which is the parent node of point c, as a predicted value of point c. 
     A prediction mode whose prediction mode value is 2 (referred to as prediction mode 2, hereinafter) may be set for a linear prediction based on point p0 and point p1. That is, the three-dimensional data encoding device may calculate, as a predicted value of point c, a prediction result of a linear prediction based on geometry information of point p0, which is the parent node of point c, and geometry information of point p1, which is the grandparent node of point c. 
       Predicted value=2× p 0− p 1  (Equation T1)
 
     In Equation T1, p0 denotes geometry information of point p0, and p1 denotes geometry information of point p1. 
     A prediction mode whose prediction mode value is 3 (referred to as prediction mode 3, hereinafter) may be set for a parallelogram prediction based on point p0, point p1, and point p2. That is, the three-dimensional data encoding device may calculate, as a predicted value of point c, a prediction result of a parallelogram prediction based on geometry information of point p0, which is the parent node of point c, geometry information of point p1, which is the grandparent node of point c, and geometry information of point p2, which is the great grandparent node of point c. Specifically, the three-dimensional data encoding device calculates a predicted value of point c in prediction mode 3 according to the following equation T2. 
       Predicted value= p 0+ p 1− p 2  (Equation T2)
 
     In Equation T2, p0 denotes geometry information of point p0, p1 denotes geometry information of point p1, and p2 denotes geometry information of point p2. 
     A prediction mode whose prediction mode value is 4 (referred to as prediction mode 4, hereinafter) may be set for a differential prediction with respect to point p1. That is, the three-dimensional data encoding device may calculate geometry information of point p1, which is the grandparent node of point c, as a predicted value of point c. 
     A prediction mode whose prediction mode value is 5 (referred to as prediction mode 5, hereinafter) may be set for a differential prediction with respect to point p2. That is, the three-dimensional data encoding device may calculate geometry information of point p2, which is the great grandparent node of point c, as a predicted value of point c. 
     A prediction mode whose prediction mode value is 6 (referred to as prediction mode 6, hereinafter) may be set for an average of geometry information of any two or more of point p0, point p1, and point p2. That is, the three-dimensional data encoding device may calculate, as a predicted value of point c, an average value of any two or more of geometry information of point p0, which is the parent node of point c, geometry information of point p1, which is the grandparent node of point c, and geometry information of point p2, which is the great grandparent node of point c. For example, when the three-dimensional data encoding device uses geometry information of point p0 and geometry information of point p1 for calculation of a predicted value, the three-dimensional data encoding device calculates a predicted value of point c in prediction mode 6 according to the following Equation T3. 
       Predicted value=( p 0+ p 1)/2  (Equation T3)
 
     In Equation T3, p0 denotes geometry information of point p0, and p1 denotes geometry information of point p1. 
     A prediction mode whose prediction mode value is 7 (referred to as prediction mode 7, hereinafter) may be set for a non-linear prediction based on distance d0 between point p0 and point p1 and distance d1 between point p2 and point p1. That is, the three-dimensional data encoding device may calculate, as a predicted value of point c, a prediction result of a non-linear prediction based on distance d0 and distance d1. 
     Note that the prediction method assigned to each prediction mode is not limited to the example described above. The eight prediction modes described above and the eight prediction methods described above need not be combined in the manner described above, and can be combined in any manner. For example, when prediction modes are encoded by an entropy encoding, such as arithmetic encoding, a prediction method of high frequency of use may be assigned to prediction mode 0. In this way, the encoding efficiency can be improved. The three-dimensional data encoding device may can also improve the encoding efficiency by dynamically changing the assignment of prediction modes according to the frequency of use of the prediction modes while performing the encoding process. For example, the three-dimensional data encoding device may count the frequency of use of each prediction mode in the encoding and assign a prediction mode indicated by a smaller value to a prediction method of a higher frequency of use. In this way, the encoding efficiency can be improved. Note that M denotes a prediction mode count indicating the number of prediction modes, and in the example described above, there are eight prediction modes 0 to 7, and therefore, M=8. 
     As predicted values (px, py, pz) of geometry information (x, y, z) of a three-dimensional point, the three-dimensional data encoding device may calculate predicted values used for calculation of geometry information of a three-dimensional point to be encoded based on geometry information of a three-dimensional point that is at a short distance from the three-dimensional point to be encoded among peripheral three-dimensional points of the three-dimensional point to be encoded. The three-dimensional data encoding device may add prediction mode information (pred_mode) for each three-dimensional point so that a predicted value to be calculated can be selected according to the prediction mode. 
     For example, when the total number of prediction modes is M, it is possible that geometry information of nearest three-dimensional point p0 is assigned to prediction mode 0, . . . , and geometry information of three-dimensional point p2 is assigned to prediction mode M−1, and the prediction mode used for prediction is added for each three-dimensional point to the bitstream. 
     Note that prediction mode count M may be added to the bitstream. The value of prediction mode count M need not be added to the bitstream, and may be defined by profile, level or the like of a standard. The value of prediction mode count M calculated from number N of three-dimensional points used for prediction may also be used. For example, prediction mode count M may be calculated according to M=N+1. 
       FIG. 136  is a diagram illustrating a second example of a table that indicates a predicted value calculated in each prediction mode according to Embodiment 8. 
     The table shown in  FIG. 136  is an example in the case where number N of three-dimensional points used for prediction is 4, and prediction mode count M=5. 
     In the second example, a predicted value of geometry information of point c is calculated based on geometry information of at least any one of point p0, point p1, and point p2. The prediction mode is added for each three-dimensional point to be encoded. The predicted value is calculated according to the prediction mode added. 
       FIG. 137  is a diagram illustrating a specific example of the second example of the table that indicates a predicted value calculated in each prediction mode according to Embodiment 8. 
     For example, the three-dimensional data encoding device may select prediction mode 1 and encode geometry information (x, y, z) of a three-dimensional point to be encoded based on predicted values (p0x, p0y, p0z), respectively. In that case, “1”, which is a prediction mode value indicating selected prediction mode 1, is added to the bitstream. 
     As described, when selecting a prediction mode for calculating a predicted value of each of three elements included in the geometry information of the three-dimensional point to be encoded, the three-dimensional data encoding device may select a prediction mode common to the three elements. 
       FIG. 138  is a diagram illustrating a third example of the table that indicates a predicted value calculated in each prediction mode according to Embodiment 8. 
     The table shown in  FIG. 138  is an example in the case where number N of three-dimensional points used for prediction is 2, and prediction mode count M=5. 
     In the third example, a predicted value of geometry information of point c is calculated based on geometry information of at least any one of point p0 and point p1. The prediction mode is added for each three-dimensional point to be encoded. The predicted value is calculated according to the prediction mode added. 
     Note that, when the number of peripheral three-dimensional points of point c (neighboring point count) is less than 3, as in the third example, any prediction mode to which no predicted value has been assigned may be set as “not available”. When a prediction mode set as “not available” occurs, another prediction method may be assigned to the prediction mode. For example, geometry information of point p2 may be assigned to the prediction mode as a predicted value. Alternatively, a predicted value assigned to another prediction mode may be assigned to the prediction mode. For example, geometry information of point p1, which is assigned to prediction mode 4, may be assigned to prediction mode 3, which is set as “not available”. In that case, geometry information of point p2 may be re-assigned to prediction mode 4. In this way, when a prediction mode set as “not available” occurs, the encoding efficiency can be improved by re-assigning a prediction method. 
     Note that when geometry information has three elements, such as in the case of the three-dimensional Cartesian coordinate system or the polar coordinate system, predicted values may be calculated in different modes for the three elements. For example, when the three elements are represented by x, y, and z of coordinates (x, y, z) in the three-dimensional Cartesian coordinate system, the predicted value of each of the three elements may be calculated in a prediction mode selected for the element. For example, prediction mode values of prediction mode pred_mode_x for calculating a predicted value of element x (that is, x coordinate), prediction mode pred_mode_y for calculating a predicted value of element y (that is, y coordinate), and prediction mode pred_mode_z for calculating a predicted value of element z (that is, z coordinate) may be selected. In that case, as the prediction mode values indicating the prediction modes of the elements, the values in the tables in  FIG. 139  to  FIG. 141  described later may be used, and these prediction mode values may be added to the bitstream. Note that although coordinates in the three-dimensional Cartesian coordinate system have been described above as an example of geometry information, the description holds true for coordinates in the polar coordinate system. 
     As described, when selecting a prediction mode for calculating a predicted value of each of three elements included in the geometry information of the three-dimensional point to be encoded, the three-dimensional data encoding device may select a different prediction mode for each of three elements. 
     Predicted values of two or more of a plurality of elements of geometry information may be calculated in a common prediction mode. For example, when the three elements are represented by x, y, and z of coordinates (x, y, z) in the three-dimensional Cartesian coordinate system, a prediction mode value of prediction mode pred_mode_x for calculating a predicted value of element x and prediction mode pred_mode_yz for calculating predicted values of elements y and z may be selected. In that case, as the prediction mode values indicating the prediction modes of the elements, the values in the tables in  FIG. 139  to  FIG. 141  described later may be used, and these prediction mode values may be added to the bitstream. 
     As described, when selecting a prediction mode for calculating a predicted value of each of three elements included in the geometry information of the three-dimensional point to be encoded, the three-dimensional data encoding device may select a common prediction mode for two of the three elements and select a different prediction mode than the prediction mode for the two elements for the remaining one element. 
       FIG. 139  is a diagram illustrating a fourth example of the table that indicates a predicted value calculated in each prediction mode. Specifically, the fourth example is an example in the case where geometry information used for a predicted value is the value of element x of geometry information of a peripheral three-dimensional point. 
     As shown in  FIG. 139 , a predicted value calculated in prediction mode pred_mode_x represented by a prediction mode value of “0” is 0. A predicted value calculated in prediction mode pred_mode_x represented by a prediction mode value of “1” is p0x, which is the x coordinate of point p0. A predicted value calculated in prediction mode pred_mode_x represented by a prediction mode value of “2” is (2×p0x−p1x), which is the prediction result of the linear prediction based on the x coordinate of point p0 and the x coordinate of point p1. A predicted value calculated in prediction mode pred_mode_x represented by a prediction mode value of “3” is (p0x+p1x−p2x), which is the prediction result of the parallelogram prediction based on the x coordinate of point p0, the x coordinate of point p1, and the x coordinate of point p2. A predicted value calculated in prediction mode pred_mode_x represented by a prediction mode value of “4” is p1x, which is the x coordinate of point p1. 
     Note that when prediction mode pred_mode_x represented by a prediction mode value of “1” in the table of  FIG. 139  is selected, for example, the x coordinate of the geometry information of the three-dimensional point to be encoded may be encoded using predicted value p0x. In that case, “1” as the prediction mode value is added to the bitstream. 
       FIG. 140  is a diagram illustrating a fifth example of the table that indicates a predicted value calculated in each prediction mode. Specifically, the fifth example is an example in the case where geometry information used for a predicted value is the value of element y of geometry information of a peripheral three-dimensional point. 
     As shown in  FIG. 140 , a predicted value calculated in prediction mode pred_mode_y represented by a prediction mode value of “0” is 0. A predicted value calculated in prediction mode pred_mode_y represented by a prediction mode value of “1” is p0y, which is the y coordinate of point p0. A predicted value calculated in prediction mode pred_mode_y represented by a prediction mode value of “2” is (2×p0y−p1y), which is the prediction result of the linear prediction based on they coordinate of point p0 and they coordinate of point p1. A predicted value calculated in prediction mode pred_mode_y represented by a prediction mode value of “3” is (p0y+p1y−p2y), which is the prediction result of the parallelogram prediction based on the y coordinate of point p0, the y coordinate of point p1, and the y coordinate of point p2. A predicted value calculated in prediction mode pred_mode_y represented by a prediction mode value of “4” is p1y, which is they coordinate of point p1. 
     Note that when prediction mode pred_mode_y represented by a prediction mode value of “1” in the table of  FIG. 140  is selected, for example, the y coordinate of the geometry information of the three-dimensional point to be encoded may be encoded using predicted value p0y. In that case, “1” as the prediction mode value is added to the bitstream. 
       FIG. 141  is a diagram illustrating a sixth example of the table that indicates a predicted value calculated in each prediction mode. Specifically, the sixth example is an example in the case where geometry information used for a predicted value is the value of element z of geometry information of a peripheral three-dimensional point. 
     As shown in  FIG. 141 , a predicted value calculated in prediction mode pred_mode_z represented by a prediction mode value of “0” is 0. A predicted value calculated in prediction mode pred_mode_z represented by a prediction mode value of “1” is p0z, which is the z coordinate of point p0. A predicted value calculated in prediction mode pred_mode_z represented by a prediction mode value of “2” is (2×p0z−p1z), which is the prediction result of the linear prediction based on the z coordinate of point p0 and the z coordinate of point p1. A predicted value calculated in prediction mode pred_mode_z represented by a prediction mode value of “3” is (p0z+p1z−p2z), which is the prediction result of the parallelogram prediction based on the z coordinate of point p0, the z coordinate of point p1, and the z coordinate of point p2. A predicted value calculated in prediction mode pred_mode_z represented by a prediction mode value of “4” is p1z, which is the z coordinate of point p1. 
     Note that when prediction mode pred_mode_z represented by a prediction mode value of “1” in the table of  FIG. 141  is selected, for example, the z coordinate of the geometry information of the three-dimensional point to be encoded may be encoded using predicted value p0z. In that case, “1” as the prediction mode value is added to the bitstream. 
       FIG. 142  is a diagram illustrating a seventh example of the table that indicates a predicted value calculated in each prediction mode. Specifically, the seventh example is an example in the case where geometry information used for a predicted value are the values of element y and element z of geometry information of a peripheral three-dimensional point. 
     As shown in  FIG. 142 , predicted values calculated in prediction mode pred_mode_yz represented by a prediction mode value of “0” are 0. Predicted values calculated in prediction mode pred_mode_yz represented by a prediction mode value of “1” are (p0y, p0z), which are the y coordinate and z coordinate of point p0. Predicted values calculated in prediction mode pred_mode_yz represented by a prediction mode value of “2” are (2×p0y−p1y, 2×p0z−p1z), which are the prediction result of the linear prediction based on the y coordinate and z coordinate of point p0 and the y coordinate and z coordinate of point p1. Predicted values calculated in prediction mode pred_mode_yz represented by a prediction mode value of “3” are (p0y+p1y−p2y, p0z+p1z−p2z), which are the prediction result of the parallelogram prediction based on the y coordinate and z coordinate of point p0, the y coordinate and z coordinate of point p1, and the y coordinate and z coordinate of point p2. Predicted values calculated in prediction mode pred_mode_yz represented by a prediction mode value of “4” are (p1y, p1z), which are the y coordinate and z coordinate of point p1. 
     Note that when prediction mode pred_mode_yz represented by a prediction mode value of “1” in the table of  FIG. 142  is selected, for example, the y coordinate and z coordinate of the geometry information of the three-dimensional point to be encoded may be encoded using predicted values (p0y, p0z). In that case, “1” as the prediction mode value is added to the bitstream. 
     In the tables of the fourth to seventh examples, the correspondence between the prediction modes and the prediction methods for calculating predicted values are the same as the correspondence in the table of the second example described above. 
     The prediction mode in the encoding may be selected by RD optimization. For example, cost cost(P) in the case where certain prediction mode P is selected may be calculated, and prediction mode P for which cost(P) is at the minimum may be selected. Cost cost(P) may be calculated from prediction residual residual_value(P) in the case where the predicted value in prediction mode P is used, number of bits bit(P) required for encoding prediction mode P, and a λ value, which is an adjustment parameter, according to equation D1. 
       cost( P )=abs(residual_value( P ))+λ×bit( P )  (Equation D1)
 
     abs(x) denotes an absolute value of x. 
     Instead of abs(x), the square of x may be used. 
     By using above equation D1, a prediction mode can be selected by considering the balance between the magnitude of the prediction residual and the number of bits required for encoding the prediction mode. Note that the adjustment parameter λ may be set to be different values according to the value of a quantization scale. For example, it is possible that when the quantization scale is small (when the bit rate is high), the λ value is decreased so that a prediction mode in which prediction residual residual_value(P) is small is selected and the prediction precision is improved as far as possible, while when the quantization scale is large (when the bit rate is low), the λ value is increased so that an appropriate prediction mode is selected by considering number of bits bit(P) required for encoding prediction mode P. 
     Note that the case where the quantization scale is small means a case where the quantization scale is smaller than a first quantization scale, for example. The case where the quantization scale is large means a case where the quantization scale is larger than a second quantization scale that is larger than or equal to the first quantization scale. The λ value may be set to be smaller as the quantization scale is smaller. 
     Prediction residual residual_value(P) is calculated by subtracting the predicted value in prediction mode P from the geometry information of the three-dimensional point to be encoded. Note that instead of reflecting prediction residual residual_value(P) in the cost calculation, prediction residual residual_value(P) may be quantized, inverse-quantized, and added to the predicted value to determine a decoded value, and the difference (encoding error) between the original geometry information of the three-dimensional point and the decoded value obtained using prediction mode P may be reflected in the cost value. This allows a prediction mode with a small encoding error to be selected. 
     When a prediction mode is binarized and then encoded, for example, number of bits bit(P) required for encoding prediction mode P may be the bit count after the binarization. 
     For example, when prediction mode count M=5, as shown in  FIG. 143 , a prediction mode value representing a prediction mode with a truncated unary code having a maximum value of 5 based on prediction mode count M may be binarized In that case, number of bits bit(P) required for encoding the prediction mode value is 1 when the prediction mode value is “0”, 2 when the prediction mode value is “1”, 3 when the prediction mode value is “2”, and 4 when the prediction mode value is “3” or “4”. By using the truncated unary code, the bit count decreases as the value of the prediction mode value decreases. Therefore, the code amount can be reduced for a prediction mode value representing a prediction mode that is likely to be selected, for example, a prediction mode in which a predicted value with which cost(P) is likely to be at the minimum is calculated, such as the predicted value of 0 calculated when the prediction mode value is “0” or the geometry information of three-dimensional point p0 calculated as a predicted value when the prediction mode value is “1”, that is, the geometry information of a three-dimensional point that is at a small distance from the three-dimensional point to be encoded. 
     As described, the three-dimensional data encoding device may encode the prediction mode value representing selected prediction mode with the prediction mode count. Specifically, the three-dimensional data encoding device may encode a prediction mode value with a truncated unary code whose maximum value is the prediction mode count. 
     When the maximum value of the prediction mode count is not determined, as shown in  FIG. 144 , a prediction mode value representing a prediction mode may be binarized with a unary code. When the probabilities of occurrence of the prediction modes are close to each other, as shown in FIG.  145 , a prediction mode value representing a prediction mode may be binarized with a fixed code to reduce the code amount. 
     As the value of number of bits bit(P) required for encoding the prediction mode value representing prediction mode P, binary data of the prediction mode value representing prediction mode P may be arithmetically encoded, and the code amount of the arithmetically encoded binary data may be used. In that case, the cost can be calculated with more precise required bit count bit(P), so that a prediction mode can be more properly selected. 
     Note that  FIG. 143  is a diagram illustrating a first example of a binarization table in the case where a prediction mode value is binarized and encoded according to Embodiment 8. Specifically, the first example is an example in which prediction mode count M=5, and a prediction mode value is binarized with a truncated unary code. 
     Note that  FIG. 144  is a diagram illustrating a second example of the binarization table in the case where a prediction mode value is binarized and encoded according to Embodiment 8. Specifically, the second example is an example in which prediction mode count M=5, and a prediction mode value is binarized with a unary code. 
     Note that  FIG. 145  is a diagram illustrating a third example of the binarization table in the case where a prediction mode value is binarized and encoded according to Embodiment 8. Specifically, the third example is an example in which prediction mode count M=5, and a prediction mode value is binarized with a fixed code. 
     The prediction mode value representing the prediction mode (pred_mode) may be binarized and then arithmetically encoded before being added to the bitstream. The prediction mode value may be binarized with a truncated unary code using the value of prediction mode count M as described above, for example. In that case, the maximum bit count after the binarization of the prediction mode value is M−1. 
     The binary data resulting from the binarization may be arithmetically encoded using an encoding table. In that case, the encoding efficiency may be improved by encoding the binary data using a different encoding table for each bit. Furthermore, in order to reduce the number of encoding tables, the leading one bit of the binary data may be encoded using encoding table A for the leading bit, and each bit of the remaining bits of the binary data may be encoded using encoding table B for the remaining bits. For example, when encoding binary data “1110” whose prediction mode value is “3” shown in  FIG. 146 , the leading one bit “1” may be encoded using encoding table A, and each bit of the remaining bits “110” may be encoded using encoding table B. 
     Note that  FIG. 146  is a diagram for describing an example of encoding of binary data in a binarization table in the case where a prediction mode value is binarized and encoded according to Embodiment 8. The binarization table in  FIG. 146  is an example in the case where prediction mode count M=5, and a prediction mode value is binarized with a truncated unary code. 
     In this way, the encoding efficiency can be improved by using a different encoding table depending on the position of the bit in the binary data, while reducing the number of encoding tables. Note that, when encoding the remaining bits, each bit may be arithmetically encoded using a different encoding table, or each bit may be decoded using a different encoding table based on the result of the arithmetic encoding. 
     When a prediction mode value is binarized and encoded with a truncated unary code using prediction mode count M, prediction mode count M used for the truncated unary code may be added to the header or the like of the bitstream, in order that the prediction mode can be identified from the binary data decoded on the decoder side. The header of the bitstream is a sequence parameter set (SPS), a geometry parameter set (GPS), or a slice header, for example. Maximum possible value MaxM of the prediction mode count may be defined by a standard or the like, and the value of MaxM−M (M&lt;=MaxM) may be added to the header. Prediction mode count M need not be added to the stream, and may be defined by profile or level of a standard or the like. 
     Note that the prediction mode value binarized with a truncated unary code can be arithmetically encoded by using different encoding tables for the leading bit part and the remaining part as described above. Note that the probabilities of occurrence of 0 and 1 in each encoding table may be updated according to the value of the binary data that has actually occurred. The probabilities of occurrence of 0 and 1 in one of the encoding tables may be fixed. By reducing the number of updates of the probabilities of occurrence in this way, the processing amount can be reduced. For example, it is possible that the probabilities of occurrence for the leading bit part is updated, while the probabilities of occurrence for the remaining bit part is fixed. 
       FIG. 147  is a flowchart illustrating an example of encoding of a prediction mode value according to Embodiment 8.  FIG. 148  is a flowchart illustrating an example of decoding of a prediction mode value according to Embodiment 8. 
     As shown in  FIG. 147 , in encoding of a prediction mode value, the prediction mode value is first binarized with a truncated unary code using prediction mode count M (S 9701 ). 
     The binary data of the truncated unary code is then arithmetically encoded (S 9702 ). In this way, the binary data is included in the bitstream as a prediction mode. 
     As shown in  FIG. 148 , in decoding of a prediction mode value, a bitstream is first arithmetically decoded using prediction mode count M to generate binary data of a truncated unary code (S 9711 ). 
     A prediction mode value is then calculated from the binary data of the truncated unary code (S 9712 ). 
     Although an example where a prediction mode value representing a prediction mode (pred_mode) is binarized with a truncated unary code using the value of prediction mode count M has been shown as a method of binarizing a prediction mode value representing a prediction mode (pred_mode), the present invention is not necessarily limited to this. For example, a prediction mode value may be binarized with a truncated unary code using number L (L&lt;=M) of prediction modes to which a predicted value is assigned. For example, when prediction mode count M=5, if there is one peripheral three-dimensional point available for prediction of a certain three-dimensional point to be encoded, two prediction modes may be “available”, and the remaining three prediction modes may be “not available” as shown in  FIG. 149 . For example, as shown in  FIG. 149 , when prediction modes M=5, there may be one peripheral three-dimensional point of the three-dimensional point to be encoded that is available for prediction, and no predicted value may be assigned to the prediction modes represented by prediction mode values of “2”, “3”, and “4”. 
     In that case, as shown in  FIG. 150 , if the prediction mode value is binarized with a truncated unary code whose maximum value is number L of prediction modes to which a predicted value is assigned, the bit count after the binarization may be able to be reduced compared with the case where the prediction mode value is binarized with a truncated unary code using prediction mode count M. In this case, for example, L=3, and therefore, the bit count can be reduced by binarizing the prediction mode value with a truncated unary code whose maximum value is 3. In this way, by binarizing the prediction mode value with a truncated unary code whose maximum value is number L of prediction modes to which a predicted value is assigned, the bit count after the binarization of the prediction mode value can be reduced. 
     The binary data resulting from the binarization may be arithmetically encoded using an encoding table. In that case, the encoding efficiency may be improved by encoding the binary data using a different encoding table for each bit. Furthermore, in order to reduce the number of encoding tables, the leading one bit of the binary data may be encoded using encoding table A for the leading bit, and each bit of the remaining bits of the binary data may be encoded using encoding table B for the remaining bits. For example, when encoding binary data “1” whose prediction mode value is “1” shown in  FIG. 150 , the leading one bit “1” is encoded using encoding table A. There is no remaining bit, and therefore, further encoding is not needed. If there is any remaining bit, the remaining bit may be encoded using encoding table B. 
     Note that  FIG. 150  is a diagram for describing an example of encoding of binary data in a binarization table in the case where a prediction mode value is binarized and encoded according to Embodiment 8. The binarization table in  FIG. 150  is an example in the case where a prediction mode value is binarized with a truncated unary code, provided with number L of prediction modes to which a predicted value is assigned is 2. 
     In this way, the encoding efficiency can be improved by using a different encoding table depending on the position of the bit in the binary data, while reducing the number of encoding tables. Note that, when encoding the remaining bits, each bit may be arithmetically encoded using a different encoding table, or each bit may be decoded using a different encoding table based on the result of the arithmetic encoding. 
     When a prediction mode value is binarized and encoded with a truncated unary code using number L of prediction modes to which a predicted value is assigned, a prediction mode may be decoded on the decoder side by assigning a predicted value to a prediction mode in the same manner as in the encoding to calculate number L and using calculated number L to decode the prediction mode, in order that the prediction mode can be identified from the binary data decoded on the decoder side. 
     Note that the prediction mode value binarized with a truncated unary code can be arithmetically encoded by using different encoding tables for the leading bit part and the remaining part as described above. Note that the probabilities of occurrence of 0 and 1 in each encoding table may be updated according to the value of the binary data that has actually occurred. The probabilities of occurrence of 0 and 1 in one of the encoding tables may be fixed. By reducing the number of updates of the probabilities of occurrence in this way, the processing amount can be reduced. For example, it is possible that the probabilities of occurrence for the leading bit part is updated, while the probabilities of occurrence for the remaining bit part is fixed. 
       FIG. 151  is a flowchart illustrating another example of encoding of a prediction mode value according to Embodiment 8.  FIG. 152  is a flowchart illustrating another example of decoding of a prediction mode value according to Embodiment 8. 
     As shown in  FIG. 151 , in encoding of a prediction mode value, number L of prediction modes to which a predicted value is assigned is first calculated (S 9721 ). 
     The prediction mode value is then binarized with a truncated unary code using number L (S 9722 ). 
     The binary data of the truncated unary code is then arithmetically encoded (S 9723 ). 
     As shown in  FIG. 152 , in decoding of a prediction mode value, number L of prediction modes to which a predicted value is assigned is first calculated (S 9731 ). 
     The bitstream is then arithmetically decoded using number L to generate binary data of a truncated unary code (S 9732 ). 
     A prediction mode value is then calculated from the binary data of the truncated unary code (S 9733 ). 
     The prediction mode value need not be added to every geometry information. For example, it is possible that when a certain condition is satisfied, the prediction mode is fixed, and no prediction mode value is added to the bitstream, while when the certain condition is not satisfied, a prediction mode is selected, and a prediction mode value is added to the bitstream. For example, it is possible that when condition A is satisfied, the prediction mode value is fixed at “2”, and the predicted value is calculated by linear prediction based on peripheral three-dimensional points, and when condition A is not satisfied, one prediction mode is selected from among a plurality of prediction modes, and the prediction mode value representing the selected prediction mode is added to the bitstream. 
     Certain condition A may be that distance d0 between point p1 and point p0 and distance d1 between point p2 and point p1 are calculated, and absolute difference value distdiff=|d0−d1| is less than threshold Thfix. When the absolute difference value is less than threshold Thfix, the three-dimensional data encoding device determines that the difference between the predicted value of the linear prediction and the geometry information of the point to be processed is small, fixes the prediction mode value at “2”, and encodes no prediction mode value. In this way, the three-dimensional data encoding device can generate an appropriate predicted value while reducing the code amount required for encoding the prediction mode. Note that when the absolute difference value is greater than or equal to threshold Thfix, the three-dimensional data encoding device may select a prediction mode and encode the prediction mode value representing the selected prediction mode. 
     Note that threshold Thfix may be added to the header or the like of the bitstream, and the encoder may be able to encode by changing the value of threshold Thfix. For example, in encoding at high bit rate, the encoder may set the value of threshold Thfix to be smaller than in encoding at low bit rate and add the value of threshold Thfix to the header, thereby increasing the cases where encoding is performed by selecting a prediction mode, so that the prediction residual is minimized. In encoding at low bit rate, the encoder sets the value of threshold Thfix to be greater than in encoding at high bit rate, adds the value of threshold Thfix to the header, and perform the encoding with a fixed prediction mode. In this way, by increasing the cases where encoding is performed with a fixed prediction mode in encoding at low bit rate, the encoding efficiency can be improved while reducing the bit amount involved with the encoding of the prediction mode. Threshold Thfix need not be added to the bitstream, and may be defined by profile or level of a standard. 
     N peripheral three-dimensional points of the three-dimensional point to be encoded that are used for prediction are N three-dimensional points encoded and decoded the distance from the three-dimensional point to be encoded is less than threshold THd. The maximum value of N may be added to the bitstream as NumNeighborPoint. The value of N need not always agree with the value of NumNeighborPoint, such as when the number of peripheral three-dimensional points encoded and decoded is less than the value of NumNeighborPoint. 
     Although an example has been shown where the prediction mode value is fixed at “2” when absolute difference value distdiff used for prediction is less than threshold Thfix[i], the present invention is not necessarily limited to this, and the prediction mode value may be fixed at any of “0” to “M−1”. The prediction mode value fixed may be added to the bitstream. 
       FIG. 153  is a flowchart illustrating an example of a process of determining whether or not to fix the prediction mode value according to condition A in encoding according to Embodiment 8.  FIG. 154  is a flowchart illustrating an example of a process of determining whether to set the prediction mode value at a fixed value or decode the prediction mode value according to condition A in decoding according to Embodiment 8. 
     As shown in  FIG. 153 , the three-dimensional data encoding device first calculates distance d0 between point p1 and point p0 and distance d1 between point p2 and point p1, and calculates absolute difference value distdiff=|d0−d1| (S 9741 ). 
     The three-dimensional data encoding device then determines whether absolute difference value distdiff is less than threshold Thfix or not (S 9742 ). Note that threshold Thfix may be encoded and added to the header or the like of the stream. 
     When absolute difference value distdiff is less than threshold Thfix (if Yes in S 9742 ), the three-dimensional data encoding device determines the prediction mode value to be “2” (S 9743 ). 
     On the other hand, when absolute difference value distdiff is greater than or equal to threshold Thfix (if No in S 9742 ), the three-dimensional data encoding device sets one prediction mode from among a plurality of prediction modes (S 9744 ). 
     The three-dimensional data encoding device then arithmetically encodes the prediction mode value representing the set prediction mode (S 9745 ). Specifically, the three-dimensional data encoding device arithmetically encodes the prediction mode value by performing steps S 9701  and S 9702  described above with reference to  FIG. 147 . Note that the three-dimensional data encoding device may arithmetically encode prediction mode pred_mode after binarizing the prediction mode with a truncated unary code using the number of prediction modes to which a predicted value is assigned. That is, the three-dimensional data encoding device may arithmetically encode the prediction mode value by performing steps S 9721  to S 9723  described above with reference to  FIG. 151 . 
     The three-dimensional data encoding device calculates a predicted value in the prediction mode determined in step S 9743  or the prediction mode set in step S 9745 , and outputs the calculated predicted value (S 9746 ). When using the prediction mode value determined in step S 9743 , the three-dimensional data encoding device calculates the predicted value in the prediction mode represented by the prediction mode value of “2” by linear prediction based on the geometry information of N peripheral three-dimensional points. 
     As shown in  FIG. 154 , the three-dimensional data decoding device first calculates distance d0 between point p1 and point p0 and distance d1 between point p2 and point p1, and calculates absolute difference value distdiff=|d0−d1| (S 9751 ). 
     The three-dimensional data decoding device then determines whether absolute difference value distdiff is less than threshold Thfix or not (S 9752 ). Note that threshold Thfix may be set by decoding the header or the like of the stream. 
     When absolute difference value distdiff is less than threshold Thfix (if Yes in S 9752 ), the three-dimensional data decoding device determines the prediction mode value to be “2” (S 9753 ). 
     On the other hand, when absolute difference value distdiff is greater than or equal to threshold Thfix (if No in S 9752 ), the three-dimensional data decoding device decodes the prediction mode value from the bitstream (S 9754 ). 
     The three-dimensional data decoding device calculates a predicted value in the prediction mode represented by the prediction mode value determined in step S 9753  or the prediction mode value decoded in step S 9754 , and outputs the calculated predicted value (S 9755 ). When using the prediction mode value determined in step S 9753 , the three-dimensional data decoding device calculates the predicted value in the prediction mode represented by the prediction mode value of “2” by linear prediction based on the geometry information of N peripheral three-dimensional points. 
       FIG. 155  is a diagram illustrating an example of a syntax of a header of geometry information. NumNeighborPoint, NumPredMode, Thfix, QP, and unique_point_per_leaf in the syntax in  FIG. 155  will be sequentially described. 
     NumNeighborPoint denotes an upper limit of the number of peripheral points used for generation of a predicted value of geometry information of a three-dimensional point. When number M of peripheral points is less than NumNeighborPoint (M&lt;NumNeighborPoint), a predicted value may be calculated using the M peripheral points in the predicted value calculation process. 
     NumPredMode denotes total number M of prediction modes used for prediction of geometry information. Note that maximum possible value MaxM of the prediction mode count may be defined by a standard or the like. The three-dimensional data encoding device may add the value of (MaxM−M) (0&lt;M&lt;=MaxM) to the header as NumPredMode, and binarize and encode (MaxM−1) with a truncated unary code. Prediction mode count NumPredMode need not be added to the bitstream, and the value of NumPredMode may be defined by profile or level of a standard or the like. The prediction mode count may be defined as NumNeighborPoint+NumPredMode. 
     Thfix is a threshold for determining whether to fix the prediction mode or not. Distance d0 between point p1 and point p0 and distance d1 between point p2 and point p1 used for prediction are calculated, and the prediction mode is fixed to be α if absolute difference value distdiff=|d0−d1| is less than threshold Thfix[i]. α is a prediction mode for calculating a predicted value based on a linear prediction, and is “2” in the embodiment described here. Note that Thfix need not be added to the bitstream, and the value may be defined by profile or level of a standard or the like. 
     QP denotes a quantization parameter used for quantizing geometry information. The three-dimensional data encoding device may calculate a quantization step from the quantization parameter, and quantize geometry information using the calculated quantization step. 
     unique_point_per_leaf is information that indicates whether a duplicated point (a point having the same geometry information as another point) is included in the bitstream or not. When unique_point_per_leaf=1, it shows that there are no duplicated points in the bitstream. When unique_point_per_leaf=0, it shows that there is one or more duplicated points in the bitstream. 
     Note that although the determination of whether to fix the prediction mode or not has been described as being performed using the absolute difference value between distance d0 and distance d1 in this embodiment, the present invention is not limited to this, and the determination may be made in any manner. For example, the determination may be performed by calculating distance d0 between point p1 and point p0. Specifically, it may be determined that point p1 cannot be used for prediction and the prediction mode value may be fixed at “1” (a predicted value of p0) when distance d0 is greater than a threshold, and a prediction mode may be set otherwise. In this way, the encoding efficiency can be improved while reducing the overhead. 
     NumNeighborPoint, NumPredMode, Thfix, and unique_point_per_leaf described above may be entropy-encoded and added to the header. For example, these values may be binarized and arithmetically encoded. These values may be encoded with a fixed length, in order to reduce the processing amount. 
       FIG. 156  is a diagram illustrating an example of a syntax of geometry information. NumOfPoint, child_count, pred_mode, and residual_value[j] in the syntax in  FIG. 156  will be sequentially described. 
     NumOfPoint denotes the total number of three-dimensional points included in a bitstream. 
     child count denotes the number of child nodes of an i-th three-dimensional point (node[i]). 
     pred_mode denotes a prediction mode for encoding or decoding geometry information of the i-th three-dimensional point. pred_mode assumes a value from 0 to M−1 (M denotes the total number of prediction modes). When pred_mode is not in the bitstream (when the condition that distdiff&gt;=Thfix[i] &amp;&amp; NumPredMode&gt;1 is not satisfied), pred_mode may be estimated to be fixed value α. α is a prediction mode for calculating a predicted value based on a linear prediction, and is “2” in the embodiment described here. Note that a is not limited to “2”, and any value of 0 to M−1 may be set as an estimated value. An estimated value in the case where pred_mode is not in the bitstream may be additionally added to the header or the like. pred_mode may be binarized and arithmetically encoded with a truncated unary code using the number of prediction modes to which a predicted value is assigned. 
     Note that when NumPredMode=1, that is, when the prediction mode count is 1, the three-dimensional data encoding device need not encode a prediction mode value representing a prediction mode and may generate a bitstream that includes no prediction mode value. When the three-dimensional data decoding device obtains a bitstream that includes no prediction mode value, the three-dimensional data decoding device may calculate a predicted value of a particular prediction mode in the predicted value calculation. The particular prediction mode is a previously determined prediction mode. 
     residual_value[j] denotes encoded data of a prediction residual between geometry information and a predicted value thereof. residual_value[0] may represent element x of the geometry information, residual_value[1] may represent element y of the geometry information, and residual_value[2] may represent element z of the geometry information. 
       FIG. 157  is a diagram illustrating another example of the syntax of geometry information. The example in  FIG. 157  is a modification of the example in  FIG. 156 . 
     As shown in  FIG. 157 , pred_mode may denote a prediction mode for each of three elements of geometry information (x, y, z). That is, pred_mode[0] denotes a prediction mode for element x, pred_mode[1] denotes a prediction mode for element y, and pred_mode[2] denotes a prediction mode for element z. pred_mode[0], pred_mode[1], and pred_mode[2] may be added to the bitstream. 
     Embodiment 9 
       FIG. 158  is a diagram illustrating an example of a prediction tree used in a three-dimensional data encoding method according to Embodiment 9. 
     In Embodiment 9, unlike Embodiment 8, the depth of each node may be calculated when generating a prediction tree in the prediction tree generation method. 
     For example, the root of the prediction tree may be set at a depth=0, the child nodes of the root are set at a depth=1, and the child nodes of the child nodes may be set at a depth=2. Here, a possible value of pred_mode may be changed according to the value of the depth. That is, in setting the prediction mode, the three-dimensional data encoding device may set a prediction mode for predicting each three-dimensional point based on the depth of the three-dimensional point in the hierarchical structure. For example, pred_mode may be limited to a value smaller than or equal to the value of the depth. That is, the prediction mode value may be set to be a value smaller than or equal to the value of the depth of each three-dimensional point in the hierarchical structure. 
     When pred_mode is binarized and arithmetically encoded with a truncated unary code according to the prediction mode count, pred_mode may be binarized with a truncated unary code using the prediction mode count=min (depth, prediction mode count M). In this way, the bit length of the binary data of pred_mode in the case where depth&lt;M can be reduced, and the encoding efficiency can be improved. 
     An example has been shown where, in the prediction tree generation method, when three-dimensional point A is added to the prediction tree, nearest point B thereof is searched for, and three-dimensional point A is added to the child nodes of three-dimensional point B. Here, as the method of searching for the nearest point, any method can be used. For example, the kd-tree method can be used to search for the nearest point. In that case, the nearest point can be efficiently searched for, and the encoding efficiency can be improved. 
     Alternatively, the nearest neighbor method may be used to search for the nearest point. In that case, the nearest point can be searched for while reducing the processing load, and the processing amount and the encoding efficiency can be balanced. When searching for the nearest point in the nearest neighbor method, a search range may be set. In that case, the processing amount can be reduced. 
     The three-dimensional data encoding device may quantize and encode prediction residual residual_value. For example, the three-dimensional data encoding device may add quantization parameter QP to the header of a slice or the like, quantize residual_value using Qstep calculated from QP, and binarize and arithmetically encode the quantized value. In that case, the three-dimensional data decoding device may decode the geometry information by applying an inverse quantization to the quantized value of residual_value using the same Qstep and adding the result to the predicted value. In that case, the decoded geometry information may be added to the prediction tree. In this way, even when the quantization is applied, the three-dimensional data encoding device or the three-dimensional data decoding device can calculate the predicted value from the decoded geometry information, so that the three-dimensional data encoding device can generate a bitstream that can be properly decoded by the three-dimensional data decoding device. Note that although an example has been shown where the nearest point of a three-dimensional point is searched for and added to the prediction tree when generating the prediction tree, the present invention is not necessarily limited to this, and the prediction tree can be generated in any method or in any order. For example, when the input three-dimensional points are data obtained by lidar, the prediction tree may be generated by adding the three-dimensional points in the order of scanning of lidar. In that case, the prediction precision can be improved, and the encoding efficiency can be improved. 
       FIG. 159  is a diagram illustrating another example of the syntax of geometry information. residual_is_zero, residual_sign, residual_bitcount_minus1, and residual_bit[k] in the syntax in  FIG. 159  will be sequentially described. 
     residual_is_zero is information that indicates whether residual_value is 0 or not. For example, when residual_is_zero=1, it shows that residual_value is 0, and when residual_is_zero=0, it shows that residual_value is not 0. Note that when pred_mode=0 (without prediction, and the predicted value being 0), the possibility that residual_value is 0 is low, so that residual_is_zero need not be encoded and added to the bitstream. When pred_mode=0, the three-dimensional data decoding device need not decode residual_is_zero from the bitstream, and may estimate that residual_is_zero=0. 
     residual_sign is sign information (sign bit) that indicates whether residual_value is positive or negative. For example, when residual_sign=1, it shows that residual_value is negative, and when residual_sign=0, it shows that residual_value is positive. 
     Note that when pred_mode=0, the predicted value is 0, and therefore, residual_value is always positive or 0. Therefore, the three-dimensional data encoding device need not encode residual_sign and add residual_sign to the bitstream. That is, when a prediction mode in which the predicted value is calculated to be 0 is set, the three-dimensional data encoding device need not encode the sign information that indicates whether the prediction residual is positive or negative and may generate a bitstream including no sign information. When pred_mode=0, the three-dimensional data decoding device need not decode residual_sign from the bitstream, and may estimate that residual_sign=0. That is, when the three-dimensional data decoding device obtains a bitstream including no sign information that indicates whether the prediction residual is positive or negative, the three-dimensional data decoding device can regard the prediction residual as 0 or a positive value. 
     residual_bitcount_minus1 indicates a number obtained by subtracting 1 from the bit count of residual_bit. That is, residual_bitcount is equal to a number obtained by adding 1 to residual_bitcount_minus1. 
     residual_bit[k] denotes k-th bit information in the case where the absolute value of residual_value is binarized with a fixed length in accordance with the value of residual_bitcount. 
     Note that when condition A is defined as “unique_point_per_leaf=1 (there is no duplicated point) when geometry information of any one of point p0, point p1, and point p2 is directly used as a predicted value as in prediction mode 1”, all of residual_is_zero[0] for element x, residual_is_zero[1] for element y, and residual_is_zero[2] for element z are not 0 at the same time, and therefore, residual_is_zero for any one element need not be added to the bitstream. 
     For example, when condition A is true, and residual_is_zero[0] and residual_is_zero[1] are 0, the three-dimensional data encoding device need not add residual_is_zero[2] to the bitstream. In that case, the three-dimensional data decoding device may estimate that residual_is_zero[2], which has not been added to the bitstream, is 1. 
     (Modifications) 
     Although an example where a prediction tree is generated using geometry information (x, y, z) of three-dimensional points, and the geometry information is encoded and decoded has been shown in this embodiment, the present invention is not necessarily limited to this. For example, the predictive encoding using the prediction tree may be applied to the encoding of attribute information (such as color or reflectance) of three-dimensional points. The prediction tree generated in the encoding of geometry information may be used in the encoding of attribute information. In that case, a prediction tree does not have to be generated in the encoding of attribute information, and the processing amount can be reduced. 
       FIG. 160  is a diagram illustrating an example of a configuration of a prediction tree used for encoding of both geometry information and attribute information. 
     As shown in  FIG. 160 , each node in this prediction tree includes child_count, g_pred_mode, g_residual_value, a_pred_mode, and a_residual_value. g_pred_mode denotes a prediction mode for geometry information. g_residual_value denotes a prediction residual for geometry information. a_pred_mode denotes a prediction mode for attribute information. a_residual_value denotes a prediction mode for attribute information. 
     Here, child_count may be shared by geometry information and attribute information. In this way, the overhead can be reduced, and the encoding efficiency can be improved. 
     Note that child_count may be independently added for each of geometry information and attribute information. In this way, the three-dimensional data decoding device can independently decode geometry information and attribute information. For example, the three-dimensional data decoding device can decode attribute information alone. 
     Note that the three-dimensional data encoding device may generate a different prediction tree for each of geometry information and attribute information. In this way, the three-dimensional data encoding device can generate an appropriate prediction tree for each of geometry information and attribute information and can improve the encoding efficiency. In that case, the three-dimensional data encoding device may add, to the bitstream, information (such as child_count) required by the three-dimensional data decoding device to reconstruct the prediction tree for each of the geometry information and the attribute information. Note that the three-dimensional data encoding device may add, to the header or the like, identification information that indicates whether or not the prediction tree is to be shared by the geometry information and the attribute information. In this way, whether the prediction tree is to be shared by the geometry information and the attribute information can be adaptively switched, and the balance between the encoding efficiency and the processing amount can be controlled. 
       FIG. 161  is a flowchart illustrating an example of a three-dimensional data encoding method according to a modification of Embodiment 9. 
     The three-dimensional data encoding device generates a prediction tree using geometry information of a plurality of three-dimensional points (S 9761 ). 
     The three-dimensional data encoding device then encodes node information included in each node in the prediction tree and a prediction residual of geometry information (S 9762 ). Specifically, the three-dimensional data encoding device calculates a predicted value for predicting geometry information of each node, calculates a prediction residual, which is the difference between the calculated predicted value and the geometry information of the node, and encodes the node information and the prediction residual of the geometry information. 
     The three-dimensional data encoding device then encodes the node information included in each node in the prediction tree and a prediction residual of attribute information (S 9763 ). Specifically, the three-dimensional data encoding device calculates a predicted value for predicting attribute information of each node, calculates a prediction residual, which is the difference between the calculated predicted value and the attribute information of the node, and encodes the node information and the prediction residual of the attribute information. 
       FIG. 162  is a flowchart illustrating an example of a three-dimensional data decoding method according to a modification of Embodiment 9. 
     The three-dimensional data decoding device decodes node information to reconstruct the prediction tree (S 9771 ). 
     The three-dimensional data decoding device then decodes geometry information of a node (S 9772 ). Specifically, the three-dimensional data decoding device decodes geometry information of each node by calculating a predicted value for the geometry information and summing the calculated predicted value and the obtained prediction residual. 
     The three-dimensional data decoding device then decodes attribute information of a node (S 9773 ). Specifically, the three-dimensional data decoding device decodes attribute information of each node by calculating a predicted value for the attribute information and summing the calculated predicted value and the obtained prediction residual. 
     The three-dimensional data decoding device then determines whether decoding of all nodes is completed or not (S 9774 ). When decoding of all nodes is completed, the three-dimensional data decoding device ends the three-dimensional data decoding method. When decoding of all nodes is not completed, the three-dimensional data decoding device performs steps S 9771  to S 9773  for the node(s) yet to be processed. 
       FIG. 163  is a diagram illustrating an example of a syntax of a header of attribute information. NumNeighborPoint, NumPredMode, Thfix, QP, and unique_point_per_leaf in the syntax in  FIG. 163  will be sequentially described. 
     NumNeighborPoint denotes an upper limit of the number of peripheral points used for generation of a predicted value of attribute information of a three-dimensional point. When number M of peripheral points is less than NumNeighborPoint (M&lt;NumNeighborPoint), a predicted value may be calculated using the M peripheral points in the predicted value calculation process. 
     NumPredMode denotes total number M of prediction modes used for prediction of attribute information. Note that maximum possible value MaxM of the prediction mode count may be defined by a standard or the like. The three-dimensional data encoding device may add the value of (MaxM−M) (0&lt;M&lt;=MaxM) to the header as NumPredMode, and binarize and encode (MaxM−1) with a truncated unary code. Prediction mode count NumPredMode need not be added to the bitstream, and the value of NumPredMode may be defined by profile or level of a standard or the like. The prediction mode count may be defined as NumNeighborPoint+NumPredMode. 
     Thfix is a threshold for determining whether to fix the prediction mode or not. Distance d0 between point p1 and point p0 and distance d1 between point p2 and point p1 used for prediction are calculated, and the prediction mode is fixed to be α if absolute difference value distdiff=|d0−d1| is less than threshold Thfix[i]. α is a prediction mode for calculating a predicted value based on a linear prediction, and is “2” in the embodiment described here. Note that Thfix need not be added to the bitstream, and the value may be defined by profile or level of a standard or the like. 
     QP denotes a quantization parameter used for quantizing attribute information. The three-dimensional data encoding device may calculate a quantization step from the quantization parameter, and quantize attribute information using the calculated quantization step. 
     unique_point_per_leaf is information that indicates whether a duplicated point (a point having the same geometry information as another point) is included in the bitstream or not. When unique_point_per_leaf=1, it shows that there are no duplicated points in the bitstream. When unique_point_per_leaf=0, it shows that there is one or more duplicated points in the bitstream. 
     Note that although the determination of whether to fix the prediction mode or not has been described as being performed using the absolute difference value between distance d0 and distance d1 in this embodiment, the present invention is not limited to this, and the determination may be made in any manner. For example, the determination may be performed by calculating distance d0 between point p1 and point p0. Specifically, it may be determined that point p1 cannot be used for prediction and the prediction mode value may be fixed at “1” (a predicted value of p0) when distance d0 is greater than a threshold, and a prediction mode may be set otherwise. In this way, the encoding efficiency can be improved while reducing the overhead. 
     It is possible that NumNeighborPoint, NumPredMode, Thfix, or unique_point_per_leaf described above is shared with the geometry information and is not added to attribute_header. In this way, the overhead can be reduced. 
     NumNeighborPoint, NumPredMode, Thfix, and unique_point_per_leaf described above may be entropy-encoded and added to the header. For example, these values may be binarized and arithmetically encoded. These values may be encoded with a fixed length, in order to reduce the processing amount. 
       FIG. 164  is a diagram illustrating another example of a syntax of attribute information. NumOfPoint, child_count, pred_mode, dimension, residual_is_zero, residual_sign, residual_bitcount_minus1, and residual_bit[k] in the syntax in  FIG. 164  will be sequentially described. 
     NumOfPoint denotes the total number of three-dimensional points included in a bitstream. NumOfPoint may be the same as NumOfPoint of the geometry information. 
     child_count denotes the number of child nodes of an i-th three-dimensional point (node[i]). Note that this child_count may be the same as child_count of the geometry information. When this child_count is the same as child_count of the geometry information, this child_count need not be added to attribute data. In this way, the overhead can be reduced. 
     pred_mode denotes a prediction mode for encoding or decoding attribute information of the i-th three-dimensional point. pred_mode assumes a value from 0 to M−1 (M denotes the total number of prediction modes). When pred_mode is not in the bitstream (when the conditions that distdiff&gt;=Thfix[i] &amp;&amp; NumPredMode&gt;1 are not satisfied), pred_mode may be estimated to be fixed value α. α is a prediction mode for calculating a predicted value based on a linear prediction, and is “2” in the embodiment described here. Note that α is not limited to “2”, and any value of 0 to M−1 may be set as an estimated value. An estimated value in the case where pred_mode is not in the bitstream may be additionally added to the header or the like. pred_mode may be binarized and arithmetically encoded with a truncated unary code using the number of prediction modes to which a predicted value is assigned. 
     dimension is information that indicates the dimension of the attribute information. dimension may be added to the header, such as SPS. For example, dimension may be set at “3” when the attribute information is color, and may be set at “1” when the attribute information is reflectance. 
     residual_is_zero is information that indicates whether residual_value is 0 or not. For example, when residual_is_zero=1, it shows that residual_value is 0, and when residual_is_zero=0, it shows that residual_value is not 0. Note that when pred_mode=0 (without prediction, and the predicted value being 0), the possibility that residual_value is 0 is low, so that residual_is_zero need not be encoded and added to the bitstream. When pred_mode=0, the three-dimensional data decoding device need not decode residual_is_zero from the bitstream, and may estimate that residual_is_zero=0. 
     residual_sign is sign information (sign bit) that indicates whether residual_value is positive or negative. For example, when residual_sign=1, it shows that residual_value is negative, and when residual_sign=0, it shows that residual_value is positive. 
     Note that when pred_mode=0 (without prediction, the predicted value being 0), residual_value is always positive, and therefore, the three-dimensional data encoding device need not encode residual_sign and add residual_sign to the bitstream. That is, when the prediction residual is positive, the three-dimensional data encoding device need not encode the sign information that indicates whether the prediction residual is positive or negative and may generate a bitstream including no sign information, and when the prediction residual is negative, the three-dimensional data encoding device may generate a bitstream including the sign information. When pred_mode=0, the three-dimensional data decoding device need not decode residual_sign from the bitstream, and may estimate that residual_sign=0. That is, the three-dimensional data decoding device can regard the prediction residual as a positive value when the three-dimensional data decoding device obtains a bitstream including no sign information that indicates whether the prediction residual is positive or negative, and can regard the prediction residual as a negative value when the three-dimensional data decoding device obtains a bitstream including the sign information. 
     residual_bitcount_minus1 indicates a number obtained by subtracting 1 from the bit count of residual_bit. That is, residual_bitcount is equal to a number obtained by adding 1 to residual_bitcount_minus1. 
     residual_bit[k] denotes k-th bit information in the case where the absolute value of residual_value is binarized with a fixed length in accordance with the value of residual_bitcount. 
     Note that when condition A is defined as “unique_point_per_leaf=1 (there is no duplicated point) when attribute information of any one of point p0, point p1, and point p2 is directly used as a predicted value as in prediction mode 1”, all of residual_is_zero[0] for element x, residual_is_zero[1] for element y, and residual_is_zero[2] for element z are not 0 at the same time, and therefore, residual_is_zero for any one element need not be added to the bitstream. 
     For example, when condition A is true, and residual_is_zero[0] and residual_is_zero[1] are 0, the three-dimensional data encoding device need not add residual_is_zero[2] to the bitstream. In that case, the three-dimensional data decoding device may estimate that residual_is_zero[2], which has not been added to the bitstream, is 1. 
       FIG. 165  is a diagram illustrating an example of a syntax of geometry information and attribute information. 
     As shown in  FIG. 165 , encoded information of geometry information and attribute information may be stored in one data unit. Here, g_* represents encoded information concerning geometry, and a_* represents encoded information concerning attribute information. In this way, geometry information and attribute information can be decoded at the same time. 
     As described above, the three-dimensional data encoding device according to one aspect of the present embodiment performs the process shown by  FIG. 166 . The three-dimensional encoding device performs a three-dimensional data encoding method for encoding three-dimensional points having a hierarchical structure. The three-dimensional data encoding device sets one prediction mode out of two or more prediction modes each for calculating a predicted value of an item of first geometry information of a first three-dimensional point using one or more items of second geometry information of one or more second three-dimensional points surrounding the first three-dimensional point (S 9781 ). Next, the three-dimensional data encoding device calculates a predicted value of the one prediction mode set (S 9782 ). Then, the three-dimensional data encoding device calculates a prediction residual that is a difference between the item of first geometry information and the predicted value calculated (S 9783 ). After that, the three-dimensional data encoding device generates a first bitstream including the one prediction mode set and the prediction residual (S 9784 ). In the setting (S 9781 ), the one prediction mode is set based on a depth of the first three-dimensional point in the hierarchical structure. 
     According to this, geometry information can be encoded using a predicted value in one prediction mode among two or more prediction modes that is set based on the depth in the hierarchical structure, so that the encoding efficiency of the geometry information can be improved. 
     For example, in the setting (S 9784 ), the three-dimensional data encoding device sets a prediction mode value that is less than or equal to a value of the depth of the first three-dimensional point in the hierarchical structure. The prediction mode value indicates the one prediction mode. 
     For example, the first bitstream further includes a prediction mode count indicating a total number of the two or more prediction modes. 
     For example, in the generating (S 9784 ), the three-dimensional data encoding device encodes a prediction mode value indicating the one prediction mode set using the prediction mode count. The first bitstream includes the prediction mode value encoded as the one prediction mode set. 
     For example, in the generating (S 9784 ), the three-dimensional data encoding device encodes the prediction mode value using a truncated unary code in which the prediction mode count is set as a maximum value. Therefore, the code amount of the prediction mode value can be reduced. 
     For example, each of the item of first geometry information and the one or more items of second geometry information includes three elements. In the setting (S 9781 ), the three-dimensional data encoding device sets, for the three elements in common, a prediction mode for calculating a predicted value of each of the three elements included in the item of first geometry information. Therefore, the code amount of the prediction mode value can be reduced. 
     For example, each of the item of first geometry information and the one or more items of second geometry information includes three elements. In the setting (S 9781 ), the three-dimensional data encoding device sets, for the three elements independently of each other, a prediction mode for calculating a predicted value of each of the three elements included in the item of first geometry information. Therefore, the three-dimensional data decoding device can independently decode each element. 
     For example, each of the item of first geometry information and the one or more items of second geometry information includes three elements. In the setting (S 9781 ), the three-dimensional data encoding device sets, for two elements among the three elements in common, a prediction mode for calculating a predicted value of each of the three elements included in the item of first geometry information, and sets the prediction mode for a remaining one element independently of the two elements. Therefore, the code amount of the prediction mode value can be reduced for the two elements. Therefore, the three-dimensional data decoding device can independently decode the remaining one element. 
     For example, in the generating (S 9784 ), when the prediction mode count is 1, the three-dimensional data encoding device does not encode the prediction mode value, and generates a second bitstream not including the prediction mode value indicating the one prediction mode. Therefore, the code amount of the bitstream can be reduced. 
     For example, in the generating (S 9784 ), when a prediction mode in which the predicted value calculated in the calculating is 0 is set, the three-dimensional data encoding device does not encode an item of positive and negative information, and generates a third bitstream not including the item of positive and negative information, the item of positive and negative information indicating whether the prediction residual is positive or negative. Therefore, the code amount of the bitstream can be reduced. 
     For example, the three-dimensional data encoding device includes a processor and memory, and the processor performs the above-described process using the memory. 
     The three-dimensional data decoding device according to one aspect of the present embodiment performs the process shown by  FIG. 167 . The three-dimensional data decoding device performs a three-dimensional decoding method for decoding three-dimensional points having a hierarchical structure. The three-dimensional data decoding device obtains a first bitstream including an encoded prediction mode of a first three-dimensional point among the three-dimensional points and an encoded prediction residual (S 9791 ). Next, the three-dimensional data decoding device decodes a prediction mode value indicating the encoded prediction mode, and the encoded prediction residual (S 9792 ). Then, the three-dimensional data decoding device calculates a predicted value of a prediction mode obtained in the decoding and indicated by the prediction mode value (S 9793 ). After that, the three-dimensional data decoding device calculates an item of first geometry information of the first three-dimensional point by adding the predicted value and a prediction residual obtained in the decoding (S 9794 ). The encoded prediction mode included in the first bitstream is a prediction mode set based on a depth of the first three-dimensional point in the hierarchical structure. 
     According to this, geometry information can be encoded using a predicted value in one prediction mode among two or more prediction modes that is set based on the depth in the hierarchical structure, so that the encoding efficiency of the geometry information can be improved. 
     For example, the prediction mode value indicating the encoded prediction mode included in the first bitstream is less than or equal to a value of the depth of the first three-dimensional point in the hierarchical structure. 
     For example, the first bitstream includes a prediction mode count indicating a total number of two or more prediction modes. 
     For example, in the decoding (S 9792 ), the three-dimensional data decoding device decodes the prediction mode value using a truncated unary code in which the total number of the two or more prediction modes is set as a maximum value. 
     For example, each of the item of first geometry information and one or more items of second geometry information of one or more second three-dimensional points includes three elements, the one or more second three-dimensional points surrounding the first three-dimensional point. A prediction mode for calculating a predicted value of each of the three elements included in the item of first geometry information is set for the three elements in common. 
     For example, each of the item of first geometry information and one or more items of second geometry information of one or more second three-dimensional points includes three elements, the one or more second three-dimensional points surrounding the first three-dimensional point. A prediction mode for calculating a predicted value of each of the three elements included in the item of first geometry information is set for the three elements independently of each other. 
     For example, each of the item of first geometry information and one or more items of second geometry information of one or more second three-dimensional points includes three elements, the one or more second three-dimensional points surrounding the first three-dimensional point. A prediction mode for calculating a predicted value of each of the three elements included in the item of first geometry information is set for two elements among the three elements in common, and is set for a remaining one element independently of the two elements. 
     For example, in the obtaining (S 9791 ), when a second bitstream not including the prediction mode value is obtained in the obtaining, the three-dimensional data decoding device calculates a predicted value of a specific prediction mode in the calculating of the predicted value. 
     For example, in the obtaining (S 9791 ), when a third bitstream not including positive and negative information is obtained in the obtaining, the three-dimensional data decoding device uses the prediction residual as 0 or a positive number in the calculating of the item of first geometry information (S 9794 ). 
     For example, the three-dimensional data decoding device includes a processor and memory, and the processor performs the above-described process using the memory. 
     Embodiment 10 
     The following describes the structure of three-dimensional data creation device  810  according to the present embodiment.  FIG. 168  is a block diagram of an exemplary structure of three-dimensional data creation device  810  according to the present embodiment. Such three-dimensional data creation device  810  is equipped, for example, in a vehicle. Three-dimensional data creation device  810  transmits and receives three-dimensional data to and from an external cloud-based traffic monitoring system, a preceding vehicle, or a following vehicle, and creates and stores three-dimensional data. 
     Three-dimensional data creation device  810  includes data receiver  811 , communication unit  812 , reception controller  813 , format converter  814 , a plurality of sensors  815 , three-dimensional data creator  816 , three-dimensional data synthesizer  817 , three-dimensional data storage  818 , communication unit  819 , transmission controller  820 , format converter  821 , and data transmitter  822 . 
     Data receiver  811  receives three-dimensional data  831  from a cloud-based traffic monitoring system or a preceding vehicle. Three-dimensional data  831  includes, for example, information on a region undetectable by sensors  815  of the own vehicle, such as a point cloud, visible light video, depth information, sensor position information, and speed information. 
     Communication unit  812  communicates with the cloud-based traffic monitoring system or the preceding vehicle to transmit a data transmission request, etc. to the cloud-based traffic monitoring system or the preceding vehicle. 
     Reception controller  813  exchanges information, such as information on supported formats, with a communications partner via communication unit  812  to establish communication with the communications partner. 
     Format converter  814  applies format conversion, etc. on three-dimensional data  831  received by data receiver  811  to generate three-dimensional data  832 . Format converter  814  also decompresses or decodes three-dimensional data  831  when three-dimensional data  831  is compressed or encoded. 
     A plurality of sensors  815  are a group of sensors, such as visible light cameras and infrared cameras, that obtain information on the outside of the vehicle and generate sensor information  833 . Sensor information  833  is, for example, three-dimensional data such as a point cloud (point group data), when sensors  815  are laser sensors such as LiDARs. Note that a single sensor may serve as a plurality of sensors  815 . 
     Three-dimensional data creator  816  generates three-dimensional data  834  from sensor information  833 . Three-dimensional data  834  includes, for example, information such as a point cloud, visible light video, depth information, sensor position information, and speed information. 
     Three-dimensional data synthesizer  817  synthesizes three-dimensional data  834  created on the basis of sensor information  833  of the own vehicle with three-dimensional data  832  created by the cloud-based traffic monitoring system or the preceding vehicle, etc., thereby forming three-dimensional data  835  of a space that includes the space ahead of the preceding vehicle undetectable by sensors  815  of the own vehicle. 
     Three-dimensional data storage  818  stores generated three-dimensional data  835 , etc. 
     Communication unit  819  communicates with the cloud-based traffic monitoring system or the following vehicle to transmit a data transmission request, etc. to the cloud-based traffic monitoring system or the following vehicle. 
     Transmission controller  820  exchanges information such as information on supported formats with a communications partner via communication unit  819  to establish communication with the communications partner. Transmission controller  820  also determines a transmission region, which is a space of the three-dimensional data to be transmitted, on the basis of three-dimensional data formation information on three-dimensional data  832  generated by three-dimensional data synthesizer  817  and the data transmission request from the communications partner. 
     More specifically, transmission controller  820  determines a transmission region that includes the space ahead of the own vehicle undetectable by a sensor of the following vehicle, in response to the data transmission request from the cloud-based traffic monitoring system or the following vehicle. Transmission controller  820  judges, for example, whether a space is transmittable or whether the already transmitted space includes an update, on the basis of the three-dimensional data formation information to determine a transmission region. For example, transmission controller  820  determines, as a transmission region, a region that is: a region specified by the data transmission request; and a region, corresponding three-dimensional data  835  of which is present. Transmission controller  820  then notifies format converter  821  of the format supported by the communications partner and the transmission region. 
     Of three-dimensional data  835  stored in three-dimensional data storage  818 , format converter  821  converts three-dimensional data  836  of the transmission region into the format supported by the receiver end to generate three-dimensional data  837 . Note that format converter  821  may compress or encode three-dimensional data  837  to reduce the data amount. 
     Data transmitter  822  transmits three-dimensional data  837  to the cloud-based traffic monitoring system or the following vehicle. Such three-dimensional data  837  includes, for example, information on a blind spot, which is a region hidden from view of the following vehicle, such as a point cloud ahead of the own vehicle, visible light video, depth information, and sensor position information. 
     Note that an example has been described in which format converter  814  and format converter  821  perform format conversion, etc., but format conversion may not be performed. 
     With the above structure, three-dimensional data creation device  810  obtains, from an external device, three-dimensional data  831  of a region undetectable by sensors  815  of the own vehicle, and synthesizes three-dimensional data  831  with three-dimensional data  834  that is based on sensor information  833  detected by sensors  815  of the own vehicle, thereby generating three-dimensional data  835 . Three-dimensional data creation device  810  is thus capable of generating three-dimensional data of a range undetectable by sensors  815  of the own vehicle. 
     Three-dimensional data creation device  810  is also capable of transmitting, to the cloud-based traffic monitoring system or the following vehicle, etc., three-dimensional data of a space that includes the space ahead of the own vehicle undetectable by a sensor of the following vehicle, in response to the data transmission request from the cloud-based traffic monitoring system or the following vehicle. 
     The following describes the steps performed by three-dimensional data creation device  810  of transmitting three-dimensional data to a following vehicle.  FIG. 169  is a flowchart showing exemplary steps performed by three-dimensional data creation device  810  of transmitting three-dimensional data to a cloud-based traffic monitoring system or a following vehicle. 
     First, three-dimensional data creation device  810  generates and updates three-dimensional data  835  of a space that includes space on the road ahead of the own vehicle (S 801 ). More specifically, three-dimensional data creation device  810  synthesizes three-dimensional data  834  created on the basis of sensor information  833  of the own vehicle with three-dimensional data  831  created by the cloud-based traffic monitoring system or the preceding vehicle, etc., for example, thereby forming three-dimensional data  835  of a space that also includes the space ahead of the preceding vehicle undetectable by sensors  815  of the own vehicle. 
     Three-dimensional data creation device  810  then judges whether any change has occurred in three-dimensional data  835  of the space included in the space already transmitted (S 802 ). 
     When a change has occurred in three-dimensional data  835  of the space included in the space already transmitted due to, for example, a vehicle or a person entering such space from outside (Yes in S 802 ), three-dimensional data creation device  810  transmits, to the cloud-based traffic monitoring system or the following vehicle, the three-dimensional data that includes three-dimensional data  835  of the space in which the change has occurred (S 803 ). 
     Three-dimensional data creation device  810  may transmit three-dimensional data in which a change has occurred, at the same timing of transmitting three-dimensional data that is transmitted at a predetermined time interval, or may transmit three-dimensional data in which a change has occurred soon after the detection of such change. Stated differently, three-dimensional data creation device  810  may prioritize the transmission of three-dimensional data of the space in which a change has occurred to the transmission of three-dimensional data that is transmitted at a predetermined time interval. 
     Also, three-dimensional data creation device  810  may transmit, as three-dimensional data of a space in which a change has occurred, the whole three-dimensional data of the space in which such change has occurred, or may transmit only a difference in the three-dimensional data (e.g., information on three-dimensional points that have appeared or vanished, or information on the displacement of three-dimensional points). 
     Three-dimensional data creation device  810  may also transmit, to the following vehicle, meta-data on a risk avoidance behavior of the own vehicle such as hard breaking warning, before transmitting three-dimensional data of the space in which a change has occurred. This enables the following vehicle to recognize at an early stage that the preceding vehicle is to perform hard braking, etc., and thus to start performing a risk avoidance behavior at an early stage such as speed reduction. 
     When no change has occurred in three-dimensional data  835  of the space included in the space already transmitted (No in S 802 ), or after step S 803 , three-dimensional data creation device  810  transmits, to the cloud-based traffic monitoring system or the following vehicle, three-dimensional data of the space included in the space having a predetermined shape and located ahead of the own vehicle by distance L (S 804 ). 
     The processes of step S 801  through step S 804  are repeated, for example at a predetermined time interval. 
     When three-dimensional data  835  of the current space to be transmitted includes no difference from the three-dimensional map, three-dimensional data creation device  810  may not transmit three-dimensional data  837  of the space. 
     In the present embodiment, a client device transmits sensor information obtained through a sensor to a server or another client device. 
     A structure of a system according to the present embodiment will first be described.  FIG. 170  is a diagram showing the structure of a transmission/reception system of a three-dimensional map and sensor information according to the present embodiment. This system includes server  901 , and client devices  902 A and  902 B. Note that client devices  902 A and  902 B are also referred to as client device  902  when no particular distinction is made therebetween. 
     Client device  902  is, for example, a vehicle-mounted device equipped in a mobile object such as a vehicle. Server  901  is, for example, a cloud-based traffic monitoring system, and is capable of communicating with the plurality of client devices  902 . 
     Server  901  transmits the three-dimensional map formed by a point cloud to client device  902 . Note that a structure of the three-dimensional map is not limited to a point cloud, and may also be another structure expressing three-dimensional data such as a mesh structure. 
     Client device  902  transmits the sensor information obtained by client device  902  to server  901 . The sensor information includes, for example, at least one of information obtained by LiDAR, a visible light image, an infrared image, a depth image, sensor position information, or sensor speed information. 
     The data to be transmitted and received between server  901  and client device  902  may be compressed in order to reduce data volume, and may also be transmitted uncompressed in order to maintain data precision. When compressing the data, it is possible to use a three-dimensional compression method on the point cloud based on, for example, an octree structure. It is possible to use a two-dimensional image compression method on the visible light image, the infrared image, and the depth image. The two-dimensional image compression method is, for example, MPEG-4 AVC or HEVC standardized by MPEG. 
     Server  901  transmits the three-dimensional map managed by server  901  to client device  902  in response to a transmission request for the three-dimensional map from client device  902 . Note that server  901  may also transmit the three-dimensional map without waiting for the transmission request for the three-dimensional map from client device  902 . For example, server  901  may broadcast the three-dimensional map to at least one client device  902  located in a predetermined space. Server  901  may also transmit the three-dimensional map suited to a position of client device  902  at fixed time intervals to client device  902  that has received the transmission request once. Server  901  may also transmit the three-dimensional map managed by server  901  to client device  902  every time the three-dimensional map is updated. 
     Client device  902  sends the transmission request for the three-dimensional map to server  901 . For example, when client device  902  wants to perform the self-location estimation during traveling, client device  902  transmits the transmission request for the three-dimensional map to server  901 . 
     Note that in the following cases, client device  902  may send the transmission request for the three-dimensional map to server  901 . Client device  902  may send the transmission request for the three-dimensional map to server  901  when the three-dimensional map stored by client device  902  is old. For example, client device  902  may send the transmission request for the three-dimensional map to server  901  when a fixed period has passed since the three-dimensional map is obtained by client device  902 . 
     Client device  902  may also send the transmission request for the three-dimensional map to server  901  before a fixed time when client device  902  exits a space shown in the three-dimensional map stored by client device  902 . For example, client device  902  may send the transmission request for the three-dimensional map to server  901  when client device  902  is located within a predetermined distance from a boundary of the space shown in the three-dimensional map stored by client device  902 . When a movement path and a movement speed of client device  902  are understood, a time when client device  902  exits the space shown in the three-dimensional map stored by client device  902  may be predicted based on the movement path and the movement speed of client device  902 . 
     Client device  902  may also send the transmission request for the three-dimensional map to server  901  when an error during alignment of the three-dimensional data and the three-dimensional map created from the sensor information by client device  902  is at least at a fixed level. 
     Client device  902  transmits the sensor information to server  901  in response to a transmission request for the sensor information from server  901 . Note that client device  902  may transmit the sensor information to server  901  without waiting for the transmission request for the sensor information from server  901 . For example, client device  902  may periodically transmit the sensor information during a fixed period when client device  902  has received the transmission request for the sensor information from server  901  once. Client device  902  may determine that there is a possibility of a change in the three-dimensional map of a surrounding area of client device  902  having occurred, and transmit this information and the sensor information to server  901 , when the error during alignment of the three-dimensional data created by client device  902  based on the sensor information and the three-dimensional map obtained from server  901  is at least at the fixed level. 
     Server  901  sends a transmission request for the sensor information to client device  902 . For example, server  901  receives position information, such as GPS information, about client device  902  from client device  902 . Server  901  sends the transmission request for the sensor information to client device  902  in order to generate a new three-dimensional map, when it is determined that client device  902  is approaching a space in which the three-dimensional map managed by server  901  contains little information, based on the position information about client device  902 . Server  901  may also send the transmission request for the sensor information, when wanting to (i) update the three-dimensional map, (ii) check road conditions during snowfall, a disaster, or the like, or (iii) check traffic congestion conditions, accident/incident conditions, or the like. 
     Client device  902  may set an amount of data of the sensor information to be transmitted to server  901  in accordance with communication conditions or bandwidth during reception of the transmission request for the sensor information to be received from server  901 . Setting the amount of data of the sensor information to be transmitted to server  901  is, for example, increasing/reducing the data itself or appropriately selecting a compression method. 
       FIG. 171  is a block diagram showing an example structure of client device  902 . Client device  902  receives the three-dimensional map formed by a point cloud and the like from server  901 , and estimates a self-location of client device  902  using the three-dimensional map created based on the sensor information of client device  902 . Client device  902  transmits the obtained sensor information to server  901 . 
     Client device  902  includes data receiver  1011 , communication unit  1012 , reception controller  1013 , format converter  1014 , sensors  1015 , three-dimensional data creator  1016 , three-dimensional image processor  1017 , three-dimensional data storage  1018 , format converter  1019 , communication unit  1020 , transmission controller  1021 , and data transmitter  1022 . 
     Data receiver  1011  receives three-dimensional map  1031  from server  901 . Three-dimensional map  1031  is data that includes a point cloud such as a WLD or a SWLD. Three-dimensional map  1031  may include compressed data or uncompressed data. 
     Communication unit  1012  communicates with server  901  and transmits a data transmission request (e.g., transmission request for three-dimensional map) to server  901 . 
     Reception controller  1013  exchanges information, such as information on supported formats, with a communications partner via communication unit  1012  to establish communication with the communications partner. 
     Format converter  1014  performs a format conversion and the like on three-dimensional map  1031  received by data receiver  1011  to generate three-dimensional map  1032 . Format converter  1014  also performs a decompression or decoding process when three-dimensional map  1031  is compressed or encoded. Note that format converter  1014  does not perform the decompression or decoding process when three-dimensional map  1031  is uncompressed data. 
     Sensors  1015  are a group of sensors, such as LiDARs, visible light cameras, infrared cameras, or depth sensors that obtain information about the outside of a vehicle equipped with client device  902 , and generate sensor information  1033 . Sensor information  1033  is, for example, three-dimensional data such as a point cloud (point group data) when sensors  1015  are laser sensors such as LiDARs. Note that a single sensor may serve as sensors  1015 . 
     Three-dimensional data creator  1016  generates three-dimensional data  1034  of a surrounding area of the own vehicle based on sensor information  1033 . For example, three-dimensional data creator  1016  generates point cloud data with color information on the surrounding area of the own vehicle using information obtained by LiDAR and visible light video obtained by a visible light camera. 
     Three-dimensional image processor  1017  performs a self-location estimation process and the like of the own vehicle, using (i) the received three-dimensional map  1032  such as a point cloud, and (ii) three-dimensional data  1034  of the surrounding area of the own vehicle generated using sensor information  1033 . Note that three-dimensional image processor  1017  may generate three-dimensional data  1035  about the surroundings of the own vehicle by merging three-dimensional map  1032  and three-dimensional data  1034 , and may perform the self-location estimation process using the created three-dimensional data  1035 . 
     Three-dimensional data storage  1018  stores three-dimensional map  1032 , three-dimensional data  1034 , three-dimensional data  1035 , and the like. 
     Format converter  1019  generates sensor information  1037  by converting sensor information  1033  to a format supported by a receiver end. Note that format converter  1019  may reduce the amount of data by compressing or encoding sensor information  1037 . Format converter  1019  may omit this process when format conversion is not necessary. Format converter  1019  may also control the amount of data to be transmitted in accordance with a specified transmission range. 
     Communication unit  1020  communicates with server  901  and receives a data transmission request (transmission request for sensor information) and the like from server  901 . 
     Transmission controller  1021  exchanges information, such as information on supported formats, with a communications partner via communication unit  1020  to establish communication with the communications partner. 
     Data transmitter  1022  transmits sensor information  1037  to server  901 . Sensor information  1037  includes, for example, information obtained through sensors  1015 , such as information obtained by LiDAR, a luminance image obtained by a visible light camera, an infrared image obtained by an infrared camera, a depth image obtained by a depth sensor, sensor position information, and sensor speed information. 
     A structure of server  901  will be described next.  FIG. 172  is a block diagram showing an example structure of server  901 . Server  901  transmits sensor information from client device  902  and creates three-dimensional data based on the received sensor information. Server  901  updates the three-dimensional map managed by server  901  using the created three-dimensional data. Server  901  transmits the updated three-dimensional map to client device  902  in response to a transmission request for the three-dimensional map from client device  902 . 
     Server  901  includes data receiver  1111 , communication unit  1112 , reception controller  1113 , format converter  1114 , three-dimensional data creator  1116 , three-dimensional data merger  1117 , three-dimensional data storage  1118 , format converter  1119 , communication unit  1120 , transmission controller  1121 , and data transmitter  1122 . 
     Data receiver  1111  receives sensor information  1037  from client device  902 . Sensor information  1037  includes, for example, information obtained by LiDAR, a luminance image obtained by a visible light camera, an infrared image obtained by an infrared camera, a depth image obtained by a depth sensor, sensor position information, sensor speed information, and the like. 
     Communication unit  1112  communicates with client device  902  and transmits a data transmission request (e.g., transmission request for sensor information) and the like to client device  902 . 
     Reception controller  1113  exchanges information, such as information on supported formats, with a communications partner via communication unit  1112  to establish communication with the communications partner. 
     Format converter  1114  generates sensor information  1132  by performing a decompression or decoding process when received sensor information  1037  is compressed or encoded. Note that format converter  1114  does not perform the decompression or decoding process when sensor information  1037  is uncompressed data. 
     Three-dimensional data creator  1116  generates three-dimensional data  1134  of a surrounding area of client device  902  based on sensor information  1132 . For example, three-dimensional data creator  1116  generates point cloud data with color information on the surrounding area of client device  902  using information obtained by LiDAR and visible light video obtained by a visible light camera. 
     Three-dimensional data merger  1117  updates three-dimensional map  1135  by merging three-dimensional data  1134  created based on sensor information  1132  with three-dimensional map  1135  managed by server  901 . 
     Three-dimensional data storage  1118  stores three-dimensional map  1135  and the like. 
     Format converter  1119  generates three-dimensional map  1031  by converting three-dimensional map  1135  to a format supported by the receiver end. Note that format converter  1119  may reduce the amount of data by compressing or encoding three-dimensional map  1135 . Format converter  1119  may omit this process when format conversion is not necessary. Format converter  1119  may also control the amount of data to be transmitted in accordance with a specified transmission range. 
     Communication unit  1120  communicates with client device  902  and receives a data transmission request (transmission request for three-dimensional map) and the like from client device  902 . 
     Transmission controller  1121  exchanges information, such as information on supported formats, with a communications partner via communication unit  1120  to establish communication with the communications partner. 
     Data transmitter  1122  transmits three-dimensional map  1031  to client device  902 . Three-dimensional map  1031  is data that includes a point cloud such as a WLD or a SWLD. Three-dimensional map  1031  may include one of compressed data and uncompressed data. 
     An operational flow of client device  902  will be described next.  FIG. 173  is a flowchart of an operation when client device  902  obtains the three-dimensional map. 
     Client device  902  first requests server  901  to transmit the three-dimensional map (point cloud, etc.) (S 1001 ). At this point, by also transmitting the position information about client device  902  obtained through GPS and the like, client device  902  may also request server  901  to transmit a three-dimensional map relating to this position information. 
     Client device  902  next receives the three-dimensional map from server  901  (S 1002 ). When the received three-dimensional map is compressed data, client device  902  decodes the received three-dimensional map and generates an uncompressed three-dimensional map (S 1003 ). 
     Client device  902  next creates three-dimensional data  1034  of the surrounding area of client device  902  using sensor information  1033  obtained by sensors  1015  (S 1004 ). Client device  902  next estimates the self-location of client device  902  using three-dimensional map  1032  received from server  901  and three-dimensional data  1034  created using sensor information  1033  (S 1005 ). 
       FIG. 174  is a flowchart of an operation when client device  902  transmits the sensor information. Client device  902  first receives a transmission request for the sensor information from server  901  (S 1011 ). Client device  902  that has received the transmission request transmits sensor information  1037  to server  901  (S 1012 ). Note that client device  902  may generate sensor information  1037  by compressing each piece of information using a compression method suited to each piece of information, when sensor information  1033  includes a plurality of pieces of information obtained by sensors  1015 . 
     An operational flow of server  901  will be described next.  FIG. 175  is a flowchart of an operation when server  901  obtains the sensor information. Server  901  first requests client device  902  to transmit the sensor information (S 1021 ). Server  901  next receives sensor information  1037  transmitted from client device  902  in accordance with the request (S 1022 ). Server  901  next creates three-dimensional data  1134  using the received sensor information  1037  (S 1023 ). Server  901  next reflects the created three-dimensional data  1134  in three-dimensional map  1135  (S 1024 ). 
       FIG. 176  is a flowchart of an operation when server  901  transmits the three-dimensional map. Server  901  first receives a transmission request for the three-dimensional map from client device  902  (S 1031 ). Server  901  that has received the transmission request for the three-dimensional map transmits the three-dimensional map to client device  902  (S 1032 ). At this point, server  901  may extract a three-dimensional map of a vicinity of client device  902  along with the position information about client device  902 , and transmit the extracted three-dimensional map. Server  901  may compress the three-dimensional map formed by a point cloud using, for example, an octree structure compression method, and transmit the compressed three-dimensional map. 
     The following describes variations of the present embodiment. 
     Server  901  creates three-dimensional data  1134  of a vicinity of a position of client device  902  using sensor information  1037  received from client device  902 . Server  901  next calculates a difference between three-dimensional data  1134  and three-dimensional map  1135 , by matching the created three-dimensional data  1134  with three-dimensional map  1135  of the same area managed by server  901 . Server  901  determines that a type of anomaly has occurred in the surrounding area of client device  902 , when the difference is greater than or equal to a predetermined threshold. For example, it is conceivable that a large difference occurs between three-dimensional map  1135  managed by server  901  and three-dimensional data  1134  created based on sensor information  1037 , when land subsidence and the like occurs due to a natural disaster such as an earthquake. 
     Sensor information  1037  may include information indicating at least one of a sensor type, a sensor performance, and a sensor model number. Sensor information  1037  may also be appended with a class ID and the like in accordance with the sensor performance. For example, when sensor information  1037  is obtained by LiDAR, it is conceivable to assign identifiers to the sensor performance. A sensor capable of obtaining information with precision in units of several millimeters is class  1 , a sensor capable of obtaining information with precision in units of several centimeters is class  2 , and a sensor capable of obtaining information with precision in units of several meters is class  3 . Server  901  may estimate sensor performance information and the like from a model number of client device  902 . For example, when client device  902  is equipped in a vehicle, server  901  may determine sensor specification information from a type of the vehicle. In this case, server  901  may obtain information on the type of the vehicle in advance, and the information may also be included in the sensor information. Server  901  may change a degree of correction with respect to three-dimensional data  1134  created using sensor information  1037 , using obtained sensor information  1037 . For example, when the sensor performance is high in precision (class  1 ), server  901  does not correct three-dimensional data  1134 . When the sensor performance is low in precision (class  3 ), server  901  corrects three-dimensional data  1134  in accordance with the precision of the sensor. For example, server  901  increases the degree (intensity) of correction with a decrease in the precision of the sensor. 
     Server  901  may simultaneously send the transmission request for the sensor information to the plurality of client devices  902  in a certain space. Server  901  does not need to use all of the sensor information for creating three-dimensional data  1134  and may, for example, select sensor information to be used in accordance with the sensor performance, when having received a plurality of pieces of sensor information from the plurality of client devices  902 . For example, when updating three-dimensional map  1135 , server  901  may select high-precision sensor information (class  1 ) from among the received plurality of pieces of sensor information, and create three-dimensional data  1134  using the selected sensor information. 
     Server  901  is not limited to only being a server such as a cloud-based traffic monitoring system, and may also be another (vehicle-mounted) client device.  FIG. 177  is a diagram of a system structure in this case. 
     For example, client device  902 C sends a transmission request for sensor information to client device  902 A located nearby, and obtains the sensor information from client device  902 A. Client device  902 C then creates three-dimensional data using the obtained sensor information of client device  902 A, and updates a three-dimensional map of client device  902 C. This enables client device  902 C to generate a three-dimensional map of a space that can be obtained from client device  902 A, and fully utilize the performance of client device  902 C. For example, such a case is conceivable when client device  902 C has high performance. 
     In this case, client device  902 A that has provided the sensor information is given rights to obtain the high-precision three-dimensional map generated by client device  902 C. Client device  902 A receives the high-precision three-dimensional map from client device  902 C in accordance with these rights. 
     Server  901  may send the transmission request for the sensor information to the plurality of client devices  902  (client device  902 A and client device  902 B) located nearby client device  902 C. When a sensor of client device  902 A or client device  902 B has high performance, client device  902 C is capable of creating the three-dimensional data using the sensor information obtained by this high-performance sensor. 
       FIG. 178  is a block diagram showing a functionality structure of server  901  and client device  902 . Server  901  includes, for example, three-dimensional map compression/decoding processor  1201  that compresses and decodes the three-dimensional map and sensor information compression/decoding processor  1202  that compresses and decodes the sensor information. 
     Client device  902  includes three-dimensional map decoding processor  1211  and sensor information compression processor  1212 . Three-dimensional map decoding processor  1211  receives encoded data of the compressed three-dimensional map, decodes the encoded data, and obtains the three-dimensional map. Sensor information compression processor  1212  compresses the sensor information itself instead of the three-dimensional data created using the obtained sensor information, and transmits the encoded data of the compressed sensor information to server  901 . With this structure, client device  902  does not need to internally store a processor that performs a process for compressing the three-dimensional data of the three-dimensional map (point cloud, etc.), as long as client device  902  internally stores a processor that performs a process for decoding the three-dimensional map (point cloud, etc.). This makes it possible to limit costs, power consumption, and the like of client device  902 . 
     As stated above, client device  902  according to the present embodiment is equipped in the mobile object, and creates three-dimensional data  1034  of a surrounding area of the mobile object using sensor information  1033  that is obtained through sensor  1015  equipped in the mobile object and indicates a surrounding condition of the mobile object. Client device  902  estimates a self-location of the mobile object using the created three-dimensional data  1034 . Client device  902  transmits obtained sensor information  1033  to server  901  or another client device  902 . 
     This enables client device  902  to transmit sensor information  1033  to server  901  or the like. This makes it possible to further reduce the amount of transmission data compared to when transmitting the three-dimensional data. Since there is no need for client device  902  to perform processes such as compressing or encoding the three-dimensional data, it is possible to reduce the processing amount of client device  902 . As such, client device  902  is capable of reducing the amount of data to be transmitted or simplifying the structure of the device. 
     Client device  902  further transmits the transmission request for the three-dimensional map to server  901  and receives three-dimensional map  1031  from server  901 . In the estimating of the self-location, client device  902  estimates the self-location using three-dimensional data  1034  and three-dimensional map  1032 . 
     Sensor information  1033  includes at least one of information obtained by a laser sensor, a luminance image, an infrared image, a depth image, sensor position information, or sensor speed information. 
     Sensor information  1033  includes information that indicates a performance of the sensor. 
     Client device  902  encodes or compresses sensor information  1033 , and in the transmitting of the sensor information, transmits sensor information  1037  that has been encoded or compressed to server  901  or another client device  902 . This enables client device  902  to reduce the amount of data to be transmitted. 
     For example, client device  902  includes a processor and memory. The processor performs the above processes using the memory. 
     Server  901  according to the present embodiment is capable of communicating with client device  902  equipped in the mobile object, and receives sensor information  1037  that is obtained through sensor  1015  equipped in the mobile object and indicates a surrounding condition of the mobile object. Server  901  creates three-dimensional data  1134  of a surrounding area of the mobile object using received sensor information  1037 . 
     With this, server  901  creates three-dimensional data  1134  using sensor information  1037  transmitted from client device  902 . This makes it possible to further reduce the amount of transmission data compared to when client device  902  transmits the three-dimensional data. Since there is no need for client device  902  to perform processes such as compressing or encoding the three-dimensional data, it is possible to reduce the processing amount of client device  902 . As such, server  901  is capable of reducing the amount of data to be transmitted or simplifying the structure of the device. 
     Server  901  further transmits a transmission request for the sensor information to client device  902 . 
     Server  901  further updates three-dimensional map  1135  using the created three-dimensional data  1134 , and transmits three-dimensional map  1135  to client device  902  in response to the transmission request for three-dimensional map  1135  from client device  902 . 
     Sensor information  1037  includes at least one of information obtained by a laser sensor, a luminance image, an infrared image, a depth image, sensor position information, or sensor speed information. 
     Sensor information  1037  includes information that indicates a performance of the sensor. 
     Server  901  further corrects the three-dimensional data in accordance with the performance of the sensor. This enables the three-dimensional data creation method to improve the quality of the three-dimensional data. 
     In the receiving of the sensor information, server  901  receives a plurality of pieces of sensor information  1037  received from a plurality of client devices  902 , and selects sensor information  1037  to be used in the creating of three-dimensional data  1134 , based on a plurality of pieces of information that each indicates the performance of the sensor included in the plurality of pieces of sensor information  1037 . This enables server  901  to improve the quality of three-dimensional data  1134 . 
     Server  901  decodes or decompresses received sensor information  1037 , and creates three-dimensional data  1134  using sensor information  1132  that has been decoded or decompressed. This enables server  901  to reduce the amount of data to be transmitted. 
     For example, server  901  includes a processor and memory. The processor performs the above processes using the memory. 
     The following will describe a variation of the present embodiment.  FIG. 179  is a diagram illustrating a configuration of a system according to the present embodiment. The system illustrated in  FIG. 179  includes server  2001 , client device  2002 A, and client device  2002 B. 
     Client device  2002 A and client device  2002 B are each provided in a mobile object such as a vehicle, and transmit sensor information to server  2001 . Server  2001  transmits a three-dimensional map (a point_cloud) to client device  2002 A and client device  2002 B. 
     Client device  2002 A includes sensor information obtainer  2011 , storage  2012 , and data transmission possibility determiner  2013 . It should be noted that client device  2002 B has the same configuration. Additionally, when client device  2002 A and client device  2002 B are not particularly distinguished below, client device  2002 A and client device  2002 B are also referred to as client device  2002 . 
       FIG. 180  is a flowchart illustrating operation of client device  2002  according to the present embodiment. 
     Sensor information obtainer  2011  obtains a variety of sensor information using sensors (a group of sensors) provided in a mobile object. In other words, sensor information obtainer  2011  obtains sensor information obtained by the sensors (the group of sensors) provided in the mobile object and indicating a surrounding state of the mobile object. Sensor information obtainer  2011  also stores the obtained sensor information into storage  2012 . This sensor information includes at least one of information obtained by LiDAR, a visible light image, an infrared image, or a depth image. Additionally, the sensor information may include at least one of sensor position information, speed information, obtainment time information, or obtainment location information. Sensor position information indicates a position of a sensor that has obtained sensor information. Speed information indicates a speed of the mobile object when a sensor obtained sensor information. Obtainment time information indicates a time when a sensor obtained sensor information. Obtainment location information indicates a position of the mobile object or a sensor when the sensor obtained sensor information. 
     Next, data transmission possibility determiner  2013  determines whether the mobile object (client device  2002 ) is in an environment in which the mobile object can transmit sensor information to server  2001  (S 2002 ). For example, data transmission possibility determiner  2013  may specify a location and a time at which client device  2002  is present using GPS information etc., and may determine whether data can be transmitted. Additionally, data transmission possibility determiner  2013  may determine whether data can be transmitted, depending on whether it is possible to connect to a specific access point. 
     When client device  2002  determines that the mobile object is in the environment in which the mobile object can transmit the sensor information to server  2001  (YES in S 2002 ), client device  2002  transmits the sensor information to server  2001  (S 2003 ). In other words, when client device  2002  becomes capable of transmitting sensor information to server  2001 , client device  2002  transmits the sensor information held by client device  2002  to server  2001 . For example, an access point that enables high-speed communication using millimeter waves is provided in an intersection or the like. When client device  2002  enters the intersection, client device  2002  transmits the sensor information held by client device  2002  to server  2001  at high speed using the millimeter-wave communication. 
     Next, client device  2002  deletes from storage  2012  the sensor information that has been transmitted to server  2001  (S 2004 ). It should be noted that when sensor information that has not been transmitted to server  2001  meets predetermined conditions, client device  2002  may delete the sensor information. For example, when an obtainment time of sensor information held by client device  2002  precedes a current time by a certain time, client device  2002  may delete the sensor information from storage  2012 . In other words, when a difference between the current time and a time when a sensor obtained sensor information exceeds a predetermined time, client device  2002  may delete the sensor information from storage  2012 . Besides, when an obtainment location of sensor information held by client device  2002  is separated from a current location by a certain distance, client device  2002  may delete the sensor information from storage  2012 . In other words, when a difference between a current position of the mobile object or a sensor and a position of the mobile object or the sensor when the sensor obtained sensor information exceeds a predetermined distance, client device  2002  may delete the sensor information from storage  2012 . Accordingly, it is possible to reduce the capacity of storage  2012  of client device  2002 . 
     When client device  2002  does not finish obtaining sensor information (NO in S 2005 ), client device  2002  performs step S 2001  and the subsequent steps again. Further, when client device  2002  finishes obtaining sensor information (YES in S 2005 ), client device  2002  completes the process. 
     Client device  2002  may select sensor information to be transmitted to server  2001 , in accordance with communication conditions. For example, when high-speed communication is available, client device  2002  preferentially transmits sensor information (e.g., information obtained by LiDAR) of which the data size held in storage  2012  is large. Additionally, when high-speed communication is not readily available, client device  2002  transmits sensor information (e.g., a visible light image) which has high priority and of which the data size held in storage  2012  is small. Accordingly, client device  2002  can efficiently transmit sensor information held in storage  2012 , in accordance with network conditions 
     Client device  2002  may obtain, from server  2001 , time information indicating a current time and location information indicating a current location. Moreover, client device  2002  may determine an obtainment time and an obtainment location of sensor information based on the obtained time information and location information. In other words, client device  2002  may obtain time information from server  2001  and generate obtainment time information using the obtained time information. Client device  2002  may also obtain location information from server  2001  and generate obtainment location information using the obtained location information. 
     For example, regarding time information, server  2001  and client device  2002  perform clock synchronization using a means such as the Network Time Protocol (NTP) or the Precision Time Protocol (PTP). This enables client device  2002  to obtain accurate time information. What&#39;s more, since it is possible to synchronize clocks between server  2001  and client devices  2002 , it is possible to synchronize times included in pieces of sensor information obtained by separate client devices  2002 . As a result, server  2001  can handle sensor information indicating a synchronized time. It should be noted that a means of synchronizing clocks may be any means other than the NTP or PTP. In addition, GPS information may be used as the time information and the location information. 
     Server  2001  may specify a time or a location and obtain pieces of sensor information from client devices  2002 . For example, when an accident occurs, in order to search for a client device in the vicinity of the accident, server  2001  specifies an accident occurrence time and an accident occurrence location and broadcasts sensor information transmission requests to client devices  2002 . Then, client device  2002  having sensor information obtained at the corresponding time and location transmits the sensor information to server  2001 . In other words, client device  2002  receives, from server  2001 , a sensor information transmission request including specification information specifying a location and a time. When sensor information obtained at a location and a time indicated by the specification information is stored in storage  2012 , and client device  2002  determines that the mobile object is present in the environment in which the mobile object can transmit the sensor information to server  2001 , client device  2002  transmits, to server  2001 , the sensor information obtained at the location and the time indicated by the specification information. Consequently, server  2001  can obtain the pieces of sensor information pertaining to the occurrence of the accident from client devices  2002 , and use the pieces of sensor information for accident analysis etc. 
     It should be noted that when client device  2002  receives a sensor information transmission request from server  2001 , client device  2002  may refuse to transmit sensor information. Additionally, client device  2002  may set in advance which pieces of sensor information can be transmitted. Alternatively, server  2001  may inquire of client device  2002  each time whether sensor information can be transmitted. 
     A point may be given to client device  2002  that has transmitted sensor information to server  2001 . This point can be used in payment for, for example, gasoline expenses, electric vehicle (EV) charging expenses, a highway toll, or rental car expenses. After obtaining sensor information, server  2001  may delete information for specifying client device  2002  that has transmitted the sensor information. For example, this information is a network address of client device  2002 . Since this enables the anonymization of sensor information, a user of client device  2002  can securely transmit sensor information from client device  2002  to server  2001 . Server  2001  may include servers. For example, by servers sharing sensor information, even when one of the servers breaks down, the other servers can communicate with client device  2002 . Accordingly, it is possible to avoid service outage due to a server breakdown. 
     A specified location specified by a sensor information transmission request indicates an accident occurrence location etc., and may be different from a position of client device  2002  at a specified time specified by the sensor information transmission request. For this reason, for example, by specifying, as a specified location, a range such as within XX meters of a surrounding area, server  2001  can request information from client device  2002  within the range. Similarly, server  2001  may also specify, as a specified time, a range such as within N seconds before and after a certain time. As a result, server  2001  can obtain sensor information from client device  2002  present for a time from t−N to t+N and in a location within XX meters from absolute position S. When client device  2002  transmits three-dimensional data such as LiDAR, client device  2002  may transmit data created immediately after time t. 
     Server  2001  may separately specify information indicating, as a specified location, a location of client device  2002  from which sensor information is to be obtained, and a location at which sensor information is desirably obtained. For example, server  2001  specifies that sensor information including at least a range within YY meters from absolute position S is to be obtained from client device  2002  present within XX meters from absolute position S. When client device  2002  selects three-dimensional data to be transmitted, client device  2002  selects one or more pieces of three-dimensional data so that the one or more pieces of three-dimensional data include at least the sensor information including the specified range. Each of the one or more pieces of three-dimensional data is a random-accessible unit of data. In addition, when client device  2002  transmits a visible light image, client device  2002  may transmit pieces of temporally continuous image data including at least a frame immediately before or immediately after time t. 
     When client device  2002  can use physical networks such as 5G, Wi-Fi, or modes in 5G for transmitting sensor information, client device  2002  may select a network to be used according to the order of priority notified by server  2001 . Alternatively, client device  2002  may select a network that enables client device  2002  to ensure an appropriate bandwidth based on the size of transmit data. Alternatively, client device  2002  may select a network to be used, based on data transmission expenses etc. A transmission request from server  2001  may include information indicating a transmission deadline, for example, performing transmission when client device  2002  can start transmission by time t. When server  2001  cannot obtain sufficient sensor information within a time limit, server  2001  may issue a transmission request again. 
     Sensor information may include header information indicating characteristics of sensor data along with compressed or uncompressed sensor data. Client device  2002  may transmit header information to server  2001  via a physical network or a communication protocol that is different from a physical network or a communication protocol used for sensor data. For example, client device  2002  transmits header information to server  2001  prior to transmitting sensor data. Server  2001  determines whether to obtain the sensor data of client device  2002 , based on a result of analysis of the header information. For example, header information may include information indicating a point cloud obtainment density, an elevation angle, or a frame rate of LiDAR, or information indicating, for example, a resolution, an SN ratio, or a frame rate of a visible light image. Accordingly, server  2001  can obtain the sensor information from client device  2002  having the sensor data of determined quality. 
     As stated above, client device  2002  is provided in the mobile object, obtains sensor information that has been obtained by a sensor provided in the mobile object and indicates a surrounding state of the mobile object, and stores the sensor information into storage  2012 . Client device  2002  determines whether the mobile object is present in an environment in which the mobile object is capable of transmitting the sensor information to server  2001 , and transmits the sensor information to server  2001  when the mobile object is determined to be present in the environment in which the mobile object is capable of transmitting the sensor information to server  2001 . 
     Additionally, client device  2002  further creates, from the sensor information, three-dimensional data of a surrounding area of the mobile object, and estimates a self-location of the mobile object using the three-dimensional data created. 
     Besides, client device  2002  further transmits a transmission request for a three-dimensional map to server  2001 , and receives the three-dimensional map from server  2001 . In the estimating, client device  2002  estimates the self-location using the three-dimensional data and the three-dimensional map. 
     It should be noted that the above process performed by client device  2002  may be realized as an information transmission method for use in client device  2002 . 
     In addition, client device  2002  may include a processor and memory. Using the memory, the processor may perform the above process. 
     Next, a sensor information collection system according to the present embodiment will be described.  FIG. 181  is a diagram illustrating a configuration of the sensor information collection system according to the present embodiment. As illustrated in  FIG. 181 , the sensor information collection system according to the present embodiment includes terminal  2021 A, terminal  2021 B, communication device  2022 A, communication device  2022 B, network  2023 , data collection server  2024 , map server  2025 , and client device  2026 . It should be noted that when terminal  2021 A and terminal  2021 B are not particularly distinguished, terminal  2021 A and terminal  2021 B are also referred to as terminal  2021 . Additionally, when communication device  2022 A and communication device  2022 B are not particularly distinguished, communication device  2022 A and communication device  2022 B are also referred to as communication device  2022 . 
     Data collection server  2024  collects data such as sensor data obtained by a sensor included in terminal  2021  as position-related data in which the data is associated with a position in a three-dimensional space. 
     Sensor data is data obtained by, for example, detecting a surrounding state of terminal  2021  or an internal state of terminal  2021  using a sensor included in terminal  2021 . Terminal  2021  transmits, to data collection server  2024 , one or more pieces of sensor data collected from one or more sensor devices in locations at which direct communication with terminal  2021  is possible or at which communication with terminal  2021  is possible by the same communication system or via one or more relay devices. 
     Data included in position-related data may include, for example, information indicating an operating state, an operating log, a service use state, etc. of a terminal or a device included in the terminal. In addition, the data include in the position-related data may include, for example, information in which an identifier of terminal  2021  is associated with a position or a movement path etc. of terminal  2021 . 
     Information indicating a position included in position-related data is associated with, for example, information indicating a position in three-dimensional data such as three-dimensional map data. The details of information indicating a position will be described later. 
     Position-related data may include at least one of the above-described time information or information indicating an attribute of data included in the position-related data or a type (e.g., a model number) of a sensor that has created the data, in addition to position information that is information indicating a position. The position information and the time information may be stored in a header area of the position-related data or a header area of a frame that stores the position-related data. Further, the position information and the time information may be transmitted and/or stored as metadata associated with the position-related data, separately from the position-related data. 
     Map server  2025  is connected to, for example, network  2023 , and transmits three-dimensional data such as three-dimensional map data in response to a request from another device such as terminal  2021 . Besides, as described in the aforementioned embodiments, map server  2025  may have, for example, a function of updating three-dimensional data using sensor information transmitted from terminal  2021 . 
     Data collection server  2024  is connected to, for example, network  2023 , collects position-related data from another device such as terminal  2021 , and stores the collected position-related data into a storage of data collection server  2024  or a storage of another server. In addition, data collection server  2024  transmits, for example, metadata of collected position-related data or three-dimensional data generated based on the position-related data, to terminal  2021  in response to a request from terminal  2021 . 
     Network  2023  is, for example, a communication network such as the Internet. Terminal  2021  is connected to network  2023  via communication device  2022 . Communication device  2022  communicates with terminal  2021  using one communication system or switching between communication systems. Communication device  2022  is a communication satellite that performs communication using, for example, (1) a base station compliant with Long-Term Evolution (LTE) etc., (2) an access point (AP) for Wi-Fi or millimeter-wave communication etc., (3) a low-power wide-area (LPWA) network gateway such as SIGFOX, LoRaWAN, or Wi-SUN, or (4) a satellite communication system such as DVB-S2. 
     It should be noted that a base station may communicate with terminal  2021  using a system classified as an LPWA network such as Narrowband Internet of Things (NB IoT) or LTE-M, or switching between these systems. 
     Here, although, in the example given, terminal  2021  has a function of communicating with communication device  2022  that uses two types of communication systems, and communicates with map server  2025  or data collection server  2024  using one of the communication systems or switching between the communication systems and between communication devices  2022  to be a direct communication partner; a configuration of the sensor information collection system and terminal  2021  is not limited to this. For example, terminal  2021  need not have a function of performing communication using communication systems, and may have a function of performing communication using one of the communication systems. Terminal  2021  may also support three or more communication systems. Additionally, each terminal  2021  may support a different communication system. 
     Terminal  2021  includes, for example, the configuration of client device  902  illustrated in  FIG. 171 . Terminal  2021  estimates a self-location etc. using received three-dimensional data. Besides, terminal  2021  associates sensor data obtained from a sensor and position information obtained by self-location estimation to generate position-related data. 
     Position information appended to position-related data indicates, for example, a position in a coordinate system used for three-dimensional data. For example, the position information is coordinate values represented using a value of a latitude and a value of a longitude. Here, terminal  2021  may include, in the position information, a coordinate system serving as a reference for the coordinate values and information indicating three-dimensional data used for location estimation, along with the coordinate values. Coordinate values may also include altitude information. 
     The position information may be associated with a data unit or a space unit usable for encoding the above three-dimensional data. Such a unit is, for example, WLD, GOS, SPC, VLM, or VXL. Here, the position information is represented by, for example, an identifier for identifying a data unit such as the SPC corresponding to position-related data. It should be noted that the position information may include, for example, information indicating three-dimensional data obtained by encoding a three-dimensional space including a data unit such as the SPC or information indicating a detailed position within the SPC, in addition to the identifier for identifying the data unit such as the SPC. The information indicating the three-dimensional data is, for example, a file name of the three-dimensional data. 
     As stated above, by generating position-related data associated with position information based on location estimation using three-dimensional data, the system can give more accurate position information to sensor information than when the system appends position information based on a self-location of a client device (terminal  2021 ) obtained using a GPS to sensor information. As a result, even when another device uses the position-related data in another service, there is a possibility of more accurately determining a position corresponding to the position-related data in an actual space, by performing location estimation based on the same three-dimensional data. 
     It should be noted that although the data transmitted from terminal  2021  is the position-related data in the example given in the present embodiment, the data transmitted from terminal  2021  may be data unassociated with position information. In other words, the transmission and reception of three-dimensional data or sensor data described in the other embodiments may be performed via network  2023  described in the present embodiment. 
     Next, a different example of position information indicating a position in a three-dimensional or two-dimensional actual space or in a map space will be described. The position information appended to position-related data may be information indicating a relative position relative to a keypoint in three-dimensional data. Here, the keypoint serving as a reference for the position information is encoded as, for example, SWLD, and notified to terminal  2021  as three-dimensional data. 
     The information indicating the relative position relative to the keypoint may be, for example, information that is represented by a vector from the keypoint to the point indicated by the position information, and indicates a direction and a distance from the keypoint to the point indicated by the position information. Alternatively, the information indicating the relative position relative to the keypoint may be information indicating an amount of displacement from the keypoint to the point indicated by the position information along each of the x axis, the y axis, and the z axis. Additionally, the information indicating the relative position relative to the keypoint may be information indicating a distance from each of three or more keypoints to the point indicated by the position information. It should be noted that the relative position need not be a relative position of the point indicated by the position information represented using each keypoint as a reference, and may be a relative position of each keypoint represented with respect to the point indicated by the position information. Examples of position information based on a relative position relative to a keypoint include information for identifying a keypoint to be a reference, and information indicating the relative position of the point indicated by the position information and relative to the keypoint. When the information indicating the relative position relative to the keypoint is provided separately from three-dimensional data, the information indicating the relative position relative to the keypoint may include, for example, coordinate axes used in deriving the relative position, information indicating a type of the three-dimensional data, and/or information indicating a magnitude per unit amount (e.g., a scale) of a value of the information indicating the relative position. 
     The position information may include, for each keypoint, information indicating a relative position relative to the keypoint. When the position information is represented by relative positions relative to keypoints, terminal  2021  that intends to identify a position in an actual space indicated by the position information may calculate candidate points of the position indicated by the position information from positions of the keypoints each estimated from sensor data, and may determine that a point obtained by averaging the calculated candidate points is the point indicated by the position information. Since this configuration reduces the effects of errors when the positions of the keypoints are estimated from the sensor data, it is possible to improve the estimation accuracy for the point in the actual space indicated by the position information. Besides, when the position information includes information indicating relative positions relative to keypoints, if it is possible to detect any one of the keypoints regardless of the presence of keypoints undetectable due to a limitation such as a type or performance of a sensor included in terminal  2021 , it is possible to estimate a value of the point indicated by the position information. 
     A point identifiable from sensor data can be used as a keypoint. Examples of the point identifiable from the sensor data include a point or a point within a region that satisfies a predetermined keypoint detection condition, such as the above-described three-dimensional feature or feature of visible light data is greater than or equal to a threshold value. 
     Moreover, a marker etc. placed in an actual space may be used as a keypoint. In this case, the maker may be detected and located from data obtained using a sensor such as LiDAR or a camera. For example, the marker may be represented by a change in color or luminance value (degree of reflection), or a three-dimensional shape (e.g., unevenness). Coordinate values indicating a position of the marker, or a two-dimensional bar code or a bar code etc. generated from an identifier of the marker may be also used. 
     Furthermore, a light source that transmits an optical signal may be used as a marker. When a light source of an optical signal is used as a marker, not only information for obtaining a position such as coordinate values or an identifier but also other data may be transmitted using an optical signal. For example, an optical signal may include contents of service corresponding to the position of the marker, an address for obtaining contents such as a URL, or an identifier of a wireless communication device for receiving service, and information indicating a wireless communication system etc. for connecting to the wireless communication device. The use of an optical communication device (a light source) as a marker not only facilitates the transmission of data other than information indicating a position but also makes it possible to dynamically change the data. 
     Terminal  2021  finds out a correspondence relationship of keypoints between mutually different data using, for example, a common identifier used for the data, or information or a table indicating the correspondence relationship of the keypoints between the data. When there is no information indicating a correspondence relationship between keypoints, terminal  2021  may also determine that when coordinates of a keypoint in three-dimensional data are converted into a position in a space of another three-dimensional data, a keypoint closest to the position is a corresponding keypoint. 
     When the position information based on the relative position described above is used, terminal  2021  that uses mutually different three-dimensional data or services can identify or estimate a position indicated by the position information with respect to a common keypoint included in or associated with each three-dimensional data. As a result, terminal  2021  that uses the mutually different three-dimensional data or the services can identify or estimate the same position with higher accuracy. 
     Even when map data or three-dimensional data represented using mutually different coordinate systems are used, since it is possible to reduce the effects of errors caused by the conversion of a coordinate system, it is possible to coordinate services based on more accurate position information. 
     Hereinafter, an example of functions provided by data collection server  2024  will be described. Data collection server  2024  may transfer received position-related data to another data server. When there are data servers, data collection server  2024  determines to which data server received position-related data is to be transferred, and transfers the position-related data to a data server determined as a transfer destination. 
     Data collection server  2024  determines a transfer destination based on, for example, transfer destination server determination rules preset to data collection server  2024 . The transfer destination server determination rules are set by, for example, a transfer destination table in which identifiers respectively associated with terminals  2021  are associated with transfer destination data servers. 
     Terminal  2021  appends an identifier associated with terminal  2021  to position-related data to be transmitted, and transmits the position-related data to data collection server  2024 . Data collection server  2024  determines a transfer destination data server corresponding to the identifier appended to the position-related data, based on the transfer destination server determination rules set out using the transfer destination table etc.; and transmits the position-related data to the determined data server. The transfer destination server determination rules may be specified based on a determination condition set using a time, a place, etc. at which position-related data is obtained. Here, examples of the identifier associated with transmission source terminal  2021  include an identifier unique to each terminal  2021  or an identifier indicating a group to which terminal  2021  belongs. 
     The transfer destination table need not be a table in which identifiers associated with transmission source terminals are directly associated with transfer destination data servers. For example, data collection server  2024  holds a management table that stores tag information assigned to each identifier unique to terminal  2021 , and a transfer destination table in which the pieces of tag information are associated with transfer destination data servers. Data collection server  2024  may determine a transfer destination data server based on tag information, using the management table and the transfer destination table. Here, the tag information is, for example, control information for management or control information for providing service assigned to a type, a model number, an owner of terminal  2021  corresponding to the identifier, a group to which terminal  2021  belongs, or another identifier. Moreover, in the transfer destination able, identifiers unique to respective sensors may be used instead of the identifiers associated with transmission source terminals  2021 . Furthermore, the transfer destination server determination rules may be set by client device  2026 . 
     Data collection server  2024  may determine data servers as transfer destinations, and transfer received position-related data to the data servers. According to this configuration, for example, when position-related data is automatically backed up or when, in order that position-related data is commonly used by different services, there is a need to transmit the position-related data to a data server for providing each service, it is possible to achieve data transfer as intended by changing a setting of data collection server  2024 . As a result, it is possible to reduce the number of steps necessary for building and changing a system, compared to when a transmission destination of position-related data is set for each terminal  2021 . 
     Data collection server  2024  may register, as a new transfer destination, a data server specified by a transfer request signal received from a data server; and transmit position-related data subsequently received to the data server, in response to the transfer request signal. 
     Data collection server  2024  may store position-related data received from terminal  2021  into a recording device, and transmit position-related data specified by a transmission request signal received from terminal  2021  or a data server to request source terminal  2021  or the data server in response to the transmission request signal. 
     Data collection server  2024  may determine whether position-related data is suppliable to a request source data server or terminal  2021 , and transfer or transmit the position-related data to the request source data server or terminal  2021  when determining that the position-related data is suppliable. 
     When data collection server  2024  receives a request for current position-related data from client device  2026 , even if it is not a timing for transmitting position-related data by terminal  2021 , data collection server  2024  may send a transmission request for the current position-related data to terminal  2021 , and terminal  2021  may transmit the current position-related data in response to the transmission request. 
     Although terminal  2021  transmits position information data to data collection server  2024  in the above description, data collection server  2024  may have a function of managing terminal  2021  such as a function necessary for collecting position-related data from terminal  2021  or a function used when collecting position-related data from terminal  2021 . 
     Data collection server  2024  may have a function of transmitting, to terminal  2021 , a data request signal for requesting transmission of position information data, and collecting position-related data. 
     Management information such as an address for communicating with terminal  2021  from which data is to be collected or an identifier unique to terminal  2021  is registered in advance in data collection server  2024 . Data collection server  2024  collects position-related data from terminal  2021  based on the registered management information. Management information may include information such as types of sensors included in terminal  2021 , the number of sensors included in terminal  2021 , and communication systems supported by terminal  2021 . 
     Data collection server  2024  may collect information such as an operating state or a current position of terminal  2021  from terminal  2021 . 
     Registration of management information may be instructed by client device  2026 , or a process for the registration may be started by terminal  2021  transmitting a registration request to data collection server  2024 . Data collection server  2024  may have a function of controlling communication between data collection server  2024  and terminal  2021 . 
     Communication between data collection server  2024  and terminal  2021  may be established using a dedicated line provided by a service provider such as a mobile network operator (MNO) or a mobile virtual network operator (MVNO), or a virtual dedicated line based on a virtual private network (VPN). According to this configuration, it is possible to perform secure communication between terminal  2021  and data collection server  2024 . 
     Data collection server  2024  may have a function of authenticating terminal  2021  or a function of encrypting data to be transmitted and received between data collection server  2024  and terminal  2021 . Here, the authentication of terminal  2021  or the encryption of data is performed using, for example, an identifier unique to terminal  2021  or an identifier unique to a terminal group including terminals  2021 , which is shared in advance between data collection server  2024  and terminal  2021 . Examples of the identifier include an international mobile subscriber identity (IMSI) that is a unique number stored in a subscriber identity module (SIM) card. An identifier for use in authentication and an identifier for use in encryption of data may be identical or different. 
     The authentication or the encryption of data between data collection server  2024  and terminal  2021  is feasible when both data collection server  2024  and terminal  2021  have a function of performing the process. The process does not depend on a communication system used by communication device  2022  that performs relay. Accordingly, since it is possible to perform the common authentication or encryption without considering whether terminal  2021  uses a communication system, the user&#39;s convenience of system architecture is increased. However, the expression “does not depend on a communication system used by communication device  2022  that performs relay” means a change according to a communication system is not essential. In other words, in order to improve the transfer efficiency or ensure security, the authentication or the encryption of data between data collection server  2024  and terminal  2021  may be changed according to a communication system used by a relay device. 
     Data collection server  2024  may provide client device  2026  with a User Interface (UI) that manages data collection rules such as types of position-related data collected from terminal  2021  and data collection schedules. Accordingly, a user can specify, for example, terminal  2021  from which data is to be collected using client device  2026 , a data collection time, and a data collection frequency. Additionally, data collection server  2024  may specify, for example, a region on a map from which data is to be desirably collected, and collect position-related data from terminal  2021  included in the region. 
     When the data collection rules are managed on a per terminal  2021  basis, client device  2026  presents, on a screen, a list of terminals  2021  or sensors to be managed. The user sets, for example, a necessity for data collection or a collection schedule for each item in the list. 
     When a region on a map from which data is to be desirably collected is specified, client device  2026  presents, on a screen, a two-dimensional or three-dimensional map of a region to be managed. The user selects the region from which data is to be collected on the displayed map. Examples of the region selected on the map include a circular or rectangular region having a point specified on the map as the center, or a circular or rectangular region specifiable by a drag operation. Client device  2026  may also select a region in a preset unit such as a city, an area or a block in a city, or a main road, etc. Instead of specifying a region using a map, a region may be set by inputting values of a latitude and a longitude, or a region may be selected from a list of candidate regions derived based on inputted text information. Text information is, for example, a name of a region, a city, or a landmark. 
     Moreover, data may be collected while the user dynamically changes a specified region by specifying one or more terminals  2021  and setting a condition such as within 100 meters of one or more terminals  2021 . 
     When client device  2026  includes a sensor such as a camera, a region on a map may be specified based on a position of client device  2026  in an actual space obtained from sensor data. For example, client device  2026  may estimate a self-location using sensor data, and specify, as a region from which data is to be collected, a region within a predetermined distance from a point on a map corresponding to the estimated location or a region within a distance specified by the user. Client device  2026  may also specify, as the region from which the data is to be collected, a sensing region of the sensor, that is, a region corresponding to obtained sensor data. Alternatively, client device  2026  may specify, as the region from which the data is to be collected, a region based on a location corresponding to sensor data specified by the user. Either client device  2026  or data collection server  2024  may estimate a region on a map or a location corresponding to sensor data. 
     When a region on a map is specified, data collection server  2024  may specify terminal  2021  within the specified region by collecting current position information of each terminal  2021 , and may send a transmission request for position-related data to specified terminal  2021 . When data collection server  2024  transmits information indicating a specified region to terminal  2021 , determines whether terminal  2021  is present within the specified region, and determines that terminal  2021  is present within the specified region, rather than specifying terminal  2021  within the region, terminal  2021  may transmit position-related data. 
     Data collection server  2024  transmits, to client device  2026 , data such as a list or a map for providing the above-described User Interface (UI) in an application executed by client device  2026 . Data collection server  2024  may transmit, to client device  2026 , not only the data such as the list or the map but also an application program. Additionally, the above UI may be provided as contents created using HTML displayable by a browser. It should be noted that part of data such as map data may be supplied from a server, such as map server  2025 , other than data collection server  2024 . 
     When client device  2026  receives an input for notifying the completion of an input such as pressing of a setup key by the user, client device  2026  transmits the inputted information as configuration information to data collection server  2024 . Data collection server  2024  transmits, to each terminal  2021 , a signal for requesting position-related data or notifying position-related data collection rules, based on the configuration information received from client device  2026 , and collects the position-related data. 
     Next, an example of controlling operation of terminal  2021  based on additional information added to three-dimensional or two-dimensional map data will be described. 
     In the present configuration, object information that indicates a position of a power feeding part such as a feeder antenna or a feeder coil for wireless power feeding buried under a road or a parking lot is included in or associated with three-dimensional data, and such object information is provided to terminal  2021  that is a vehicle or a drone. 
     A vehicle or a drone that has obtained the object information to get charged automatically moves so that a position of a charging part such as a charging antenna or a charging coil included in the vehicle or the drone becomes opposite to a region indicated by the object information, and such vehicle or a drone starts to charge itself. It should be noted that when a vehicle or a drone has no automatic driving function, a direction to move in or an operation to perform is presented to a driver or an operator by using an image displayed on a screen, audio, etc. When a position of a charging part calculated based on an estimated self-location is determined to fall within the region indicated by the object information or a predetermined distance from the region, an image or audio to be presented is changed to a content that puts a stop to driving or operating, and the charging is started. 
     Object information need not be information indicating a position of a power feeding part, and may be information indicating a region within which placement of a charging part results in a charging efficiency greater than or equal to a predetermined threshold value. A position indicated by object information may be represented by, for example, the central point of a region indicated by the object information, a region or a line within a two-dimensional plane, or a region, a line, or a plane within a three-dimensional space. 
     According to this configuration, since it is possible to identify the position of the power feeding antenna unidentifiable by sensing data of LiDAR or an image captured by the camera, it is possible to highly accurately align a wireless charging antenna included in terminal  2021  such as a vehicle with a wireless power feeding antenna buried under a road. As a result, it is possible to increase a charging speed at the time of wireless charging and improve the charging efficiency. 
     Object information may be an object other than a power feeding antenna. For example, three-dimensional data includes, for example, a position of an AP for millimeter-wave wireless communication as object information. Accordingly, since terminal  2021  can identify the position of the AP in advance, terminal  2021  can steer a directivity of beam to a direction of the object information and start communication. As a result, it is possible to improve communication quality such as increasing transmission rates, reducing the duration of time before starting communication, and extending a communicable period. 
     Object information may include information indicating a type of an object corresponding to the object information. In addition, when terminal  2021  is present within a region in an actual space corresponding to a position in three-dimensional data of the object information or within a predetermined distance from the region, the object information may include information indicating a process to be performed by terminal  2021 . 
     Object information may be provided by a server different from a server that provides three-dimensional data. When object information is provided separately from three-dimensional data, object groups in which object information used by the same service is stored may be each provided as separate data according to a type of a target service or a target device. 
     Three-dimensional data used in combination with object information may be point cloud data of WLD or keypoint data of SWLD. 
     In the three-dimensional data encoding device, when attribute information of a current three-dimensional point to be encoded is layer-encoded using Levels of Detail (LoDs), the three-dimensional data decoding device may decode the attribute information in layers down to LoD required by the three-dimensional data decoding device and need not decode the attribute information in layers not required. For example, when the total number of LoDs for the attribute information in a bitstream generated by the three-dimensional data encoding device is N, the three-dimensional data decoding device may decode M LoDs (M&lt;N), i.e., layers from the uppermost layer LoD0 to LoD(M−1), and need not decode the remaining LoDs, i.e., layers down to LoD(N−1). With this, while reducing the processing load, the three-dimensional data decoding device can decode the attribute information in layers from LoD0 to LoD(M−1) required by the three-dimensional data decoding device. 
       FIG. 182  is a diagram illustrating the foregoing use case. In the example shown in  FIG. 182 , a server stores a three-dimensional map obtained by encoding three-dimensional geometry information and attribute information. The server (the three-dimensional data encoding device) broadcasts the three-dimensional map to client devices (the three-dimensional data decoding devices: for example, vehicles, drones, etc.) in an area managed by the server, and each client device uses the three-dimensional map received from the server to perform a process for identifying the self-position of the client device or a process for displaying map information to a user or the like who operates the client device. 
     The following describes an example of the operation in this case. First, the server encodes the geometry information of the three-dimensional map using an octree structure or the like. Then, the sever layer-encodes the attribute information of the three-dimensional map using N LoDs established based on the geometry information. The server stores a bitstream of the three-dimensional map obtained by the layer-encoding. 
     Next, in response to a send request for the map information from the client device in the area managed by the server, the server sends the bitstream of the encoded three-dimensional map to the client device. 
     The client device receives the bitstream of the three-dimensional map sent from the server, and decodes the geometry information and the attribute information of the three-dimensional map in accordance with the intended use of the client device. For example, when the client device performs highly accurate estimation of the self-position using the geometry information and the attribute information in N LoDs, the client device determines that a decoding result to the dense three-dimensional points is necessary as the attribute information, and decodes all the information in the bitstream. 
     Moreover, when the client device displays the three-dimensional map information to a user or the like, the client device determines that a decoding result to the sparse three-dimensional points is necessary as the attribute information, and decodes the geometry information and the attribute information in M LoDs (M&lt;N) starting from an upper layer LoD0. 
     In this way, the processing load of the client device can be reduced by changing LoDs for the attribute information to be decoded in accordance with the intended use of the client device. 
     In the example shown in  FIG. 182 , for example, the three-dimensional map includes geometry information and attribute information. The geometry information is encoded using the octree. The attribute information is encoded using N LoDs. 
     Client device A performs highly accurate estimation of the self-position. In this case, client device A determines that all the geometry information and all the attribute information are necessary, and decodes all the geometry information and all the attribute information constructed from N LoDs in the bitstream. 
     Client device B displays the three-dimensional map to a user. In this case, client device B determines that the geometry information and the attribute information in M LoDs (M&lt;N) are necessary, and decodes the geometry information and the attribute information constructed from M LoDs in the bitstream. 
     It is to be noted that the server may broadcast the three-dimensional map to the client devices, or multicast or unicast the three-dimensional map to the client devices. 
     The following describes a variation of the system according to the present embodiment. In the three-dimensional data encoding device, when attribute information of a current three-dimensional point to be encoded is layer-encoded using LoDs, the three-dimensional data encoding device may encode the attribute information in layers down to LoD required by the three-dimensional data decoding device and need not encode the attribute information in layers not required. For example, when the total number of LoDs is N, the three-dimensional data encoding device may generate a bitstream by encoding M LoDs (M&lt;N), i.e., layers from the uppermost layer LoD0 to LoD(M−1), and not encoding the remaining LoDs, i.e., layers down to LoD(N−1). With this, in response to a request from the three-dimensional data decoding device, the three-dimensional data encoding device can provide a bitstream in which the attribute information from LoD0 to LoD(M−1) required by the three-dimensional data decoding device is encoded. 
       FIG. 183  is a diagram illustrating the foregoing use case. In the example shown in  FIG. 183 , a server stores a three-dimensional map obtained by encoding three-dimensional geometry information and attribute information. The server (the three-dimensional data encoding device) unicasts, in response to a request from the client device, the three-dimensional map to a client device (the three-dimensional data decoding device: for example, a vehicle, a drone, etc.) in an area managed by the server, and the client device uses the three-dimensional map received from the server to perform a process for identifying the self-position of the client device or a process for displaying map information to a user or the like who operates the client device. 
     The following describes an example of the operation in this case. First, the server encodes the geometry information of the three-dimensional map using an octree structure, or the like. Then, the sever generates a bitstream of three-dimensional map A by layer-encoding the attribute information of the three-dimensional map using N LoDs established based on the geometry information, and stores the generated bitstream in the server. The sever also generates a bitstream of three-dimensional map B by layer-encoding the attribute information of the three-dimensional map using M LoDs (M&lt;N) established based on the geometry information, and stores the generated bitstream in the server. 
     Next, the client device requests the server to send the three-dimensional map in accordance with the intended use of the client device. For example, when the client device performs highly accurate estimation of the self-position using the geometry information and the attribute information in N LoDs, the client device determines that a decoding result to the dense three-dimensional points is necessary as the attribute information, and requests the server to send the bitstream of three-dimensional map A. Moreover, when the client device displays the three-dimensional map information to a user or the like, the client device determines that a decoding result to the sparse three-dimensional points is necessary as the attribute information, and requests the server to send the bitstream of three-dimensional map B including the geometry information and the attribute information in M LoDs (M&lt;N) starting from an upper layer LoD0. Then, in response to the send request for the map information from the client device, the server sends the bitstream of encoded three-dimensional map A or B to the client device. 
     The client device receives the bitstream of three-dimensional map A or B sent from the server in accordance with the intended use of the client device, and decodes the received bitstream. In this way, the server changes a bitstream to be sent, in accordance with the intended use of the client device. With this, it is possible to reduce the processing load of the client device. 
     In the example shown in  FIG. 183 , the server stores three-dimensional map A and three-dimensional map B. The server generates three-dimensional map A by encoding the geometry information of the three-dimensional map using, for example, an octree structure, and encoding the attribute information of the three-dimensional map using N LoDs. In other words, NumLoD included in the bitstream of three-dimensional map A indicates N. 
     The server also generates three-dimensional map B by encoding the geometry information of the three-dimensional map using, for example, an octree structure, and encoding the attribute information of the three-dimensional map using M LoDs. In other words, NumLoD included in the bitstream of three-dimensional map B indicates M. 
     Client device A performs highly accurate estimation of the self-position. In this case, client device A determines that all the geometry information and all the attribute information are necessary, and requests the server to send three-dimensional map A including all the geometry information and the attribute information constructed from N LoDs. Client device A receives three-dimensional map A, and decodes all the geometry information and the attribute information constructed from N LoDs. 
     Client device B displays the three-dimensional map to a user. In this case, client device B determines that all the geometry information and the attribute information in M LoDs (M&lt;N) are necessary, and requests the server to send three-dimensional map B including all the geometry information and the attribute information constructed from M LoDs. Client device B receives three-dimensional map B, and decodes all the geometry information and the attribute information constructed from M LoDs. 
     It is to be noted that in addition to three-dimensional map B, the server (the three-dimensional data encoding device) may generate three-dimensional map C in which attribute information in the remaining N-M LoDs is encoded, and send three-dimensional map C to client device B in response to the request from client device B. Moreover, client device B may obtain the decoding result of N LoDs using the bitstreams of three-dimensional maps B and C. 
     Hereinafter, an example of an application process will be described.  FIG. 184  is a flowchart illustrating an example of the application process. When an application operation is started, a three-dimensional data demultiplexing device obtains an ISOBMFF file including point cloud data and a plurality of pieces of encoded data (S 7301 ). For example, the three-dimensional data demultiplexing device may obtain the ISOBMFF file through communication, or may read the ISOBMFF file from the accumulated data. 
     Next, the three-dimensional data demultiplexing device analyzes the general configuration information in the ISOBMFF file, and specifies the data to be used for the application (S 7302 ). For example, the three-dimensional data demultiplexing device obtains data that is used for processing, and does not obtain data that is not used for processing. 
     Next, the three-dimensional data demultiplexing device extracts one or more pieces of data to be used for the application, and analyzes the configuration information on the data (S 7303 ). 
     When the type of the data is encoded data (encoded data in S 7304 ), the three-dimensional data demultiplexing device converts the ISOBMFF to an encoded stream, and extracts a timestamp (S 7305 ). Additionally, the three-dimensional data demultiplexing device refers to, for example, the flag indicating whether or not the synchronization between data is aligned to determine whether or not the synchronization between data is aligned, and may perform a synchronization process when not aligned. 
     Next, the three-dimensional data demultiplexing device decodes the data with a predetermined method according to the timestamp and the other instructions, and processes the decoded data (S 7306 ). 
     On the other hand, when the type of the data is RAW data (RAW data in S 7304 ), the three-dimensional data demultiplexing device extracts the data and timestamp (S 7307 ). Additionally, the three-dimensional data demultiplexing device may refer to, for example, the flag indicating whether or not the synchronization between data is aligned to determine whether or not the synchronization between data is aligned, and may perform a synchronization process when not aligned. Next, the three-dimensional data demultiplexing device processes the data according to the timestamp and the other instructions (S 7308 ). 
     For example, an example will be described in which the sensor signals obtained by a beam LiDAR, a FLASH LiDAR, and a camera are encoded and multiplexed with respective different encoding schemes.  FIG. 185  is a diagram illustrating examples of the sensor ranges of a beam LiDAR, a FLASH LiDAR, and a camera. For example, the beam LiDAR detects all directions in the periphery of a vehicle (sensor), and the FLASH LiDAR and the camera detect the range in one direction (for example, the front) of the vehicle. 
     In the case of an application that integrally handles a LiDAR point cloud, the three-dimensional data demultiplexing device refers to the general configuration information, and extracts and decodes the encoded data of the beam LiDAR and the FLASH LiDAR. Additionally, the three-dimensional data demultiplexing device does not extract camera images. 
     According to the timestamps of the beam LiDAR and the FLASH LiDAR, the three-dimensional data demultiplexing device simultaneously processes the respective encoded data of the time of the same timestamp. 
     For example, the three-dimensional data demultiplexing device may present the processed data with a presentation device, may synthesize the point cloud data of the beam LiDAR and the FLASH LiDAR, or may perform a process such as rendering. 
     Additionally, in the case of an application that performs calibration between data, the three-dimensional data demultiplexing device may extract sensor geometry information, and use the sensor geometry information in the application. 
     For example, the three-dimensional data demultiplexing device may select whether to use beam LiDAR information or FLASH LiDAR information in the application, and may switch the process according to the selection result. 
     In this manner, since it is possible to adaptively change the obtaining of data and the encoding process according to the process of the application, the processing amount and the power consumption can be reduced. 
     Hereinafter, a use case in automated driving will be described.  FIG. 186  is a diagram illustrating a configuration example of an automated driving system. This automated driving system includes cloud server  7350 , and edge  7360  such as an in-vehicle device or a mobile device. Cloud server  7350  includes demultiplexer  7351 , decoders  7352 A,  7352 B, and  7355 , point cloud data synthesizer  7353 , large data accumulator  7354 , comparator  7356 , and encoder  7357 . Edge  7360  includes sensors  7361 A and  7361 B, point cloud data generators  7362 A and  7362 B, synchronizer  7363 , encoders  7364 A and  7364 B, multiplexer  7365 , update data accumulator  7366 , demultiplexer  7367 , decoder  7368 , filter  7369 , self-position estimator  7370 , and driving controller  7371 . 
     In this system, edge  7360  downloads large data, which is large point-cloud map data accumulated in cloud server  7350 . Edge  7360  performs a self-position estimation process of edge  7360  (a vehicle or a terminal) by matching the large data with the sensor information obtained by edge  7360 . Additionally, edge  7360  uploads the obtained sensor information to cloud server  7350 , and updates the large data to the latest map data. 
     Additionally, in various applications that handle point cloud data in the system, point cloud data with different encoding methods are handled. 
     Cloud server  7350  encodes and multiplexes large data. Specifically, encoder  7357  performs encoding by using a third encoding method suitable for encoding a large point cloud. Additionally, encoder  7357  multiplexes encoded data. Large data accumulator  7354  accumulates the data encoded and multiplexed by encoder  7357 . 
     Edge  7360  performs sensing. Specifically, point cloud data generator  7362 A generates first point cloud data (geometry information (geometry) and attribute information) by using the sensing information obtained by sensor  7361 A. Point cloud data generator  7362 B generates second point cloud data (geometry information and attribute information) by using the sensing information obtained by sensor  7361 B. The generated first point cloud data and second point cloud data are used for the self-position estimation or vehicle control of automated driving, or for map updating. In each process, a part of information of the first point cloud data and the second point cloud data may be used. 
     Edge  7360  performs the self-position estimation. Specifically, edge  7360  downloads large data from cloud server  7350 . Demultiplexer  7367  obtains encoded data by demultiplexing the large data in a file format. Decoder  7368  obtains large data, which is large point-cloud map data, by decoding the obtained encoded data. 
     Self-position estimator  7370  estimates the self-position in the map of a vehicle by matching the obtained large data with the first point cloud data and the second point cloud data generated by point cloud data generators  7362 A and  7362 B. Additionally, driving controller  7371  uses the matching result or the self-position estimation result for driving control. 
     Note that self-position estimator  7370  and driving controller  7371  may extract specific information, such as geometry information, of the large data, and may perform processes by using the extracted information. Additionally, filter  7369  performs a process such as correction or decimation on the first point cloud data and the second point cloud data. Self-position estimator  7370  and driving controller  7371  may use the first point cloud data and second point cloud data on which the process has been performed. Additionally, self-position estimator  7370  and driving controller  7371  may use the sensor signals obtained by sensors  7361 A and  7361 B. 
     Synchronizer  7363  performs time synchronization and geometry correction between a plurality of sensor signals or the pieces of data of a plurality of pieces of point cloud data. Additionally, synchronizer  7363  may correct the geometry information on the sensor signal or point cloud data to match the large data, based on geometry correction information on the large data and sensor data generated by the self-position estimation process. 
     Note that synchronization and geometry correction may be performed not by edge  7360 , but by cloud server  7350 . In this case, edge  7360  may multiplex the synchronization information and the geometry information to transmit the synchronization information and the geometry information to cloud server  7350 . 
     Edge  7360  encodes and multiplexes the sensor signal or point cloud data. Specifically, the sensor signal or point cloud data is encoded by using a first encoding method or a second encoding method suitable for encoding each signal. For example, encoder  7364 A generates first encoded data by encoding first point cloud data by using the first encoding method. Encoder  7364 B generates second encoded data by encoding second point cloud data by using the second encoding method. 
     Multiplexer  7365  generates a multiplexed signal by multiplexing the first encoded data, the second encoded data, the synchronization information, and the like. Update data accumulator  7366  accumulates the generated multiplexed signal. Additionally, update data accumulator  7366  uploads the multiplexed signal to cloud server  7350 . 
     Cloud server  7350  synthesizes the point cloud data. Specifically, demultiplexer  7351  obtains the first encoded data and the second encoded data by demultiplexing the multiplexed signal uploaded to cloud server  7350 . Decoder  7352 A obtains the first point cloud data (or sensor signal) by decoding the first encoded data. Decoder  7352 B obtains the second point cloud data (or sensor signal) by decoding the second encoded data. 
     Point cloud data synthesizer  7353  synthesizes the first point cloud data and the second point cloud data with a predetermined method. When the synchronization information and the geometry correction information are multiplexed in the multiplexed signal, point cloud data synthesizer  7353  may perform synthesis by using these pieces of information. 
     Decoder  7355  demultiplexes and decodes the large data accumulated in large data accumulator  7354 . Comparator  7356  compares the point cloud data generated based on the sensor signal obtained by edge  7360  with the large data held by cloud server  7350 , and determines the point cloud data that needs to be updated. Comparator  7356  updates the point cloud data that is determined to need to be updated of the large data to the point cloud data obtained from edge  7360 . 
     Encoder  7357  encodes and multiplexes the updated large data, and accumulates the obtained data in large data accumulator  7354 . 
     As described above, the signals to be handled may be different, and the signals to be multiplexed or encoding methods may be different, according to the usage or applications to be used. Even in such a case, flexible decoding and application processes are enabled by multiplexing data of various encoding schemes by using the present embodiment. Additionally, even in a case where the encoding schemes of signals are different, by conversion to an encoding scheme suitable for demultiplexing, decoding, data conversion, encoding, and multiplexing processing, it becomes possible to build various applications and systems, and to offer of flexible services. 
     Hereinafter, an example of decoding and application of divided data will be described. First, the information on divided data will be described.  FIG. 187  is a diagram illustrating a configuration example of a bitstream. The general information of divided data indicates, for each divided data, the sensor ID (sensor_id) and data ID (data_id) of the divided data. Note that the data ID is also indicated in the header of each encoded data. 
     Note that the general information of divided data illustrated in  FIG. 187  includes, in addition to the sensor ID, at least one of the sensor information (Sensor), the version (Version) of the sensor, the maker name (Maker) of the sensor, the mount information (Mount Info.) of the sensor, and the position coordinates of the sensor (World Coordinate). Accordingly, the three-dimensional data decoding device can obtain the information on various sensors from the configuration information. 
     The general information of divided data may be stored in SPS, GPS, or APS, which is the metadata, or may be stored in SEI, which is the metadata not required for encoding. Additionally, at the time of multiplexing, the three-dimensional data encoding device stores the SEI in a file of ISOBMFF. The three-dimensional data decoding device can obtain desired divided data based on the metadata. 
     In  FIG. 187 , SPS is the metadata of the entire encoded data, GPS is the metadata of the geometry information, APS is the metadata for each attribute information, G is encoded data of the geometry information for each divided data, and A1, etc. are encoded data of the attribute information for each divided data. 
     Next, an application example of divided data will be described. An example of application will be described in which an arbitrary point cloud is selected, and the selected point cloud is presented.  FIG. 188  is a flowchart of a point cloud selection process performed by this application.  FIG. 189  to FIG.  191  are diagrams illustrating screen examples of the point cloud selection process. 
     As illustrated in  FIG. 189 , the three-dimensional data decoding device that performs the application includes, for example, a UI unit that displays an input UI (user interface)  8661  for selecting an arbitrary point cloud. Input UI  8661  includes presenter  8662  that presents the selected point cloud, and an operation unit (buttons  8663  and  8664 ) that receives operations by a user. After a point cloud is selected in UI  8661 , the three-dimensional data decoding device obtains desired data from accumulator  8665 . 
     First, based on an operation by the user on input UI  8661 , the point cloud information that the user wants to display is selected (S 8631 ). Specifically, by selecting button  8663 , the point cloud based on sensor  1  is selected. By selecting button  8664 , the point cloud based on sensor  2  is selected. Alternatively, by selecting both button  8663  and button  8664 , the point cloud based on sensor  1  and the point cloud based on sensor  2  are selected. Note that it is an example of the selection method of point cloud, and it is not limited to this. 
     Next, the three-dimensional data decoding device analyzes the general information of divided data included in the multiplexed signal (bitstream) or encoded data, and specifies the data ID (data_id) of the divided data constituting the selected point cloud from the sensor ID (sensor_id) of the selected sensor (S 8632 ). Next, the three-dimensional data decoding device extracts, from the multiplexed signal, the encoded data including the specified and desired data ID, and decodes the extracted encoded data to decode the point cloud based on the selected sensor (S 8633 ). Note that the three-dimensional data decoding device does not decode the other encoded data. 
     Lastly, the three-dimensional data decoding device presents (for example, displays) the decoded point cloud (S 8634 ).  FIG. 190  illustrates an example in the case where button  8663  for sensor  1  is pressed, and the point cloud of sensor  1  is presented.  FIG. 191  illustrates an example in the case where both button  8663  for sensor  1  and button  8664  for sensor  2  are pressed, and the point clouds of sensor  1  and sensor  2  are presented. 
     A three-dimensional data encoding device, a three-dimensional data decoding device, and the like according to the embodiments of the present disclosure have been described above, but the present disclosure is not limited to these embodiments. 
     Note that each of the processors included in the three-dimensional data encoding device, the three-dimensional data decoding device, and the like according to the above embodiments is typically implemented as a large-scale integrated (LSI) circuit, which is an integrated circuit (IC). These may take the form of individual chips, or may be partially or entirely packaged into a single chip. 
     Such IC is not limited to an LSI, and thus may be implemented as a dedicated circuit or a general-purpose processor. Alternatively, a field programmable gate array (FPGA) that allows for programming after the manufacture of an LSI, or a reconfigurable processor that allows for reconfiguration of the connection and the setting of circuit cells inside an LSI may be employed. 
     Moreover, in the above embodiments, the structural components may be implemented as dedicated hardware or may be realized by executing a software program suited to such structural components. Alternatively, the structural components may be implemented by a program executor such as a CPU or a processor reading out and executing the software program recorded in a recording medium such as a hard disk or a semiconductor memory. 
     The present disclosure may also be implemented as a three-dimensional data encoding method, a three-dimensional data decoding method, or the like executed by the three-dimensional data encoding device, the three-dimensional data decoding device, and the like. 
     Also, the divisions of the functional blocks shown in the block diagrams are mere examples, and thus a plurality of functional blocks may be implemented as a single functional block, or a single functional block may be divided into a plurality of functional blocks, or one or more functions may be moved to another functional block. Also, the functions of a plurality of functional blocks having similar functions may be processed by single hardware or software in a parallelized or time-divided manner. 
     Also, the processing order of executing the steps shown in the flowcharts is a mere illustration for specifically describing the present disclosure, and thus may be an order other than the shown order. Also, one or more of the steps may be executed simultaneously (in parallel) with another step. 
     A three-dimensional data encoding device, a three-dimensional data decoding device, and the like according to one or more aspects have been described above based on the embodiments, but the present disclosure is not limited to these embodiments. The one or more aspects may thus include forms achieved by making various modifications to the above embodiments that can be conceived by those skilled in the art, as well forms achieved by combining structural components in different embodiments, without materially departing from the spirit of the present disclosure. 
     INDUSTRIAL APPLICABILITY 
     The present disclosure is applicable to a three-dimensional data encoding device and a three-dimensional data decoding device.