Patent Publication Number: US-2023141458-A1

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

Description:
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 group in a three-dimensional space. In the point cloud scheme, the positions and colors of a point group 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 group 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 MPEG-4 AVC and 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 is known (for example, see International Publication WO 2014/020663). 
     SUMMARY 
     There has been a demand for reducing an amount of processing in encoding of 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 reducing the amount of processing. 
     A three-dimensional data encoding method according to one aspect of the present disclosure includes encoding information of a current node included in an N-ary tree structure of three-dimensional points included in three-dimensional data, where N is an integer greater than or equal to 2. In the encoding, first information is encoded, the first information indicating a range for one or more referable neighboring nodes among neighboring nodes spatially neighboring the current node, and the current node is encoded with reference to a neighboring node within the range. 
     A three-dimensional data decoding method according to one aspect of the present disclosure includes decoding information of a current node included in an N-ary tree structure of three-dimensional points included in three-dimensional data, where N is an integer greater than or equal to 2. In the decoding, first information is decoded from a bitstream, the first information indicating a range for one or more referable neighboring nodes among neighboring nodes spatially neighboring the current node, and the current node is decoded with reference to a neighboring node within the range. 
     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 reducing an amount of processing. 
    
    
     
       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 showing the structure of encoded three-dimensional data according to Embodiment 1; 
         FIG.  2    is a diagram showing an example of prediction structures among SPCs that belong to the lowermost layer in a GOS according to Embodiment 1; 
         FIG.  3    is a diagram showing an example of prediction structures among layers according to Embodiment 1; 
         FIG.  4    is a diagram showing an example order of encoding GOSs according to Embodiment 1; 
         FIG.  5    is a diagram showing an example order of encoding GOSs according to Embodiment 1; 
         FIG.  6    is a block diagram of a three-dimensional data encoding device according to Embodiment 1; 
         FIG.  7    is a flowchart of encoding processes according to Embodiment 1; 
         FIG.  8    is a block diagram of a three-dimensional data decoding device according to Embodiment 1; 
         FIG.  9    is a flowchart of decoding processes according to Embodiment 1; 
         FIG.  10    is a diagram showing an example of meta information according to Embodiment 1; 
         FIG.  11    is a diagram showing an example structure of a SWLD according to Embodiment 2; 
         FIG.  12    is a diagram showing example operations performed by a server and a client according to Embodiment 2; 
         FIG.  13    is a diagram showing example operations performed by the server and a client according to Embodiment 2; 
         FIG.  14    is a diagram showing example operations performed by the server and the clients according to Embodiment 2; 
         FIG.  15    is a diagram showing example operations performed by the server and the clients according to Embodiment 2; 
         FIG.  16    is a block diagram of a three-dimensional data encoding device according to Embodiment 2; 
         FIG.  17    is a flowchart of encoding processes according to Embodiment 2; 
         FIG.  18    is a block diagram of a three-dimensional data decoding device according to Embodiment 2; 
         FIG.  19    is a flowchart of decoding processes according to Embodiment 2; 
         FIG.  20    is a diagram showing an example structure of a WLD according to Embodiment 2; 
         FIG.  21    is a diagram showing an example octree structure of the WLD according to Embodiment 2; 
         FIG.  22    is a diagram showing an example structure of a SWLD according to Embodiment 2; 
         FIG.  23    is a diagram showing an example octree structure of the SWLD according to Embodiment 2; 
         FIG.  24    is a block diagram of a three-dimensional data creation device according to Embodiment 3; 
         FIG.  25    is a block diagram of a three-dimensional data transmission device according to Embodiment 3; 
         FIG.  26    is a block diagram of a three-dimensional information processing device according to Embodiment 4; 
         FIG.  27    is a block diagram of a three-dimensional data creation device according to Embodiment 5; 
         FIG.  28    is a diagram showing a structure of a system according to Embodiment 6; 
         FIG.  29    is a block diagram of a client device according to Embodiment 6; 
         FIG.  30    is a block diagram of a server according to Embodiment 6; 
         FIG.  31    is a flowchart of a three-dimensional data creation process performed by the client device according to Embodiment 6; 
         FIG.  32    is a flowchart of a sensor information transmission process performed by the client device according to Embodiment 6; 
         FIG.  33    is a flowchart of a three-dimensional data creation process performed by the server according to Embodiment 6; 
         FIG.  34    is a flowchart of a three-dimensional map transmission process performed by the server according to Embodiment 6; 
         FIG.  35    is a diagram showing a structure of a variation of the system according to Embodiment 6; 
         FIG.  36    is a diagram showing a structure of the server and client devices according to Embodiment 6; 
         FIG.  37    is a block diagram of a three-dimensional data encoding device according to Embodiment 7; 
         FIG.  38    is a diagram showing an example of a prediction residual according to Embodiment 7; 
         FIG.  39    is a diagram showing an example of a volume according to Embodiment 7; 
         FIG.  40    is a diagram showing an example of an octree representation of the volume according to Embodiment 7; 
         FIG.  41    is a diagram showing an example of bit sequences of the volume according to Embodiment 7; 
         FIG.  42    is a diagram showing an example of an octree representation of a volume according to Embodiment 7; 
         FIG.  43    is a diagram showing an example of the volume according to Embodiment 7; 
         FIG.  44    is a diagram for describing an intra prediction process according to Embodiment 7; 
         FIG.  45    is a diagram for describing a rotation and translation process according to Embodiment 7; 
         FIG.  46    is a diagram showing an example syntax of an RT flag and RT information according to Embodiment 7; 
         FIG.  47    is a diagram for describing an inter prediction process according to Embodiment 7; 
         FIG.  48    is a block diagram of a three-dimensional data decoding device according to Embodiment 7; 
         FIG.  49    is a flowchart of a three-dimensional data encoding process performed by the three-dimensional data encoding device according to Embodiment 7; 
         FIG.  50    is a flowchart of a three-dimensional data decoding process performed by the three-dimensional data decoding device according to Embodiment 7; 
         FIG.  51    is a diagram showing a structure of a distribution system according to Embodiment 8; 
         FIG.  52    is a diagram showing an example structure of a bitstream of an encoded three-dimensional map according to Embodiment 8; 
         FIG.  53    is a diagram for describing an advantageous effect on encoding efficiency according to Embodiment 8; 
         FIG.  54    is a flowchart of processes performed by a server according to Embodiment 8; 
         FIG.  55    is a flowchart of processes performed by a client according to Embodiment 8; 
         FIG.  56    is a diagram showing an example syntax of a submap according to Embodiment 8; 
         FIG.  57    is a diagram schematically showing a switching process of an encoding type according to Embodiment 8; 
         FIG.  58    is a diagram showing an example syntax of a submap according to Embodiment 8; 
         FIG.  59    is a flowchart of a three-dimensional data encoding process according to Embodiment 8; 
         FIG.  60    is a flowchart of a three-dimensional data decoding process according to Embodiment 8; 
         FIG.  61    is a diagram schematically showing an operation of a variation of the switching process of the encoding type according to Embodiment 8; 
         FIG.  62    is a diagram schematically showing an operation of a variation of the switching process of the encoding type according to Embodiment 8; 
         FIG.  63    is a diagram schematically showing an operation of a variation of the switching process of the encoding type according to Embodiment 8; 
         FIG.  64    is a diagram schematically showing an operation of a variation of a calculation process of a differential value according to Embodiment 8; 
         FIG.  65    is a diagram schematically showing an operation of a variation of the calculation process of the differential value according to Embodiment 8; 
         FIG.  66    is a diagram schematically showing an operation of a variation of the calculation process of the differential value according to Embodiment 8; 
         FIG.  67    is a diagram schematically showing an operation of a variation of the calculation process of the differential value according to Embodiment 8; 
         FIG.  68    is a diagram showing an example syntax of a volume according to Embodiment 8; 
         FIG.  69    is a diagram showing an example of an important area according to Embodiment 9; 
         FIG.  70    is a diagram showing an example of an occupancy code according to Embodiment 9; 
         FIG.  71    is a diagram showing an example of a quadtree structure according to Embodiment 9; 
         FIG.  72    is a diagram showing an example of an occupancy code and a location code according to Embodiment 9; 
         FIG.  73    is a diagram showing an example of three-dimensional points obtained through LiDAR according to Embodiment 9; 
         FIG.  74    is a diagram showing an example of an octree structure according to Embodiment 9; 
         FIG.  75    is a diagram showing an example of hybrid encoding according to Embodiment 9; 
         FIG.  76    is a diagram for describing a method for switching between location encoding and occupancy encoding according to Embodiment 9; 
         FIG.  77    is a diagram showing an example of a location encoded bitstream according to Embodiment 9; 
         FIG.  78    is a diagram showing an example of a hybrid encoded bitstream according to Embodiment 9; 
         FIG.  79    is a diagram showing an occupancy code tree structure of important three-dimensional points according to Embodiment 9; 
         FIG.  80    is a diagram showing an occupancy code tree structure of non-important three-dimensional points according to Embodiment 9; 
         FIG.  81    is a diagram showing an example of a hybrid encoded bitstream according to Embodiment 9; 
         FIG.  82    is a diagram showing an example of a bitstream including encoding mode information according to Embodiment 9; 
         FIG.  83    is a diagram showing an example syntax according to Embodiment 9; 
         FIG.  84    is a flowchart of an encoding process according to Embodiment 9; 
         FIG.  85    is a flowchart of a node encoding process according to Embodiment 9; 
         FIG.  86    is a flowchart of a decoding process according to Embodiment 9; 
         FIG.  87    is a flowchart of a node decoding process according to Embodiment 9; 
         FIG.  88    is a diagram illustrating an example of a tree structure according to Embodiment 10; 
         FIG.  89    is a graph showing an example of the number of valid leaves of each branch according to Embodiment 10; 
         FIG.  90    is a diagram illustrating an application example of encoding schemes according to Embodiment 10; 
         FIG.  91    is a diagram illustrating an example of a dense branch area according to Embodiment 10; 
         FIG.  92    is a diagram illustrating an example of a dense three-dimensional point cloud according to Embodiment 10; 
         FIG.  93    is a diagram illustrating an example of a sparse three-dimensional point cloud according to Embodiment 10; 
         FIG.  94    is a flowchart of an encoding process according to Embodiment 10; 
         FIG.  95    is a flowchart of a decoding process according to Embodiment 10; 
         FIG.  96    is a flowchart of an encoding process according to Embodiment 10; 
         FIG.  97    is a flowchart of a decoding process according to Embodiment 10; 
         FIG.  98    is a flowchart of an encoding process according to Embodiment 10; 
         FIG.  99    is a flowchart of a decoding process according to Embodiment 10; 
         FIG.  100    is a flowchart of a process of separating three-dimensional points according to Embodiment 10; 
         FIG.  101    is a diagram illustrating an example of a syntax according to Embodiment 10; 
         FIG.  102    is a diagram illustrating an example of a dense branch according to Embodiment 10; 
         FIG.  103    is a diagram illustrating an example of a sparse branch according to Embodiment 10; 
         FIG.  104    is a flowchart of an encoding process according to a variation of Embodiment 10; 
         FIG.  105    is a flowchart of a decoding process according to the variation of Embodiment 10; 
         FIG.  106    is a flowchart of a process of separating three-dimensional points according to the variation of Embodiment 10; 
         FIG.  107    is a diagram illustrating an example of a syntax according to the variation of Embodiment 10; 
         FIG.  108    is a flowchart of an encoding process according to Embodiment 10; 
         FIG.  109    is a flowchart of a decoding process according to Embodiment 10; 
         FIG.  110    is a diagram illustrating an example of a tree structure according to Embodiment 11; 
         FIG.  111    is a diagram illustrating an example of occupancy codes according to Embodiment 11; 
         FIG.  112    is a diagram schematically illustrating an operation performed by a three-dimensional data encoding device according to Embodiment 11; 
         FIG.  113    is a diagram illustrating an example of geometry information according to Embodiment 11; 
         FIG.  114    is a diagram illustrating an example of selecting a coding table using geometry information according to Embodiment 11; 
         FIG.  115    is a diagram illustrating an example of selecting a coding table using structure information according to Embodiment 11; 
         FIG.  116    is a diagram illustrating an example of selecting a coding table using attribute information according to Embodiment 11; 
         FIG.  117    is a diagram illustrating an example of selecting a coding table using attribute information according to Embodiment 11; 
         FIG.  118    is a diagram illustrating an example of a structure of a bitstream according to Embodiment 11; 
         FIG.  119    is a diagram illustrating an example of a coding table according to Embodiment 11; 
         FIG.  120    is a diagram illustrating an example of a coding table according to Embodiment 11; 
         FIG.  121    is a diagram illustrating an example of a structure of a bitstream according to Embodiment 11; 
         FIG.  122    is a diagram illustrating an example of a coding table according to Embodiment 11; 
         FIG.  123    is a diagram illustrating an example of a coding table according to Embodiment 11; 
         FIG.  124    is a diagram illustrating an example of bit numbers of an occupancy code according to Embodiment 11; 
         FIG.  125    is a flowchart of an encoding process using geometry information according to Embodiment 11; 
         FIG.  126    is a flowchart of a decoding process using geometry information according to Embodiment 11; 
         FIG.  127    is a flowchart of an encoding process using structure information according to Embodiment 11; 
         FIG.  128    is a flowchart of a decoding process using structure information according to Embodiment 11; 
         FIG.  129    is a flowchart of an encoding process using attribute information according to Embodiment 11; 
         FIG.  130    is a flowchart of a decoding process using attribute information according to Embodiment 11; 
         FIG.  131    is a flowchart of a process of selecting a coding table using geometry information according to Embodiment 11; 
         FIG.  132    is a flowchart of a process of selecting a coding table using structure information according to Embodiment 11; 
         FIG.  133    is a flowchart of a process of selecting a coding table using attribute information according to Embodiment 11; 
         FIG.  134    is a block diagram of a three-dimensional data encoding device according to Embodiment 11; 
         FIG.  135    is a block diagram of a three-dimensional data decoding device according to Embodiment 11; 
         FIG.  136    is a diagram illustrating a reference relationship in an octree structure according to Embodiment 12; 
         FIG.  137    is a diagram illustrating a reference relationship in a spatial region according to Embodiment 12; 
         FIG.  138    is a diagram illustrating an example of neighboring reference nodes according to Embodiment 12; 
         FIG.  139    is a diagram illustrating a relationship between a parent node and nodes according to Embodiment 12; 
         FIG.  140    is a diagram illustrating an example of an occupancy code of the parent node according to Embodiment 12; 
         FIG.  141    is a block diagram of a three-dimensional data encoding device according to Embodiment 12; 
         FIG.  142    is a block diagram of a three-dimensional data decoding device according to Embodiment 12; 
         FIG.  143    is a flowchart of a three-dimensional data encoding process according to Embodiment 12; 
         FIG.  144    is a flowchart of a three-dimensional data decoding process according to Embodiment 12; 
         FIG.  145    is a diagram illustrating an example of selecting a coding table according to Embodiment 12; 
         FIG.  146    is a diagram illustrating a reference relationship in a spatial region according to Variation 1 of Embodiment 12; 
         FIG.  147    is a diagram illustrating an example of a syntax of header information according to Variation 1 of Embodiment 12; 
         FIG.  148    is a diagram illustrating an example of a syntax of header information according to Variation 1 of Embodiment 12; 
         FIG.  149    is a diagram illustrating an example of neighboring reference nodes according to Variation 2 of Embodiment 12; 
         FIG.  150    is a diagram illustrating an example of a current node and neighboring nodes according to Variation 2 of Embodiment 12; 
         FIG.  151    is a diagram illustrating a reference relationship in an octree structure according to Variation 3 of Embodiment 12; 
         FIG.  152    is a diagram illustrating a reference relationship in a spatial region according to Variation 3 of Embodiment 12; 
         FIG.  153    is a diagram illustrating an example of a syntax of header information according to Embodiment 13; 
         FIG.  154    is a diagram illustrating a configuration example of an octree when mode information according to Embodiment 13 indicates 1; 
         FIG.  155    is a diagram illustrating a configuration example of an octree when mode information according to Embodiment 13 indicates 0; 
         FIG.  156    is a diagram illustrating an example of a syntax of information of a node according to Embodiment 13; 
         FIG.  157    is a flowchart of a three-dimensional data encoding process according to Embodiment 13; 
         FIG.  158    is a flowchart of a three-dimensional data decoding process according to Embodiment 13; 
         FIG.  159    is a block diagram of a three-dimensional data encoding device according to Embodiment 13; 
         FIG.  160    is a block diagram of a three-dimensional data decoding device according to Embodiment 13; 
         FIG.  161    is a flowchart of a three-dimensional data encoding process according to Embodiment 13; 
         FIG.  162    is a flowchart of a three-dimensional data decoding process according to Embodiment 13; 
         FIG.  163    is a diagram illustrating examples of a 1-bit occupied position and a remaining bit according to Embodiment 14; 
         FIG.  164    is a diagram for illustrating a process of determining whether to apply occupied position encoding according to Embodiment 14; 
         FIG.  165    is a diagram illustrating an example of a syntax of information of a node according to Embodiment 14; 
         FIG.  166    is a flowchart of a three-dimensional data encoding process according to Embodiment 14; 
         FIG.  167    is a flowchart of an occupied position encoding process according to Embodiment 14; 
         FIG.  168    is a flowchart of a three-dimensional data decoding process according to Embodiment 14; 
         FIG.  169    is a flowchart of an occupied position decoding process according to Embodiment 14; 
         FIG.  170    is a block diagram of a three-dimensional data encoding device according to Embodiment 14; 
         FIG.  171    is a block diagram of a three-dimensional data decoding device according to Embodiment 14; 
         FIG.  172    is a flowchart of a three-dimensional data encoding process according to Embodiment 14; 
         FIG.  173    is a flowchart of a three-dimensional data decoding process according to Embodiment 14; 
         FIG.  174    is a diagram for illustrating duplicated points according to Embodiment 15; 
         FIG.  175    is a diagram for illustrating a process performed on duplicated points according to Embodiment 15; 
         FIG.  176    is a diagram illustrating an example of a syntax of header information according to Embodiment 15; 
         FIG.  177    is a diagram illustrating an example of a syntax of information of a node according to Embodiment 15; 
         FIG.  178    is a flowchart of a three-dimensional data encoding process according to Embodiment 15; 
         FIG.  179    is a flowchart of the three-dimensional data encoding process according to Embodiment 15; 
         FIG.  180    is a flowchart of a three-dimensional data decoding process according to Embodiment 15; 
         FIG.  181    is a block diagram of a three-dimensional data decoding device according to Embodiment 15; 
         FIG.  182    is a block diagram of a three-dimensional data decoding device according to Embodiment 15; 
         FIG.  183    is a flowchart of a variation of the three-dimensional data encoding process according to Embodiment 15; 
         FIG.  184    is a diagram for illustrating a process for duplicated points according to Embodiment 15; 
         FIG.  185    is a diagram illustrating an example of neighboring nodes according to Embodiment 16; 
         FIG.  186    is a diagram illustrating an example of nodes to be searched according to Embodiment 16; 
         FIG.  187    is a diagram for illustrating a search process for a neighboring node according to Embodiment 16; 
         FIG.  188    is a diagram for illustrating an update process for neighboring information according to Embodiment 16; 
         FIG.  189    is a diagram for illustrating an update process for neighboring information according to Embodiment 16; 
         FIG.  190    is a diagram for illustrating a search process for which a search threshold value is provided according to Embodiment 16; 
         FIG.  191    is a diagram illustrating an example of indexes for which Morton codes are used according to Embodiment 16; 
         FIG.  192    is a diagram illustrating an example of a queue for which Morton codes are used according to Embodiment 16; 
         FIG.  193    is a block diagram of a three-dimensional data encoding device according to Embodiment 16; 
         FIG.  194    is a block diagram of a three-dimensional data decoding device according to Embodiment 16; 
         FIG.  195    is a flowchart of a three-dimensional data encoding process according to Embodiment 16; 
         FIG.  196    is a flowchart of a three-dimensional data decoding process according to Embodiment 16; 
         FIG.  197    is a diagram illustrating an example of a syntax of header information according to Embodiment 16; 
         FIG.  198    is a diagram illustrating an example of a syntax of information of a node according to Embodiment 16; 
         FIG.  199    is a flowchart of a three-dimensional data encoding process according to Embodiment 16; 
         FIG.  200    is a flowchart of a three-dimensional data decoding process according to Embodiment 16; 
         FIG.  201    is a flowchart of a three-dimensional data encoding process according to Embodiment 16; and 
         FIG.  202    is a flowchart of a three-dimensional data decoding process according to Embodiment 16. 
     
    
    
     DETAILED DESCRIPTION OF THE EMBODIMENTS 
     A three-dimensional data encoding method according to one aspect of the present disclosure includes encoding information of a current node included in an N-ary tree structure of three-dimensional points included in three-dimensional data, where N is an integer greater than or equal to 2. In the encoding, first information is encoded, the first information indicating a range for one or more referable neighboring nodes among neighboring nodes spatially neighboring the current node, and the current node is encoded with reference to a neighboring node within the range. 
     With this, since the three-dimensional data encoding method makes it possible to limit referable neighboring nodes, the three-dimensional data encoding method makes it possible to reduce the amount of processing. 
     For example, in the encoding, a coding table may be selected based on whether the neighboring node within the range includes a three-dimensional point, and the information of the current node may be entropy encoded using the coding table selected. 
     For example, in the encoding, a search may be performed for information of the one or more referable neighboring nodes among the neighboring nodes spatially neighboring the current node, and the first information may indicate a range for the search. 
     For example, in the search, information of nodes may be searched for in a predetermined order, and the first information may indicate a total number of nodes on which the search is to be performed. 
     For example, in the search, indexes of Morton codes may be used. 
     For example, in the encoding, second information may be encoded, the second information indicating whether the range for the one or more referable neighboring nodes is to be limited, and the first information may be encoded when the second information indicates that the range for the one or more referable neighboring nodes is to be limited. 
     For example, the range for the one or more referable neighboring nodes may change according to a layer to which the current node belongs in the N-ary tree structure. 
     A three-dimensional data decoding method according to one aspect of the present disclosure includes decoding information of a current node included in an N-ary tree structure of three-dimensional points included in three-dimensional data, where N is an integer greater than or equal to 2. In the decoding, first information is decoded from a bitstream, the first information indicating a range for one or more referable neighboring nodes among neighboring nodes spatially neighboring the current node, and the current node is decoded with reference to a neighboring node within the range. 
     With this, since the three-dimensional data decoding method makes it possible to limit referable neighboring nodes, the three-dimensional data decoding method makes it possible to reduce the amount of processing. 
     For example, in the decoding, a coding table may be selected based on whether the neighboring node within the range includes a three-dimensional point, and the information of the current node may be entropy decoded using the coding table selected. 
     For example, in the decoding, a search may be performed for information of the one or more referable neighboring nodes among the neighboring nodes spatially neighboring the current node, and the first information may indicate a range for the search. 
     For example, in the search, information of nodes may be searched for in a predetermined order, and the first information may indicate a total number of nodes on which the search is to be performed. 
     For example, in the search, indexes of Morton codes may be used. 
     For example, in the decoding, second information may be decoded, the second information indicating whether the range for the one or more referable neighboring nodes is to be limited, and the first information may be decoded when the second information indicates that the range for the one or more referable neighboring nodes is to be limited. 
     For example, the range for the one or more referable neighboring nodes may change according to a layer to which the current node belongs in the N-ary tree structure. 
     A three-dimensional data encoding device according to one aspect of the present disclosure includes a processor and memory. Using the memory, the processor encodes information of a current node included in an N-ary tree structure of three-dimensional points included in three-dimensional data, where N is an integer greater than or equal to 2. In the encoding, first information is encoded, the first information indicating a range for one or more referable neighboring nodes among neighboring nodes spatially neighboring the current node, and the current node is encoded with reference to a neighboring node within the range. 
     With this, since the three-dimensional data encoding device limits referable neighboring nodes, the three-dimensional data encoding device reduces the amount of processing. 
     A three-dimensional data decoding device according to one aspect of the present disclosure includes a processor and memory. Using the memory, the processor decodes information of a current node included in an N-ary tree structure of three-dimensional points included in three-dimensional data, where N is an integer greater than or equal to 2. In the decoding, first information is decoded from a bitstream, the first information indicating a range for one or more referable neighboring nodes among neighboring nodes spatially neighboring the current node, and the current node is decoded with reference to a neighboring node within the range. 
     With this, since the three-dimensional data decoding device limits referable neighboring nodes, the three-dimensional data decoding device reduces the amount of processing. 
     Note 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. 
     The following describes embodiments with reference to the drawings. Note that the following embodiments show exemplary embodiments of the present disclosure. The numerical values, shapes, materials, structural components, the arrangement and connection of the structural components, steps, the processing order of the steps, etc. shown in the following embodiments are mere examples, and thus are not intended to limit the present disclosure. Of the structural components described in the following embodiments, structural components not recited in any one of the independent claims that indicate the broadest concepts will be described as optional structural components. 
     Embodiment 1 
     First, the data structure of encoded three-dimensional data (hereinafter also referred to as encoded data) according to the present embodiment will be described.  FIG.  1    is a diagram showing the structure of encoded three-dimensional data according to the present embodiment. 
     In the present embodiment, a three-dimensional space is divided into spaces (SPCs), which correspond to pictures in moving picture encoding, and the three-dimensional data is encoded on a SPC-by-SPC basis. Each SPC is further divided into volumes (VLMs), which correspond to macroblocks, etc. in moving picture encoding, and predictions and transforms are performed on a VLM-by-VLM basis. Each volume includes a plurality of voxels (VXLs), each being a minimum unit in which position coordinates are associated. Note that prediction is a process of generating predictive three-dimensional data analogous to a current processing unit by referring to another processing unit, and encoding a differential between the predictive three-dimensional data and the current processing unit, as in the case of predictions performed on two-dimensional images. Such prediction includes not only spatial prediction in which another prediction unit corresponding to the same time is referred to, but also temporal prediction in which a prediction unit corresponding to a different time is referred to. 
     When encoding a three-dimensional space represented by point group data such as a point cloud, for example, the three-dimensional data encoding device (hereinafter also referred to as the encoding device) encodes the points in the point group or points included in the respective voxels in a collective manner, in accordance with a voxel size. Finer voxels enable a highly-precise representation of the three-dimensional shape of a point group, while larger voxels enable a rough representation of the three-dimensional shape of a point group. 
     Note that the following describes the case where three-dimensional data is a point cloud, but three-dimensional data is not limited to a point cloud, and thus three-dimensional data of any format may be employed. 
     Also note that voxels with a hierarchical structure may be used. In such a case, when the hierarchy includes n levels, whether a sampling point is included in the n−1th level or its lower levels (the lower levels of the n-th level) may be sequentially indicated. For example, when only the n-th level is decoded, and the n−1th level or its lower levels include a sampling point, the n-th level can be decoded on the assumption that a sampling point is included at the center of a voxel in the n-th level. 
     Also, the encoding device obtains point group data, using, for example, a distance sensor, a stereo camera, a monocular camera, a gyroscope sensor, or an inertial sensor. 
     As in the case of moving picture encoding, each SPC is classified into one of at least the three prediction structures that include: intra SPC (I-SPC), which is individually decodable; predictive SPC (P-SPC) capable of only a unidirectional reference; and bidirectional SPC (B-SPC) capable of bidirectional references. Each SPC includes two types of time information: decoding time and display time. 
     Furthermore, as shown in  FIG.  1   , a processing unit that includes a plurality of SPCs is a group of spaces (GOS), which is a random access unit. Also, a processing unit that includes a plurality of GOSs is a world (WLD). 
     The spatial region occupied by each world is associated with an absolute position on earth, by use of, for example, GPS, or latitude and longitude information. Such position information is stored as meta-information. Note that meta-information may be included in encoded data, or may be transmitted separately from the encoded data. 
     Also, inside a GOS, all SPCs may be three-dimensionally adjacent to one another, or there may be a SPC that is not three-dimensionally adjacent to another SPC. 
     Note that the following also describes processes such as encoding, decoding, and reference to be performed on three-dimensional data included in processing units such as GOS, SPC, and VLM, simply as performing encoding/to encode, decoding/to decode, referring to, etc. on a processing unit. Also note that three-dimensional data included in a processing unit includes, for example, at least one pair of a spatial position such as three-dimensional coordinates and an attribute value such as color information. 
     Next, the prediction structures among SPCs in a GOS will be described. A plurality of SPCs in the same GOS or a plurality of VLMs in the same SPC occupy mutually different spaces, while having the same time information (the decoding time and the display time). 
     A SPC in a GOS that comes first in the decoding order is an I-SPC. GOSs come in two types: closed GOS and open GOS. A closed GOS is a GOS in which all SPCs in the GOS are decodable when decoding starts from the first I-SPC. Meanwhile, an open GOS is a GOS in which a different GOS is referred to in one or more SPCs preceding the first I-SPC in the GOS in the display time, and thus cannot be singly decoded. 
     Note that in the case of encoded data of map information, for example, a WLD is sometimes decoded in the backward direction, which is opposite to the encoding order, and thus backward reproduction is difficult when GOSs are interdependent. In such a case, a closed GOS is basically used. 
     Each GOS has a layer structure in height direction, and SPCs are sequentially encoded or decoded from SPCs in the bottom layer; 
       FIG.  2    is a diagram showing an example of prediction structures among SPCs that belong to the lowermost layer in a GOS.  FIG.  3    is a diagram showing an example of prediction structures among layers. 
     A GOS includes at least one I-SPC. Of the objects in a three-dimensional space, such as a person, an animal, a car, a bicycle, a signal, and a building serving as a landmark, a small-sized object is especially effective when encoded as an I-SPC. When decoding a GOS at a low throughput or at a high speed, for example, the three-dimensional data decoding device (hereinafter also referred to as the decoding device) decodes only I-SPC(s) in the GOS. 
     The encoding device may also change the encoding interval or the appearance frequency of I-SPCs, depending on the degree of sparseness and denseness of the objects in a WLD. 
     In the structure shown in  FIG.  3   , the encoding device or the decoding device encodes or decodes a plurality of layers sequentially from the bottom layer (layer  1 ). This increases the priority of data on the ground and its vicinity, which involve a larger amount of information, when, for example, a self-driving car is concerned. 
     Regarding encoded data used for a drone, for example, encoding or decoding may be performed sequentially from SPCs in the top layer in a GOS in height direction. 
     The encoding device or the decoding device may also encode or decode a plurality of layers in a manner that the decoding device can have a rough grasp of a GOS first, and then the resolution is gradually increased. The encoding device or the decoding device may perform encoding or decoding in the order of layers  3 ,  8 ,  1 ,  9  . . . , for example. 
     Next, the handling of static objects and dynamic objects will be described. 
     A three-dimensional space includes scenes or still objects such as a building and a road (hereinafter collectively referred to as static objects), and objects with motion such as a car and a person (hereinafter collectively referred to as dynamic objects). Object detection is separately performed by, for example, extracting keypoints from point cloud data, or from video of a camera such as a stereo camera. In this description, an example method of encoding a dynamic object will be described. 
     A first method is a method in which a static object and a dynamic object are encoded without distinction. A second method is a method in which a distinction is made between a static object and a dynamic object on the basis of identification information. 
     For example, a GOS is used as an identification unit. In such a case, a distinction is made between a GOS that includes SPCs constituting a static object and a GOS that includes SPCs constituting a dynamic object, on the basis of identification information stored in the encoded data or stored separately from the encoded data. 
     Alternatively, a SPC may be used as an identification unit. In such a case, a distinction is made between a SPC that includes VLMs constituting a static object and a SPC that includes VLMs constituting a dynamic object, on the basis of the identification information thus described. 
     Alternatively, a VLM or a VXL may be used as an identification unit. In such a case, a distinction is made between a VLM or a VXL that includes a static object and a VLM or a VXL that includes a dynamic object, on the basis of the identification information thus described. 
     The encoding device may also encode a dynamic object as at least one VLM or SPC, and may encode a VLM or a SPC including a static object and a SPC including a dynamic object as mutually different GOSs. When the GOS size is variable depending on the size of a dynamic object, the encoding device separately stores the GOS size as meta-information. 
     The encoding device may also encode a static object and a dynamic object separately from each other, and may superimpose the dynamic object onto a world constituted by static objects. In such a case, the dynamic object is constituted by at least one SPC, and each SPC is associated with at least one SPC constituting the static object onto which the each SPC is to be superimposed. Note that a dynamic object may be represented not by SPC(s) but by at least one VLM or VXL. 
     The encoding device may also encode a static object and a dynamic object as mutually different streams. 
     The encoding device may also generate a GOS that includes at least one SPC constituting a dynamic object. The encoding device may further set the size of a GOS including a dynamic object (GOS_M) and the size of a GOS including a static object corresponding to the spatial region of GOS_M at the same size (such that the same spatial region is occupied). This enables superimposition to be performed on a GOS-by-GOS basis. 
     SPC(s) included in another encoded GOS may be referred to in a P-SPC or a B-SPC constituting a dynamic object. In the case where the position of a dynamic object temporally changes, and the same dynamic object is encoded as an object in a GOS corresponding to a different time, referring to SPC(s) across GOSs is effective in terms of compression rate. 
     The first method and the second method may be selected in accordance with the intended use of encoded data. When encoded three-dimensional data is used as a map, for example, a dynamic object is desired to be separated, and thus the encoding device uses the second method. Meanwhile, the encoding device uses the first method when the separation of a dynamic object is not required such as in the case where three-dimensional data of an event such as a concert and a sports event is encoded. 
     The decoding time and the display time of a GOS or a SPC are storable in encoded data or as meta-information. All static objects may have the same time information. In such a case, the decoding device may determine the actual decoding time and display time. Alternatively, a different value may be assigned to each GOS or SPC as the decoding time, and the same value may be assigned as the display time. Furthermore, as in the case of the decoder model in moving picture encoding such as Hypothetical Reference Decoder (HRD) compliant with HEVC, a model may be employed that ensures that a decoder can perform decoding without fail by having a buffer of a predetermined size and by reading a bitstream at a predetermined bit rate in accordance with the decoding times. 
     Next, the topology of GOSs in a world will be described. The coordinates of the three-dimensional space in a world are represented by the three coordinate axes (x axis, y axis, and z axis) that are orthogonal to one another. A predetermined rule set for the encoding order of GOSs enables encoding to be performed such that spatially adjacent GOSs are contiguous in the encoded data. In an example shown in  FIG.  4   , for example, GOSs in the x and z planes are successively encoded. After the completion of encoding all GOSs in certain x and z planes, the value of the y axis is updated. Stated differently, the world expands in the y axis direction as the encoding progresses. The GOS index numbers are set in accordance with the encoding order. 
     Here, the three-dimensional spaces in the respective worlds are previously associated one-to-one with absolute geographical coordinates such as GPS coordinates or latitude/longitude coordinates. Alternatively, each three-dimensional space may be represented as a position relative to a previously set reference position. The directions of the x axis, the y axis, and the z axis in the three-dimensional space are represented by directional vectors that are determined on the basis of the latitudes and the longitudes, etc. Such directional vectors are stored together with the encoded data as meta-information. 
     GOSs have a fixed size, and the encoding device stores such size as meta-information. The GOS size may be changed depending on, for example, whether it is an urban area or not, or whether it is inside or outside of a room. Stated differently, the GOS size may be changed in accordance with the amount or the attributes of objects with information values. Alternatively, in the same world, the encoding device may adaptively change the GOS size or the interval between I-SPCs in GOSs in accordance with the object density, etc. For example, the encoding device sets the GOS size to smaller and the interval between I-SPCs in GOSs to shorter, as the object density is higher. 
     In an example shown in  FIG.  5   , to enable random access with a finer granularity, a GOS with a high object density is partitioned into the regions of the third to tenth GOSs. Note that the seventh to tenth GOSs are located behind the third to sixth GOSs. 
     Next, the structure and the operation flow of the three-dimensional data encoding device according to the present embodiment will be described.  FIG.  6    is a block diagram of three-dimensional data encoding device  100  according to the present embodiment.  FIG.  7    is a flowchart of an example operation performed by three-dimensional data encoding device  100 . 
     Three-dimensional data encoding device  100  shown in  FIG.  6    encodes three-dimensional data  111 , thereby generating encoded three-dimensional data  112 . Such three-dimensional data encoding device  100  includes obtainer  101 , encoding region determiner  102 , divider  103 , and encoder  104 . 
     As shown in  FIG.  7   , first, obtainer  101  obtains three-dimensional data  111 , which is point group data (S 101 ). 
     Next, encoding region determiner  102  determines a current region for encoding from among spatial regions corresponding to the obtained point group data (S 102 ). For example, in accordance with the position of a user or a vehicle, encoding region determiner  102  determines, as the current region, a spatial region around such position. 
     Next, divider  103  divides the point group data included in the current region into processing units. The processing units here means units such as GOSs and SPCs described above. The current region here corresponds to, for example, a world described above. More specifically, divider  103  divides the point group data into processing units on the basis of a predetermined GOS size, or the presence/absence/size of a dynamic object (S 103 ). Divider  103  further determines the starting position of the SPC that comes first in the encoding order in each GOS. 
     Next, encoder  104  sequentially encodes a plurality of SPCs in each GOS, thereby generating encoded three-dimensional data  112  (S 104 ). 
     Note that although an example is described here in which the current region is divided into GOSs and SPCs, after which each GOS is encoded, the processing steps are not limited to this order. For example, steps may be employed in which the structure of a single GOS is determined, which is followed by the encoding of such GOS, and then the structure of the subsequent GOS is determined. 
     As thus described, three-dimensional data encoding device  100  encodes three-dimensional data  111 , thereby generating encoded three-dimensional data  112 . More specifically, three-dimensional data encoding device  100  divides three-dimensional data into first processing units (GOSs), each being a random access unit and being associated with three-dimensional coordinates, divides each of the first processing units (GOSs) into second processing units (SPCs), and divides each of the second processing units (SPCs) into third processing units (VLMs). Each of the third processing units (VLMs) includes at least one voxel (VXL), which is the minimum unit in which position information is associated. 
     Next, three-dimensional data encoding device  100  encodes each of the first processing units (GOSs), thereby generating encoded three-dimensional data  112 . More specifically, three-dimensional data encoding device  100  encodes each of the second processing units (SPCs) in each of the first processing units (GOSs). Three-dimensional data encoding device  100  further encodes each of the third processing units (VLMs) in each of the second processing units (SPCs). 
     When a current first processing unit (GOS) is a closed GOS, for example, three-dimensional data encoding device  100  encodes a current second processing unit (SPC) included in such current first processing unit (GOS) by referring to another second processing unit (SPC) included in the current first processing unit (GOS). Stated differently, three-dimensional data encoding device  100  refers to no second processing unit (SPC) included in a first processing unit (GOS) that is different from the current first processing unit (GOS). 
     Meanwhile, when a current first processing unit (GOS) is an open GOS, three-dimensional data encoding device  100  encodes a current second processing unit (SPC) included in such current first processing unit (GOS) by referring to another second processing unit (SPC) included in the current first processing unit (GOS) or a second processing unit (SPC) included in a first processing unit (GOS) that is different from the current first processing unit (GOS). 
     Also, three-dimensional data encoding device  100  selects, as the type of a current second processing unit (SPC), one of the following: a first type (I-SPC) in which another second processing unit (SPC) is not referred to; a second type (P-SPC) in which another single second processing unit (SPC) is referred to; and a third type in which other two second processing units (SPC) are referred to. Three-dimensional data encoding device  100  encodes the current second processing unit (SPC) in accordance with the selected type. 
     Next, the structure and the operation flow of the three-dimensional data decoding device according to the present embodiment will be described.  FIG.  8    is a block diagram of three-dimensional data decoding device  200  according to the present embodiment.  FIG.  9    is a flowchart of an example operation performed by three-dimensional data decoding device  200 . 
     Three-dimensional data decoding device  200  shown in  FIG.  8    decodes encoded three-dimensional data  211 , thereby generating decoded three-dimensional data  212 . Encoded three-dimensional data  211  here is, for example, encoded three-dimensional data  112  generated by three-dimensional data encoding device  100 . Such three-dimensional data decoding device  200  includes obtainer  201 , decoding start GOS determiner  202 , decoding SPC determiner  203 , and decoder  204 . 
     First, obtainer  201  obtains encoded three-dimensional data  211  (S 201 ). Next, decoding start GOS determiner  202  determines a current GOS for decoding (S 202 ). More specifically, decoding start GOS determiner  202  refers to meta-information stored in encoded three-dimensional data  211  or stored separately from the encoded three-dimensional data to determine, as the current GOS, a GOS that includes a SPC corresponding to the spatial position, the object, or the time from which decoding is to start. 
     Next, decoding SPC determiner  203  determines the type(s) (I, P, and/or B) of SPCs to be decoded in the GOS (S 203 ). For example, decoding SPC determiner  203  determines whether to (1) decode only I-SPC(s), (2) to decode I-SPC(s) and P-SPCs, or (3) to decode SPCs of all types. Note that the present step may not be performed, when the type(s) of SPCs to be decoded are previously determined such as when all SPCs are previously determined to be decoded. 
     Next, decoder  204  obtains an address location within encoded three-dimensional data  211  from which a SPC that comes first in the GOS in the decoding order (the same as the encoding order) starts. Decoder  204  obtains the encoded data of the first SPC from the address location, and sequentially decodes the SPCs from such first SPC (S 204 ). Note that the address location is stored in the meta-information, etc. 
     Three-dimensional data decoding device  200  decodes decoded three-dimensional data  212  as thus described. More specifically, three-dimensional data decoding device  200  decodes each encoded three-dimensional data  211  of the first processing units (GOSs), each being a random access unit and being associated with three-dimensional coordinates, thereby generating decoded three-dimensional data  212  of the first processing units (GOSs). Even more specifically, three-dimensional data decoding device  200  decodes each of the second processing units (SPCs) in each of the first processing units (GOSs). Three-dimensional data decoding device  200  further decodes each of the third processing units (VLMs) in each of the second processing units (SPCs). 
     The following describes meta-information for random access. Such meta-information is generated by three-dimensional data encoding device  100 , and included in encoded three-dimensional data  112  ( 211 ). 
     In the conventional random access for a two-dimensional moving picture, decoding starts from the first frame in a random access unit that is close to a specified time. Meanwhile, in addition to times, random access to spaces (coordinates, objects, etc.) is assumed to be performed in a world. 
     To enable random access to at least three elements of coordinates, objects, and times, tables are prepared that associate the respective elements with the GOS index numbers. Furthermore, the GOS index numbers are associated with the addresses of the respective first I-SPCs in the GOSs.  FIG.  10    is a diagram showing example tables included in the meta-information. Note that not all the tables shown in  FIG.  10    are required to be used, and thus at least one of the tables is used. 
     The following describes an example in which random access is performed from coordinates as a starting point. To access the coordinates (x2, y2, and z2), the coordinates-GOS table is first referred to, which indicates that the point corresponding to the coordinates (x2, y2, and z2) is included in the second GOS. Next, the GOS-address table is referred to, which indicates that the address of the first I-SPC in the second GOS is addr(2). As such, decoder  204  obtains data from this address to start decoding. 
     Note that the addresses may either be logical addresses or physical addresses of an HDD or a memory. Alternatively, information that identifies file segments may be used instead of addresses. File segments are, for example, units obtained by segmenting at least one GOS, etc. 
     When an object spans across a plurality of GOSs, the object-GOS table may show a plurality of GOSs to which such object belongs. When such plurality of GOSs are closed GOSs, the encoding device and the decoding device can perform encoding or decoding in parallel. Meanwhile, when such plurality of GOSs are open GOSs, a higher compression efficiency is achieved by the plurality of GOSs referring to each other. 
     Example objects include a person, an animal, a car, a bicycle, a signal, and a building serving as a landmark. For example, three-dimensional data encoding device  100  extracts keypoints specific to an object from a three-dimensional point cloud, etc., when encoding a world, and detects the object on the basis of such keypoints to set the detected object as a random access point. 
     As thus described, three-dimensional data encoding device  100  generates first information indicating a plurality of first processing units (GOSs) and the three-dimensional coordinates associated with the respective first processing units (GOSs). Encoded three-dimensional data  112  ( 211 ) includes such first information. The first information further indicates at least one of objects, times, and data storage locations that are associated with the respective first processing units (GOSs). 
     Three-dimensional data decoding device  200  obtains the first information from encoded three-dimensional data  211 . Using such first information, three-dimensional data decoding device  200  identifies encoded three-dimensional data  211  of the first processing unit that corresponds to the specified three-dimensional coordinates, object, or time, and decodes encoded three-dimensional data  211 . 
     The following describes an example of other meta-information. In addition to the meta-information for random access, three-dimensional data encoding device  100  may also generate and store meta-information as described below, and three-dimensional data decoding device  200  may use such meta-information at the time of decoding. 
     When three-dimensional data is used as map information, for example, a profile is defined in accordance with the intended use, and information indicating such profile may be included in meta-information. For example, a profile is defined for an urban or a suburban area, or for a flying object, and the maximum or minimum size, etc. of a world, a SPC or a VLM, etc. is defined in each profile. For example, more detailed information is required for an urban area than for a suburban area, and thus the minimum VLM size is set to small. 
     The meta-information may include tag values indicating object types. Each of such tag values is associated with VLMs, SPCs, or GOSs that constitute an object. For example, a tag value may be set for each object type in a manner, for example, that the tag value “0” indicates “person,” the tag value “1” indicates “car,” and the tag value “2” indicates “signal.” Alternatively, when an object type is hard to judge, or such judgment is not required, a tag value may be used that indicates the size or the attribute indicating, for example, whether an object is a dynamic object or a static object. 
     The meta-information may also include information indicating a range of the spatial region occupied by a world. 
     The meta-information may also store the SPC or VXL size as header information common to the whole stream of the encoded data or to a plurality of SPCs, such as SPCs in a GOS. 
     The meta-information may also include identification information on a distance sensor or a camera that has been used to generate a point cloud, or information indicating the positional accuracy of a point group in the point cloud. 
     The meta-information may also include information indicating whether a world is made only of static objects or includes a dynamic object. 
     The following describes variations of the present embodiment. 
     The encoding device or the decoding device may encode or decode two or more mutually different SPCs or GOSs in parallel. GOSs to be encoded or decoded in parallel can be determined on the basis of meta-information, etc. indicating the spatial positions of the GOSs. 
     When three-dimensional data is used as a spatial map for use by a car or a flying object, etc. in traveling, or for creation of such a spatial map, for example, the encoding device or the decoding device may encode or decode GOSs or SPCs included in a space that is identified on the basis of GPS information, the route information, the zoom magnification, etc. 
     The decoding device may also start decoding sequentially from a space that is close to the self-location or the traveling route. The encoding device or the decoding device may give a lower priority to a space distant from the self-location or the traveling route than the priority of a nearby space to encode or decode such distant place. To “give a lower priority” means here, for example, to lower the priority in the processing sequence, to decrease the resolution (to apply decimation in the processing), or to lower the image quality (to increase the encoding efficiency by, for example, setting the quantization step to larger). 
     When decoding encoded data that is hierarchically encoded in a space, the decoding device may decode only the bottom level in the hierarchy. 
     The decoding device may also start decoding preferentially from the bottom level of the hierarchy in accordance with the zoom magnification or the intended use of the map. 
     For self-location estimation or object recognition, etc. involved in the self-driving of a car or a robot, the encoding device or the decoding device may encode or decode regions at a lower resolution, except for a region that is lower than or at a specified height from the ground (the region to be recognized). 
     The encoding device may also encode point clouds representing the spatial shapes of a room interior and a room exterior separately. For example, the separation of a GOS representing a room interior (interior GOS) and a GOS representing a room exterior (exterior GOS) enables the decoding device to select a GOS to be decoded in accordance with a viewpoint location, when using the encoded data. 
     The encoding device may also encode an interior GOS and an exterior GOS having close coordinates so that such GOSs come adjacent to each other in an encoded stream. For example, the encoding device associates the identifiers of such GOSs with each other, and stores information indicating the associated identifiers into the meta-information that is stored in the encoded stream or stored separately. This enables the decoding device to refer to the information in the meta-information to identify an interior GOS and an exterior GOS having close coordinates. 
     The encoding device may also change the GOS size or the SPC size depending on whether a GOS is an interior GOS or an exterior GOS. For example, the encoding device sets the size of an interior GOS to smaller than the size of an exterior GOS. The encoding device may also change the accuracy of extracting keypoints from a point cloud, or the accuracy of detecting objects, for example, depending on whether a GOS is an interior GOS or an exterior GOS. 
     The encoding device may also add, to encoded data, information by which the decoding device displays objects with a distinction between a dynamic object and a static object. This enables the decoding device to display a dynamic object together with, for example, a red box or letters for explanation. Note that the decoding device may display only a red box or letters for explanation, instead of a dynamic object. The decoding device may also display more particular object types. For example, a red box may be used for a car, and a yellow box may be used for a person. 
     The encoding device or the decoding device may also determine whether to encode or decode a dynamic object and a static object as a different SPC or GOS, in accordance with, for example, the appearance frequency of dynamic objects or a ratio between static objects and dynamic objects. For example, when the appearance frequency or the ratio of dynamic objects exceeds a threshold, a SPC or a GOS including a mixture of a dynamic object and a static object is accepted, while when the appearance frequency or the ratio of dynamic objects is below a threshold, a SPC or GOS including a mixture of a dynamic object and a static object is unaccepted. 
     When detecting a dynamic object not from a point cloud but from two-dimensional image information of a camera, the encoding device may separately obtain information for identifying a detection result (box or letters) and the object position, and encode these items of information as part of the encoded three-dimensional data. In such a case, the decoding device superimposes auxiliary information (box or letters) indicating the dynamic object onto a resultant of decoding a static object to display it. 
     The encoding device may also change the sparseness and denseness of VXLs or VLMs in a SPC in accordance with the degree of complexity of the shape of a static object. For example, the encoding device sets VXLs or VLMs at a higher density as the shape of a static object is more complex. The encoding device may further determine a quantization step, etc. for quantizing spatial positions or color information in accordance with the sparseness and denseness of VXLs or VLMs. For example, the encoding device sets the quantization step to smaller as the density of VXLs or VLMs is higher. 
     As described above, the encoding device or the decoding device according to the present embodiment encodes or decodes a space on a SPC-by-SPC basis that includes coordinate information. 
     Furthermore, the encoding device and the decoding device perform encoding or decoding on a volume-by-volume basis in a SPC. Each volume includes a voxel, which is the minimum unit in which position information is associated. 
     Also, using a table that associates the respective elements of spatial information including coordinates, objects, and times with GOSs or using a table that associates these elements with each other, the encoding device and the decoding device associate any ones of the elements with each other to perform encoding or decoding. The decoding device uses the values of the selected elements to determine the coordinates, and identifies a volume, a voxel, or a SPC from such coordinates to decode a SPC including such volume or voxel, or the identified SPC. 
     Furthermore, the encoding device determines a volume, a voxel, or a SPC that is selectable in accordance with the elements, through extraction of keypoints and object recognition, and encodes the determined volume, voxel, or SPC, as a volume, a voxel, or a SPC to which random access is possible. 
     SPCs are classified into three types: I-SPC that is singly encodable or decodable; P-SPC that is encoded or decoded by referring to any one of the processed SPCs; and B-SPC that is encoded or decoded by referring to any two of the processed SPCs. 
     At least one volume corresponds to a static object or a dynamic object. A SPC including a static object and a SPC including a dynamic object are encoded or decoded as mutually different GOSs. Stated differently, a SPC including a static object and a SPC including a dynamic object are assigned to different GOSs. 
     Dynamic objects are encoded or decoded on an object-by-object basis, and are associated with at least one SPC including a static object. Stated differently, a plurality of dynamic objects are individually encoded, and the obtained encoded data of the dynamic objects is associated with a SPC including a static object. 
     The encoding device and the decoding device give an increased priority to I-SPC(s) in a GOS to perform encoding or decoding. For example, the encoding device performs encoding in a manner that prevents the degradation of I-SPCs (in a manner that enables the original three-dimensional data to be reproduced with a higher fidelity after decoded). The decoding device decodes, for example, only I-SPCs. 
     The encoding device may change the frequency of using I-SPCs depending on the sparseness and denseness or the number (amount) of the objects in a world to perform encoding. Stated differently, the encoding device changes the frequency of selecting I-SPCs depending on the number or the sparseness and denseness of the objects included in the three-dimensional data. For example, the encoding device uses I-SPCs at a higher frequency as the density of the objects in a world is higher. 
     The encoding device also sets random access points on a GOS-by-GOS basis, and stores information indicating the spatial regions corresponding to the GOSs into the header information. 
     The encoding device uses, for example, a default value as the spatial size of a GOS. Note that the encoding device may change the GOS size depending on the number (amount) or the sparseness and denseness of objects or dynamic objects. For example, the encoding device sets the spatial size of a GOS to smaller as the density of objects or dynamic objects is higher or the number of objects or dynamic objects is greater. 
     Also, each SPC or volume includes a keypoint group that is derived by use of information obtained by a sensor such as a depth sensor, a gyroscope sensor, or a camera sensor. The coordinates of the keypoints are set at the central positions of the respective voxels. Furthermore, finer voxels enable highly accurate position information. 
     The keypoint group is derived by use of a plurality of pictures. A plurality of pictures include at least two types of time information: the actual time information and the same time information common to a plurality of pictures that are associated with SPCs (for example, the encoding time used for rate control, etc.). 
     Also, encoding or decoding is performed on a GOS-by-GOS basis that includes at least one SPC. 
     The encoding device and the decoding device predict P-SPCs or B-SPCs in a current GOS by referring to SPCs in a processed GOS. 
     Alternatively, the encoding device and the decoding device predict P-SPCs or B-SPCs in a current GOS, using the processed SPCs in the current GOS, without referring to a different GOS. 
     Furthermore, the encoding device and the decoding device transmit or receive an encoded stream on a world-by-world basis that includes at least one GOS. 
     Also, a GOS has a layer structure in one direction at least in a world, and the encoding device and the decoding device start encoding or decoding from the bottom layer. For example, a random accessible GOS belongs to the lowermost layer. A GOS that belongs to the same layer or a lower layer is referred to in a GOS that belongs to an upper layer. Stated differently, a GOS is spatially divided in a predetermined direction in advance to have a plurality of layers, each including at least one SPC. The encoding device and the decoding device encode or decode each SPC by referring to a SPC included in the same layer as the each SPC or a SPC included in a layer lower than that of the each SPC. 
     Also, the encoding device and the decoding device successively encode or decode GOSs on a world-by-world basis that includes such GOSs. In so doing, the encoding device and the decoding device write or read out information indicating the order (direction) of encoding or decoding as metadata. Stated differently, the encoded data includes information indicating the order of encoding a plurality of GOSs. 
     The encoding device and the decoding device also encode or decode mutually different two or more SPCs or GOSs in parallel. 
     Furthermore, the encoding device and the decoding device encode or decode the spatial information (coordinates, size, etc.) on a SPC or a GOS. 
     The encoding device and the decoding device encode or decode SPCs or GOSs included in an identified space that is identified on the basis of external information on the self-location or/and region size, such as GPS information, route information, or magnification. 
     The encoding device or the decoding device gives a lower priority to a space distant from the self-location than the priority of a nearby space to perform encoding or decoding. 
     The encoding device sets a direction at one of the directions in a world, in accordance with the magnification or the intended use, to encode a GOS having a layer structure in such direction. Also, the decoding device decodes a GOS having a layer structure in one of the directions in a world that has been set in accordance with the magnification or the intended use, preferentially from the bottom layer. 
     The encoding device changes the accuracy of extracting keypoints, the accuracy of recognizing objects, or the size of spatial regions, etc. included in a SPC, depending on whether an object is an interior object or an exterior object. Note that the encoding device and the decoding device encode or decode an interior GOS and an exterior GOS having close coordinates in a manner that these GOSs come adjacent to each other in a world, and associates their identifiers with each other for encoding and decoding. 
     Embodiment 2 
     When using encoded data of a point cloud in an actual device or service, it is desirable that necessary information be transmitted/received in accordance with the intended use to reduce the network bandwidth. However, there has been no such functionality in the structure of encoding three-dimensional data, nor an encoding method therefor. 
     The present embodiment describes a three-dimensional data encoding method and a three-dimensional data encoding device for providing the functionality of transmitting/receiving only necessary information in encoded data of a three-dimensional point cloud in accordance with the intended use, as well as a three-dimensional data decoding method and a three-dimensional data decoding device for decoding such encoded data. 
     A voxel (VXL) with a feature greater than or equal to a given amount is defined as a feature voxel (FVXL), and a world (WLD) constituted by FVXLs is defined as a sparse world (SWLD).  FIG.  11    is a diagram showing example structures of a sparse world and a world. A SWLD includes: FGOSs, each being a GOS constituted by FVXLs; FSPCs, each being a SPC constituted by FVXLs; and FVLMs, each being a VLM constituted by FVXLs. The data structure and prediction structure of a FGOS, a FSPC, and a FVLM may be the same as those of a GOS, a SPC, and a VLM. 
     A feature represents the three-dimensional position information on a VXL or the visible-light information on the position of a VXL. A large number of features are detected especially at a corner, an edge, etc. of a three-dimensional object. More specifically, such a feature is a three-dimensional feature or a visible-light feature as described below, but may be any feature that represents the position, luminance, or color information, etc. on a VXL. 
     Used as three-dimensional features are signature of histograms of orientations (SHOT) features, point feature histograms (PFH) features, or point pair feature (PPF) features. 
     SHOT features are obtained by dividing the periphery of a VXL, and calculating an inner product of the reference point and the normal vector of each divided region to represent the calculation result as a histogram. SHOT features are characterized by a large number of dimensions and high-level feature representation. 
     PFH features are obtained by selecting a large number of two point pairs in the vicinity of a VXL, and calculating the normal vector, etc. from each two point pair to represent the calculation result as a histogram. PFH features are histogram features, and thus are characterized by robustness against a certain extent of disturbance and also high-level feature representation. 
     PPF features are obtained by using a normal vector, etc. for each two points of VXLs. PPF features, for which all VXLs are used, has robustness against occlusion. 
     Used as visible-light features are scale-invariant feature transform (SIFT), speeded up robust features (SURF), or histogram of oriented gradients (HOG), etc. that use information on an image such as luminance gradient information. 
     A SWLD is generated by calculating the above-described features of the respective VXLs in a WLD to extract FVXLs. Here, the SWLD may be updated every time the WLD is updated, or may be regularly updated after the elapse of a certain period of time, regardless of the timing at which the WLD is updated. 
     A SWLD may be generated for each type of features. For example, different SWLDs may be generated for the respective types of features, such as SWLD 1  based on SHOT features and SWLD 2  based on SIFT features so that SWLDs are selectively used in accordance with the intended use. Also, the calculated feature of each FVXL may be held in each FVXL as feature information. 
     Next, the usage of a sparse world (SWLD) will be described. A SWLD includes only feature voxels (FVXLs), and thus its data size is smaller in general than that of a WLD that includes all VXLs. 
     In an application that utilizes features for a certain purpose, the use of information on a SWLD instead of a WLD reduces the time required to read data from a hard disk, as well as the bandwidth and the time required for data transfer over a network. For example, a WLD and a SWLD are held in a server as map information so that map information to be sent is selected between the WLD and the SWLD in accordance with a request from a client. This reduces the network bandwidth and the time required for data transfer. More specific examples will be described below; 
       FIG.  12    and  FIG.  13    are diagrams showing usage examples of a SWLD and a WLD. As  FIG.  12    shows, when client  1 , which is a vehicle-mounted device, requires map information to use it for self-location determination, client  1  sends to a server a request for obtaining map data for self-location estimation (S 301 ). The server sends to client  1  the SWLD in response to the obtainment request (S 302 ). Client  1  uses the received SWLD to determine the self-location (S 303 ). In so doing, client  1  obtains VXL information on the periphery of client  1  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. Client  1  then estimates the self-location information from the obtained VXL information and the SWLD. Here, the self-location information includes three-dimensional position information, orientation, etc. of client  1 . 
     As  FIG.  13    shows, when client  2 , which is a vehicle-mounted device, requires map information to use it for rendering a map such as a three-dimensional map, client  2  sends to the server a request for obtaining map data for map rendering (S 311 ). The server sends to client  2  the WLD in response to the obtainment request (S 312 ). Client  2  uses the received WLD to render a map (S 313 ). In so doing, client  2  uses, for example, an image client  2  has captured by a visible-light camera, etc. and the WLD obtained from the server to create a rendering image, and renders such created image onto a screen of a car navigation system, etc. 
     As described above, the server sends to a client a SWLD when the features of the respective VXLs are mainly required such as in the case of self-location estimation, and sends to a client a WLD when detailed VXL information is required such as in the case of map rendering. This allows for an efficient sending/receiving of map data. 
     Note that a client may self-judge which one of a SWLD and a WLD is necessary, and request the server to send a SWLD or a WLD. Also, the server may judge which one of a SWLD and a WLD to send in accordance with the status of the client or a network. 
     Next, a method will be described of switching the sending/receiving between a sparse world (SWLD) and a world (WLD). 
     Whether to receive a WLD or a SWLD may be switched in accordance with the network bandwidth.  FIG.  14    is a diagram showing an example operation in such case. For example, when a low-speed network is used that limits the usable network bandwidth, such as in a Long-Term Evolution (LTE) environment, a client accesses the server over a low-speed network (S 321 ), and obtains the SWLD from the server as map information (S 322 ). Meanwhile, when a high-speed network is used that has an adequately broad network bandwidth, such as in a WiFi environment, a client accesses the server over a high-speed network (S 323 ), and obtains the WLD from the server (S 324 ). This enables the client to obtain appropriate map information in accordance with the network bandwidth such client is using. 
     More specifically, a client receives the SWLD over an LTE network when in outdoors, and obtains the WLD over a WiFi network when in indoors such as in a facility. This enables the client to obtain more detailed map information on indoor environment. 
     As described above, a client may request for a WLD or a SWLD in accordance with the bandwidth of a network such client is using. Alternatively, the client may send to the server information indicating the bandwidth of a network such client is using, and the server may send to the client data (the WLD or the SWLD) suitable for such client in accordance with the information. Alternatively, the server may identify the network bandwidth the client is using, and send to the client data (the WLD or the SWLD) suitable for such client. 
     Also, whether to receive a WLD or a SWLD may be switched in accordance with the speed of traveling.  FIG.  15    is a diagram showing an example operation in such case. For example, when traveling at a high speed (S 331 ), a client receives the SWLD from the server (S 332 ). Meanwhile, when traveling at a low speed (S 333 ), the client receives the WLD from the server (S 334 ). This enables the client to obtain map information suitable to the speed, while reducing the network bandwidth. More specifically, when traveling on an expressway, the client receives the SWLD with a small data amount, which enables the update of rough map information at an appropriate speed. Meanwhile, when traveling on a general road, the client receives the WLD, which enables the obtainment of more detailed map information. 
     As described above, the client may request the server for a WLD or a SWLD in accordance with the traveling speed of such client. Alternatively, the client may send to the server information indicating the traveling speed of such client, and the server may send to the client data (the WLD or the SWLD) suitable to such client in accordance with the information. Alternatively, the server may identify the traveling speed of the client to send data (the WLD or the SWLD) suitable to such client. 
     Also, the client may obtain, from the server, a SWLD first, from which the client may obtain a WLD of an important region. For example, when obtaining map information, the client first obtains a SWLD for rough map information, from which the client narrows to a region in which features such as buildings, signals, or persons appear at high frequency so that the client can later obtain a WLD of such narrowed region. This enables the client to obtain detailed information on a necessary region, while reducing the amount of data received from the server. 
     The server may also create from a WLD different SWLDs for the respective objects, and the client may receive SWLDs in accordance with the intended use. This reduces the network bandwidth. For example, the server recognizes persons or cars in a WLD in advance, and creates a SWLD of persons and a SWLD of cars. The client, when wishing to obtain information on persons around the client, receives the SWLD of persons, and when wising to obtain information on cars, receives the SWLD of cars. Such types of SWLDs may be distinguished by information (flag, or type, etc.) added to the header, etc. 
     Next, the structure and the operation flow of the three-dimensional data encoding device (e.g., a server) according to the present embodiment will be described.  FIG.  16    is a block diagram of three-dimensional data encoding device  400  according to the present embodiment.  FIG.  17    is a flowchart of three-dimensional data encoding processes performed by three-dimensional data encoding device  400 . 
     Three-dimensional data encoding device  400  shown in  FIG.  16    encodes input three-dimensional data  411 , thereby generating encoded three-dimensional data  413  and encoded three-dimensional data  414 , each being an encoded stream. Here, encoded three-dimensional data  413  is encoded three-dimensional data corresponding to a WLD, and encoded three-dimensional data  414  is encoded three-dimensional data corresponding to a SWLD. Such three-dimensional data encoding device  400  includes, obtainer  401 , encoding region determiner  402 , SWLD extractor  403 , WLD encoder  404 , and SWLD encoder  405 . 
     First, as  FIG.  17    shows, obtainer  401  obtains input three-dimensional data  411 , which is point group data in a three-dimensional space (S 401 ). 
     Next, encoding region determiner  402  determines a current spatial region for encoding on the basis of a spatial region in which the point cloud data is present (S 402 ). 
     Next, SWLD extractor  403  defines the current spatial region as a WLD, and calculates the feature from each VXL included in the WLD. Then, SWLD extractor  403  extracts VXLs having an amount of features greater than or equal to a predetermined threshold, defines the extracted VXLs as FVXLs, and adds such FVXLs to a SWLD, thereby generating extracted three-dimensional data  412  (S 403 ). Stated differently, extracted three-dimensional data  412  having an amount of features greater than or equal to the threshold is extracted from input three-dimensional data  411 . 
     Next, WLD encoder  404  encodes input three-dimensional data  411  corresponding to the WLD, thereby generating encoded three-dimensional data  413  corresponding to the WLD (S 404 ). In so doing, WLD encoder  404  adds to the header of encoded three-dimensional data  413  information that distinguishes that such encoded three-dimensional data  413  is a stream including a WLD. 
     SWLD encoder  405  encodes extracted three-dimensional data  412  corresponding to the SWLD, thereby generating encoded three-dimensional data  414  corresponding to the SWLD (S 405 ). In so doing, SWLD encoder  405  adds to the header of encoded three-dimensional data  414  information that distinguishes that such encoded three-dimensional data  414  is a stream including a SWLD. 
     Note that the process of generating encoded three-dimensional data  413  and the process of generating encoded three-dimensional data  414  may be performed in the reverse order. Also note that a part or all of these processes may be performed in parallel. 
     A parameter “world_type” is defined, for example, as information added to each header of encoded three-dimensional data  413  and encoded three-dimensional data  414 . world_type=0 indicates that a stream includes a WLD, and world_type=1 indicates that a stream includes a SWLD. An increased number of values may be further assigned to define a larger number of types, e.g., world_type=2. Also, one of encoded three-dimensional data  413  and encoded three-dimensional data  414  may include a specified flag. For example, encoded three-dimensional data  414  may be assigned with a flag indicating that such stream includes a SWLD. In such a case, the decoding device can distinguish whether such stream is a stream including a WLD or a stream including a SWLD in accordance with the presence/absence of the flag. 
     Also, an encoding method used by WLD encoder  404  to encode a WLD may be different from an encoding method used by SWLD encoder  405  to encode a SWLD. 
     For example, data of a SWLD is decimated, and thus can have a lower correlation with the neighboring data than that of a WLD. For this reason, of intra prediction and inter prediction, inter prediction may be more preferentially performed in an encoding method used for a SWLD than in an encoding method used for a WLD. 
     Also, an encoding method used for a SWLD and an encoding method used for a WLD may represent three-dimensional positions differently. For example, three-dimensional coordinates may be used to represent the three-dimensional positions of FVXLs in a SWLD and an octree described below may be used to represent three-dimensional positions in a WLD, and vice versa. 
     Also, SWLD encoder  405  performs encoding in a manner that encoded three-dimensional data  414  of a SWLD has a smaller data size than the data size of encoded three-dimensional data  413  of a WLD. A SWLD can have a lower inter-data correlation, for example, than that of a WLD as described above. This can lead to a decreased encoding efficiency, and thus to encoded three-dimensional data  414  having a larger data size than the data size of encoded three-dimensional data  413  of a WLD. When the data size of the resulting encoded three-dimensional data  414  is larger than the data size of encoded three-dimensional data  413  of a WLD, SWLD encoder  405  performs encoding again to re-generate encoded three-dimensional data  414  having a reduced data size. 
     For example, SWLD extractor  403  re-generates extracted three-dimensional data  412  having a reduced number of keypoints to be extracted, and SWLD encoder  405  encodes such extracted three-dimensional data  412 . Alternatively, SWLD encoder  405  may perform more coarse quantization. More coarse quantization is achieved, for example, by rounding the data in the lowermost level in an octree structure described below. 
     When failing to decrease the data size of encoded three-dimensional data  414  of the SWLD to smaller than the data size of encoded three-dimensional data  413  of the WLD, SWLD encoder  405  may not generate encoded three-dimensional data  414  of the SWLD. Alternatively, encoded three-dimensional data  413  of the WLD may be copied as encoded three-dimensional data  414  of the SWLD. Stated differently, encoded three-dimensional data  413  of the WLD may be used as it is as encoded three-dimensional data  414  of the SWLD. 
     Next, the structure and the operation flow of the three-dimensional data decoding device (e.g., a client) according to the present embodiment will be described.  FIG.  18    is a block diagram of three-dimensional data decoding device  500  according to the present embodiment.  FIG.  19    is a flowchart of three-dimensional data decoding processes performed by three-dimensional data decoding device  500 . 
     Three-dimensional data decoding device  500  shown in  FIG.  18    decodes encoded three-dimensional data  511 , thereby generating decoded three-dimensional data  512  or decoded three-dimensional data  513 . Encoded three-dimensional data  511  here is, for example, encoded three-dimensional data  413  or encoded three-dimensional data  414  generated by three-dimensional data encoding device  400 . 
     Such three-dimensional data decoding device  500  includes obtainer  501 , header analyzer  502 , WLD decoder  503 , and SWLD decoder  504 . 
     First, as  FIG.  19    shows, obtainer  501  obtains encoded three-dimensional data  511  (S 501 ). Next, header analyzer  502  analyzes the header of encoded three-dimensional data  511  to identify whether encoded three-dimensional data  511  is a stream including a WLD or a stream including a SWLD (S 502 ). For example, the above-described parameter world_type is referred to in making such identification. 
     When encoded three-dimensional data  511  is a stream including a WLD (Yes in S 503 ), WLD decoder  503  decodes encoded three-dimensional data  511 , thereby generating decoded three-dimensional data  512  of the WLD (S 504 ). Meanwhile, when encoded three-dimensional data  511  is a stream including a SWLD (No in S 503 ), SWLD decoder  504  decodes encoded three-dimensional data  511 , thereby generating decoded three-dimensional data  513  of the SWLD (S 505 ). 
     Also, as in the case of the encoding device, a decoding method used by WLD decoder  503  to decode a WLD may be different from a decoding method used by SWLD decoder  504  to decode a SWLD. For example, of intra prediction and inter prediction, inter prediction may be more preferentially performed in a decoding method used for a SWLD than in a decoding method used for a WLD. 
     Also, a decoding method used for a SWLD and a decoding method used for a WLD may represent three-dimensional positions differently. For example, three-dimensional coordinates may be used to represent the three-dimensional positions of FVXLs in a SWLD and an octree described below may be used to represent three-dimensional positions in a WLD, and vice versa. 
     Next, an octree representation will be described, which is a method of representing three-dimensional positions. VXL data included in three-dimensional data is converted into an octree structure before encoded.  FIG.  20    is a diagram showing example VXLs in a WLD.  FIG.  21    is a diagram showing an octree structure of the WLD shown in  FIG.  20   . An example shown in  FIG.  20    illustrates three VXLs  1  to  3  that include point groups (hereinafter referred to as effective VXLs). As  FIG.  21    shows, the octree structure is made of nodes and leaves. Each node has a maximum of eight nodes or leaves. Each leaf has VXL information. Here, of the leaves shown in  FIG.  21   , leaf  1 , leaf  2 , and leaf  3  represent VXL 1 , VXL 2 , and VXL 3  shown in  FIG.  20   , respectively. 
     More specifically, each node and each leaf correspond to a three-dimensional position. Node  1  corresponds to the entire block shown in  FIG.  20   . The block that corresponds to node  1  is divided into eight blocks. Of these eight blocks, blocks including effective VXLs are set as nodes, while the other blocks are set as leaves. Each block that corresponds to a node is further divided into eight nodes or leaves. These processes are repeated by the number of times that is equal to the number of levels in the octree structure. All blocks in the lowermost level are set as leaves; 
       FIG.  22    is a diagram showing an example SWLD generated from the WLD shown in  FIG.  20   . VXL 1  and VXL 2  shown in  FIG.  20    are judged as FVXL 1  and FVXL 2  as a result of feature extraction, and thus are added to the SWLD. Meanwhile, VXL 3  is not judged as a FVXL, and thus is not added to the SWLD.  FIG.  23    is a diagram showing an octree structure of the SWLD shown in  FIG.  22   . In the octree structure shown in  FIG.  23   , leaf  3  corresponding to VXL 3  shown in  FIG.  21    is deleted. Consequently, node  3  shown in  FIG.  21    has lost an effective VXL, and has changed to a leaf. As described above, a SWLD has a smaller number of leaves in general than a WLD does, and thus the encoded three-dimensional data of the SWLD is smaller than the encoded three-dimensional data of the WLD. 
     The following describes variations of the present embodiment. 
     For self-location estimation, for example, a client, being a vehicle-mounted device, etc., may receive a SWLD from the server to use such SWLD to estimate the self-location. Meanwhile, for obstacle detection, the client may detect obstacles by use of three-dimensional information on the periphery obtained by such client 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. 
     In general, a SWLD is less likely to include VXL data on a flat region. As such, the server may hold a subsample world (subWLD) obtained by subsampling a WLD for detection of static obstacles, and send to the client the SWLD and the subWLD. This enables the client to perform self-location estimation and obstacle detection on the client&#39;s part, while reducing the network bandwidth. 
     When the client renders three-dimensional map data at a high speed, map information having a mesh structure is more useful in some cases. As such, the server may generate a mesh from a WLD to hold it beforehand as a mesh world (MWLD). For example, when wishing to perform coarse three-dimensional rendering, the client receives a MWLD, and when wishing to perform detailed three-dimensional rendering, the client receives a WLD. This reduces the network bandwidth. 
     In the above description, the server sets, as FVXLs, VXLs having an amount of features greater than or equal to the threshold, but the server may calculate FVXLs by a different method. For example, the server may judge that a VXL, a VLM, a SPC, or a GOS that constitutes a signal, or an intersection, etc. as necessary for self-location estimation, driving assist, or self-driving, etc., and incorporate such VXL, VLM, SPC, or GOS into a SWLD as a FVXL, a FVLM, a FSPC, or a FGOS. Such judgment may be made manually. Also, FVXLs, etc. that have been set on the basis of an amount of features may be added to FVXLs, etc. obtained by the above method. Stated differently, SWLD extractor  403  may further extract, from input three-dimensional data  411 , data corresponding to an object having a predetermined attribute as extracted three-dimensional data  412 . 
     Also, that a VXL, a VLM, a SPC, or a GOS is necessary for such intended usage may be labeled separately from the features. The server may separately hold, as an upper layer of a SWLD (e.g., a lane world), FVXLs of a signal or an intersection, etc. necessary for self-location estimation, driving assist, or self-driving, etc. 
     The server may also add an attribute to VXLs in a WLD on a random access basis or on a predetermined unit basis. An attribute, for example, includes information indicating whether VXLs are necessary for self-location estimation, or information indicating whether VXLs are important as traffic information such as a signal, or an intersection, etc. An attribute may also include a correspondence between VXLs and features (intersection, or road, etc.) in lane information (geographic data files (GDF), etc.). 
     A method as described below may be used to update a WLD or a SWLD. 
     Update information indicating changes, etc. in a person, a roadwork, or a tree line (for trucks) is uploaded to the server as point groups or meta data. The server updates a WLD on the basis of such uploaded information, and then updates a SWLD by use of the updated WLD. 
     The client, when detecting a mismatch between the three-dimensional information such client has generated at the time of self-location estimation and the three-dimensional information received from the server, may send to the server the three-dimensional information such client has generated, together with an update notification. In such a case, the server updates the SWLD by use of the WLD. When the SWLD is not to be updated, the server judges that the WLD itself is old. 
     In the above description, information that distinguishes whether an encoded stream is that of a WLD or a SWLD is added as header information of the encoded stream. However, when there are many types of worlds such as a mesh world and a lane world, information that distinguishes these types of the worlds may be added to header information. Also, when there are many SWLDs with different amounts of features, information that distinguishes the respective SWLDs may be added to header information. 
     In the above description, a SWLD is constituted by FVXLs, but a SWLD may include VXLs that have not been judged as FVXLs. For example, a SWLD may include an adjacent VXL used to calculate the feature of a FVXL. This enables the client to calculate the feature of a FVXL when receiving a SWLD, even in the case where feature information is not added to each FVXL of the SWLD. In such a case, the SWLD may include information that distinguishes whether each VXL is a FVXL or a VXL. 
     As described above, three-dimensional data encoding device  400  extracts, from input three-dimensional data  411  (first three-dimensional data), extracted three-dimensional data  412  (second three-dimensional data) having an amount of a feature greater than or equal to a threshold, and encodes extracted three-dimensional data  412  to generate encoded three-dimensional data  414  (first encoded three-dimensional data). 
     This three-dimensional data encoding device  400  generates encoded three-dimensional data  414  that is obtained by encoding data having an amount of a feature greater than or equal to the threshold. This reduces the amount of data compared to the case where input three-dimensional data  411  is encoded as it is. Three-dimensional data encoding device  400  is thus capable of reducing the amount of data to be transmitted. 
     Three-dimensional data encoding device  400  further encodes input three-dimensional data  411  to generate encoded three-dimensional data  413  (second encoded three-dimensional data). 
     This three-dimensional data encoding device  400  enables selective transmission of encoded three-dimensional data  413  and encoded three-dimensional data  414 , in accordance, for example, with the intended use, etc. 
     Also, extracted three-dimensional data  412  is encoded by a first encoding method, and input three-dimensional data  411  is encoded by a second encoding method different from the first encoding method. 
     This three-dimensional data encoding device  400  enables the use of an encoding method suitable for each of input three-dimensional data  411  and extracted three-dimensional data  412 . 
     Also, of intra prediction and inter prediction, the inter prediction is more preferentially performed in the first encoding method than in the second encoding method. 
     This three-dimensional data encoding device  400  enables inter prediction to be more preferentially performed on extracted three-dimensional data  412  in which adjacent data items are likely to have low correlation. 
     Also, the first encoding method and the second encoding method represent three-dimensional positions differently. For example, the second encoding method represents three-dimensional positions by octree, and the first encoding method represents three-dimensional positions by three-dimensional coordinates. 
     This three-dimensional data encoding device  400  enables the use of a more suitable method to represent the three-dimensional positions of three-dimensional data in consideration of the difference in the number of data items (the number of VXLs or FVXLs) included. 
     Also, at least one of encoded three-dimensional data  413  and encoded three-dimensional data  414  includes an identifier indicating whether the encoded three-dimensional data is encoded three-dimensional data obtained by encoding input three-dimensional data  411  or encoded three-dimensional data obtained by encoding part of input three-dimensional data  411 . Stated differently, such identifier indicates whether the encoded three-dimensional data is encoded three-dimensional data  413  of a WLD or encoded three-dimensional data  414  of a SWLD. 
     This enables the decoding device to readily judge whether the obtained encoded three-dimensional data is encoded three-dimensional data  413  or encoded three-dimensional data  414 . 
     Also, three-dimensional data encoding device  400  encodes extracted three-dimensional data  412  in a manner that encoded three-dimensional data  414  has a smaller data amount than a data amount of encoded three-dimensional data  413 . 
     This three-dimensional data encoding device  400  enables encoded three-dimensional data  414  to have a smaller data amount than the data amount of encoded three-dimensional data  413 . 
     Also, three-dimensional data encoding device  400  further extracts data corresponding to an object having a predetermined attribute from input three-dimensional data  411  as extracted three-dimensional data  412 . The object having a predetermined attribute is, for example, an object necessary for self-location estimation, driving assist, or self-driving, etc., or more specifically, a signal, an intersection, etc. 
     This three-dimensional data encoding device  400  is capable of generating encoded three-dimensional data  414  that includes data required by the decoding device. 
     Also, three-dimensional data encoding device  400  (server) further sends, to a client, one of encoded three-dimensional data  413  and encoded three-dimensional data  414  in accordance with a status of the client. 
     This three-dimensional data encoding device  400  is capable of sending appropriate data in accordance with the status of the client. 
     Also, the status of the client includes one of a communication condition (e.g., network bandwidth) of the client and a traveling speed of the client. 
     Also, three-dimensional data encoding device  400  further sends, to a client, one of encoded three-dimensional data  413  and encoded three-dimensional data  414  in accordance with a request from the client. 
     This three-dimensional data encoding device  400  is capable of sending appropriate data in accordance with the request from the client. 
     Also, three-dimensional data decoding device  500  according to the present embodiment decodes encoded three-dimensional data  413  or encoded three-dimensional data  414  generated by three-dimensional data encoding device  400  described above. 
     Stated differently, three-dimensional data decoding device  500  decodes, by a first decoding method, encoded three-dimensional data  414  obtained by encoding extracted three-dimensional data  412  having an amount of a feature greater than or equal to a threshold, extracted three-dimensional data  412  having been extracted from input three-dimensional data  411 . Three-dimensional data decoding device  500  also decodes, by a second decoding method, encoded three-dimensional data  413  obtained by encoding input three-dimensional data  411 , the second decoding method being different from the first decoding method. 
     This three-dimensional data decoding device  500  enables selective reception of encoded three-dimensional data  414  obtained by encoding data having an amount of a feature greater than or equal to the threshold and encoded three-dimensional data  413 , in accordance, for example, with the intended use, etc. Three-dimensional data decoding device  500  is thus capable of reducing the amount of data to be transmitted. Such three-dimensional data decoding device  500  further enables the use of a decoding method suitable for each of input three-dimensional data  411  and extracted three-dimensional data  412 . 
     Also, of intra prediction and inter prediction, the inter prediction is more preferentially performed in the first decoding method than in the second decoding method. 
     This three-dimensional data decoding device  500  enables inter prediction to be more preferentially performed on the extracted three-dimensional data in which adjacent data items are likely to have low correlation. 
     Also, the first decoding method and the second decoding method represent three-dimensional positions differently. For example, the second decoding method represents three-dimensional positions by octree, and the first decoding method represents three-dimensional positions by three-dimensional coordinates. 
     This three-dimensional data decoding device  500  enables the use of a more suitable method to represent the three-dimensional positions of three-dimensional data in consideration of the difference in the number of data items (the number of VXLs or FVXLs) included. 
     Also, at least one of encoded three-dimensional data  413  and encoded three-dimensional data  414  includes an identifier indicating whether the encoded three-dimensional data is encoded three-dimensional data obtained by encoding input three-dimensional data  411  or encoded three-dimensional data obtained by encoding part of input three-dimensional data  411 . Three-dimensional data decoding device  500  refers to such identifier in identifying between encoded three-dimensional data  413  and encoded three-dimensional data  414 . 
     This three-dimensional data decoding device  500  is capable of readily judging whether the obtained encoded three-dimensional data is encoded three-dimensional data  413  or encoded three-dimensional data  414 . 
     Three-dimensional data decoding device  500  further notifies a server of a status of the client (three-dimensional data decoding device  500 ). Three-dimensional data decoding device  500  receives one of encoded three-dimensional data  413  and encoded three-dimensional data  414  from the server, in accordance with the status of the client. 
     This three-dimensional data decoding device  500  is capable of receiving appropriate data in accordance with the status of the client. 
     Also, the status of the client includes one of a communication condition (e.g., network bandwidth) of the client and a traveling speed of the client. 
     Three-dimensional data decoding device  500  further makes a request of the server for one of encoded three-dimensional data  413  and encoded three-dimensional data  414 , and receives one of encoded three-dimensional data  413  and encoded three-dimensional data  414  from the server, in accordance with the request. 
     This three-dimensional data decoding device  500  is capable of receiving appropriate data in accordance with the intended use. 
     Embodiment 3 
     The present embodiment will describe a method of transmitting/receiving three-dimensional data between vehicles. For example, the three-dimensional data is transmitted/received between the own vehicle and the nearby vehicle; 
       FIG.  24    is a block diagram of three-dimensional data creation device  620  according to the present embodiment. Such three-dimensional data creation device  620 , which is included, for example, in the own vehicle, mergers first three-dimensional data  632  created by three-dimensional data creation device  620  with the received second three-dimensional data  635 , thereby creating third three-dimensional data  636  having a higher density. 
     Such three-dimensional data creation device  620  includes three-dimensional data creator  621 , request range determiner  622 , searcher  623 , receiver  624 , decoder  625 , and merger  626 . 
     First, three-dimensional data creator  621  creates first three-dimensional data  632  by use of sensor information  631  detected by the sensor included in the own vehicle. Next, request range determiner  622  determines a request range, which is the range of a three-dimensional space, the data on which is insufficient in the created first three-dimensional data  632 . 
     Next, searcher  623  searches for the nearby vehicle having the three-dimensional data of the request range, and sends request range information  633  indicating the request range to nearby vehicle  601  having been searched out (S 623 ). Next, receiver  624  receives encoded three-dimensional data  634 , which is an encoded stream of the request range, from nearby vehicle  601  (S 624 ). Note that searcher  623  may indiscriminately send requests to all vehicles included in a specified range to receive encoded three-dimensional data  634  from a vehicle that has responded to the request. Searcher  623  may send a request not only to vehicles but also to an object such as a signal and a sign, and receive encoded three-dimensional data  634  from the object. 
     Next, decoder  625  decodes the received encoded three-dimensional data  634 , thereby obtaining second three-dimensional data  635 . Next, merger  626  merges first three-dimensional data  632  with second three-dimensional data  635 , thereby creating three-dimensional data  636  having a higher density. 
     Next, the structure and operations of three-dimensional data transmission device  640  according to the present embodiment will be described.  FIG.  25    is a block diagram of three-dimensional data transmission device  640 . 
     Three-dimensional data transmission device  640  is included, for example, in the above-described nearby vehicle. Three-dimensional data transmission device  640  processes fifth three-dimensional data  652  created by the nearby vehicle into sixth three-dimensional data  654  requested by the own vehicle, encodes sixth three-dimensional data  654  to generate encoded three-dimensional data  634 , and sends encoded three-dimensional data  634  to the own vehicle. 
     Three-dimensional data transmission device  640  includes three-dimensional data creator  641 , receiver  642 , extractor  643 , encoder  644 , and transmitter  645 . 
     First, three-dimensional data creator  641  creates fifth three-dimensional data  652  by use of sensor information  651  detected by the sensor included in the nearby vehicle. Next, receiver  642  receives request range information  633  from the own vehicle. 
     Next, extractor  643  extracts from fifth three-dimensional data  652  the three-dimensional data of the request range indicated by request range information  633 , thereby processing fifth three-dimensional data  652  into sixth three-dimensional data  654 . Next, encoder  644  encodes sixth three-dimensional data  654  to generate encoded three-dimensional data  643 , which is an encoded stream. Then, transmitter  645  sends encoded three-dimensional data  634  to the own vehicle. 
     Note that although an example case is described here in which the own vehicle includes three-dimensional data creation device  620  and the nearby vehicle includes three-dimensional data transmission device  640 , each of the vehicles may include the functionality of both three-dimensional data creation device  620  and three-dimensional data transmission device  640 . 
     Embodiment 4 
     The present embodiment describes operations performed in abnormal cases when self-location estimation is performed on the basis of a three-dimensional map. 
     A three-dimensional map is expected to find its expanded use in self-driving of a vehicle and autonomous movement, etc. of a mobile object such as a robot and a flying object (e.g., a drone). Example means for enabling such autonomous movement include a method in which a mobile object travels in accordance with a three-dimensional map, while estimating its self-location on the map (self-location estimation). 
     The self-location estimation is enabled by matching a three-dimensional map with three-dimensional information on the surrounding of the own vehicle (hereinafter referred to as self-detected three-dimensional data) obtained by a sensor equipped in the own vehicle, such as a rangefinder (e.g., a LiDAR) and a stereo camera to estimate the location of the own vehicle on the three-dimensional map. 
     As in the case of an HD map suggested by HERE Technologies, for example, a three-dimensional map may include not only a three-dimensional point cloud, but also two-dimensional map data such as information on the shapes of roads and intersections, or information that changes in real-time such as information on a traffic jam and an accident. A three-dimensional map includes a plurality of layers such as layers of three-dimensional data, two-dimensional data, and meta-data that changes in real-time, from among which the device can obtain or refer to only necessary data. 
     Point cloud data may be a SWLD as described above, or may include point group data that is different from keypoints. The transmission/reception of point cloud data is basically carried out in one or more random access units. 
     A method described below is used as a method of matching a three-dimensional map with self-detected three-dimensional data. For example, the device compares the shapes of the point groups in each other&#39;s point clouds, and determines that portions having a high degree of similarity among keypoints correspond to the same position. When the three-dimensional map is formed by a SWLD, the device also performs matching by comparing the keypoints that form the SWLD with three-dimensional keypoints extracted from the self-detected three-dimensional data. 
     Here, to enable highly accurate self-location estimation, the following needs to be satisfied: (A) the three-dimensional map and the self-detected three-dimensional data have been already obtained; and (B) their accuracies satisfy a predetermined requirement. However, one of (A) and (B) cannot be satisfied in abnormal cases such as ones described below. 
     1. A three-dimensional map is unobtainable over communication. 
     2. A three-dimensional map is not present, or a three-dimensional map having been obtained is corrupt. 
     3. A sensor of the own vehicle has trouble, or the accuracy of the generated self-detected three-dimensional data is inadequate due to bad weather. 
     The following describes operations to cope with such abnormal cases. The following description illustrates an example case of a vehicle, but the method described below is applicable to mobile objects on the whole that are capable of autonomous movement, such as a robot and a drone. 
     The following describes the structure of the three-dimensional information processing device and its operation according to the present embodiment capable of coping with abnormal cases regarding a three-dimensional map or self-detected three-dimensional data.  FIG.  26    is a block diagram of an example structure of three-dimensional information processing device  700  according to the present embodiment. 
     Three-dimensional information processing device  700  is equipped, for example, in a mobile object such as a car. As shown in  FIG.  26   , three-dimensional information processing device  700  includes three-dimensional map obtainer  701 , self-detected data obtainer  702 , abnormal case judgment unit  703 , coping operation determiner  704 , and operation controller  705 . 
     Note that three-dimensional information processing device  700  may include a non-illustrated two-dimensional or one-dimensional sensor that detects a structural object or a mobile object around the own vehicle, such as a camera capable of obtaining two-dimensional images and a sensor for one-dimensional data utilizing ultrasonic or laser. Three-dimensional information processing device  700  may also include a non-illustrated communication unit that obtains a three-dimensional map over a mobile communication network, such as 4G and 5G, or via inter-vehicle communication or road-to-vehicle communication. 
     Three-dimensional map obtainer  701  obtains three-dimensional map  711  of the surroundings of the traveling route. For example, three-dimensional map obtainer  701  obtains three-dimensional map  711  over a mobile communication network, or via inter-vehicle communication or road-to-vehicle communication. 
     Next, self-detected data obtainer  702  obtains self-detected three-dimensional data  712  on the basis of sensor information. For example, self-detected data obtainer  702  generates self-detected three-dimensional data  712  on the basis of the sensor information obtained by a sensor equipped in the own vehicle. 
     Next, abnormal case judgment unit  703  conducts a predetermined check of at least one of obtained three-dimensional map  711  and self-detected three-dimensional data  712  to detect an abnormal case. Stated differently, abnormal case judgment unit  703  judges whether at least one of obtained three-dimensional map  711  and self-detected three-dimensional data  712  is abnormal. 
     When the abnormal case is detected, coping operation determiner  704  determines a coping operation to cope with such abnormal case. Next, operation controller  705  controls the operation of each of the processing units necessary to perform the coping operation. 
     Meanwhile, when no abnormal case is detected, three-dimensional information processing device  700  terminates the process. 
     Also, three-dimensional information processing device  700  estimates the location of the vehicle equipped with three-dimensional information processing device  700 , using three-dimensional map  711  and self-detected three-dimensional data  712 . Next, three-dimensional information processing device  700  performs the automatic operation of the vehicle by use of the estimated location of the vehicle. 
     As described above, three-dimensional information processing device  700  obtains, via a communication channel, map data (three-dimensional map  711 ) that includes first three-dimensional position information. The first three-dimensional position information includes, for example, a plurality of random access units, each of which is an assembly of at least one subspace and is individually decodable, the at least one subspace having three-dimensional coordinates information and serving as a unit in which each of the plurality of random access units is encoded. The first three-dimensional position information is, for example, data (SWLD) obtained by encoding keypoints, each of which has an amount of a three-dimensional feature greater than or equal to a predetermined threshold. 
     Three-dimensional information processing device  700  also generates second three-dimensional position information (self-detected three-dimensional data  712 ) from information detected by a sensor. Three-dimensional information processing device  700  then judges whether one of the first three-dimensional position information and the second three-dimensional position information is abnormal by performing, on one of the first three-dimensional position information and the second three-dimensional position information, a process of judging whether an abnormality is present. 
     Three-dimensional information processing device  700  determines a coping operation to cope with the abnormality when one of the first three-dimensional position information and the second three-dimensional position information is judged to be abnormal. Three-dimensional information processing device  700  then executes a control that is required to perform the coping operation. 
     This structure enables three-dimensional information processing device  700  to detect an abnormality regarding one of the first three-dimensional position information and the second three-dimensional position information, and to perform a coping operation therefor. 
     Embodiment 5 
     The present embodiment describes a method, etc. of transmitting three-dimensional data to a following vehicle; 
       FIG.  27    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. 
     Embodiment 6 
     In embodiment 5, an example is described in which a client device of a vehicle or the like transmits three-dimensional data to another vehicle or a server such as a cloud-based traffic monitoring system. In the present embodiment, a client device transmits sensor information obtained through a sensor to a server or a client device. 
     A structure of a system according to the present embodiment will first be described.  FIG.  28    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.  29    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  815  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.  30    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 the 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.  31    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.  32    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.  33    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.  34    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. 
     Hereinafter, variations of the present embodiment will be described. 
     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 the 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.  35    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.  36    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 the obtained sensor information  1033  to server  901  or another mobile object. 
     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  1034  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 mobile object  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 the 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 the 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. 
     Embodiment 7 
     In the present embodiment, three-dimensional data encoding and decoding methods using an inter prediction process will be described; 
       FIG.  37    is a block diagram of three-dimensional data encoding device  1300  according to the present embodiment. This three-dimensional data encoding device  1300  generates an encoded bitstream (hereinafter, also simply referred to as bitstream) that is an encoded signal, by encoding three-dimensional data. As illustrated in  FIG.  37   , three-dimensional data encoding device  1300  includes divider  1301 , subtractor  1302 , transformer  1303 , quantizer  1304 , inverse quantizer  1305 , inverse transformer  1306 , adder  1307 , reference volume memory  1308 , intra predictor  1309 , reference space memory  1310 , inter predictor  1311 , prediction controller  1312 , and entropy encoder  1313 . 
     Divider  1301  divides a plurality of volumes (VLMs) that are encoding units of each space (SPC) included in the three-dimensional data. Divider  1301  makes an octree representation (make into an octree) of voxels in each volume. Note that divider  1301  may make the spaces into an octree representation with the spaces having the same size as the volumes. Divider  1301  may also append information (depth information, etc.) necessary for making the octree representation to a header and the like of a bitstream. 
     Subtractor  1302  calculates a difference between a volume (encoding target volume) outputted by divider  1301  and a predicted volume generated through intra prediction or inter prediction, which will be described later, and outputs the calculated difference to transformer  1303  as a prediction residual.  FIG.  38    is a diagram showing an example calculation of the prediction residual. Note that bit sequences of the encoding target volume and the predicted volume shown here are, for example, position information indicating positions of three-dimensional points included in the volumes. 
     Hereinafter, a scan order of an octree representation and voxels will be described. A volume is encoded after being converted into an octree structure (made into an octree). The octree structure includes nodes and leaves. Each node has eight nodes or leaves, and each leaf has voxel (VXL) information.  FIG.  39    is a diagram showing an example structure of a volume including voxels.  FIG.  40    is a diagram showing an example of the volume shown in  FIG.  39    having been converted into the octree structure. Among the leaves shown in  FIG.  40   , leaves  1 ,  2 , and  3  respectively represent VXL  1 , VXL  2 , and VXL  3 , and represent VXLs including a point group (hereinafter, active VXLs). 
     An octree is represented by, for example, binary sequences of 1s and 0s. For example, when giving the nodes or the active VXLs a value of 1 and everything else a value of 0, each node and leaf is assigned with the binary sequence shown in  FIG.  40   . Thus, this binary sequence is scanned in accordance with a breadth-first or a depth-first scan order. For example, when scanning breadth-first, the binary sequence shown in A of  FIG.  41    is obtained. When scanning depth-first, the binary sequence shown in B of  FIG.  41    is obtained. The binary sequences obtained through this scanning are encoded through entropy encoding, which reduces an amount of information. 
     Depth information in the octree representation will be described next. Depth in the octree representation is used in order to control up to how fine a granularity point cloud information included in a volume is stored. Upon setting a great depth, it is possible to reproduce the point cloud information to a more precise level, but an amount of data for representing the nodes and leaves increases. Upon setting a small depth, however, the amount of data decreases, but some information that the point cloud information originally held is lost, since pieces of point cloud information including different positions and different colors are now considered as pieces of point cloud information including the same position and the same color. 
     For example,  FIG.  42    is a diagram showing an example in which the octree with a depth of 2 shown in  FIG.  40    is represented with a depth of 1. The octree shown in  FIG.  42    has a lower amount of data than the octree shown in  FIG.  40   . In other words, the binarized octree shown in  FIG.  42    has a lower bit count than the octree shown in  FIG.  40   . Leaf  1  and leaf  2  shown in  FIG.  40    are represented by leaf  1  shown in  FIG.  41   . In other words, the information on leaf  1  and leaf  2  being in different positions is lost; 
       FIG.  43    is a diagram showing a volume corresponding to the octree shown in  FIG.  42   . VXL  1  and VXL  2  shown in  FIG.  39    correspond to VXL  12  shown in  FIG.  43   . In this case, three-dimensional data encoding device  1300  generates color information of VXL  12  shown in  FIG.  43    using color information of VXL  1  and VXL  2  shown in  FIG.  39   . For example, three-dimensional data encoding device  1300  calculates an average value, a median, a weighted average value, or the like of the color information of VXL  1  and VXL  2  as the color information of VXL  12 . In this manner, three-dimensional data encoding device  1300  may control a reduction of the amount of data by changing the depth of the octree. 
     Three-dimensional data encoding device  1300  may set the depth information of the octree to units of worlds, units of spaces, or units of volumes. In this case, three-dimensional data encoding device  1300  may append the depth information to header information of the world, header information of the space, or header information of the volume. In all worlds, spaces, and volumes associated with different times, the same value may be used as the depth information. In this case, three-dimensional data encoding device  1300  may append the depth information to header information managing the worlds associated with all times. 
     When the color information is included in the voxels, transformer  1303  applies frequency transformation, e.g. orthogonal transformation, to a prediction residual of the color information of the voxels in the volume. For example, transformer  1303  creates a one-dimensional array by scanning the prediction residual in a certain scan order. Subsequently, transformer  1303  transforms the one-dimensional array to a frequency domain by applying one-dimensional orthogonal transformation to the created one-dimensional array. With this, when a value of the prediction residual in the volume is similar, a value of a low-frequency component increases and a value of a high-frequency component decreases. As such, it is possible to more efficiently reduce an encoding amount in quantizer  1304 . 
     Transformer  1303  does not need to use orthogonal transformation in one dimension, but may also use orthogonal transformation in two or more dimensions. For example, transformer  1303  maps the prediction residual to a two-dimensional array in a certain scan order, and applies two-dimensional orthogonal transformation to the obtained two-dimensional array. Transformer  1303  may select an orthogonal transformation method to be used from a plurality of orthogonal transformation methods. In this case, three-dimensional data encoding device  1300  appends, to the bitstream, information indicating which orthogonal transformation method is used. Transformer  1303  may select an orthogonal transformation method to be used from a plurality of orthogonal transformation methods in different dimensions. In this case, three-dimensional data encoding device  1300  appends, to the bitstream, in how many dimensions the orthogonal transformation method is used. 
     For example, transformer  1303  matches the scan order of the prediction residual to a scan order (breadth-first, depth-first, or the like) in the octree in the volume. This makes it possible to reduce overhead, since information indicating the scan order of the prediction residual does not need to be appended to the bitstream. Transformer  1303  may apply a scan order different from the scan order of the octree. In this case, three-dimensional data encoding device  1300  appends, to the bitstream, information indicating the scan order of the prediction residual. This enables three-dimensional data encoding device  1300  to efficiently encode the prediction residual. Three-dimensional data encoding device  1300  may append, to the bitstream, information (flag, etc.) indicating whether to apply the scan order of the octree, and may also append, to the bitstream, information indicating the scan order of the prediction residual when the scan order of the octree is not applied. 
     Transformer  1303  does not only transform the prediction residual of the color information, and may also transform other attribute information included in the voxels. For example, transformer  1303  may transform and encode information, such as reflectance information, obtained when obtaining a point cloud through LiDAR and the like. 
     Transformer  1303  may skip these processes when the spaces do not include attribute information such as color information. Three-dimensional data encoding device  1300  may append, to the bitstream, information (flag) indicating whether to skip the processes of transformer  1303 . 
     Quantizer  1304  generates a quantized coefficient by performing quantization using a quantization control parameter on a frequency component of the prediction residual generated by transformer  1303 . With this, the amount of information is further reduced. The generated quantized coefficient is outputted to entropy encoder  1313 . Quantizer  1304  may control the quantization control parameter in units of worlds, units of spaces, or units of volumes. In this case, three-dimensional data encoding device  1300  appends the quantization control parameter to each header information and the like. Quantizer  1304  may perform quantization control by changing a weight per frequency component of the prediction residual. For example, quantizer  1304  may precisely quantize a low-frequency component and roughly quantize a high-frequency component. In this case, three-dimensional data encoding device  1300  may append, to a header, a parameter expressing a weight of each frequency component. 
     Quantizer  1304  may skip these processes when the spaces do not include attribute information such as color information. Three-dimensional data encoding device  1300  may append, to the bitstream, information (flag) indicating whether to skip the processes of quantizer  1304 . 
     Inverse quantizer  1305  generates an inverse quantized coefficient of the prediction residual by performing inverse quantization on the quantized coefficient generated by quantizer  1304  using the quantization control parameter, and outputs the generated inverse quantized coefficient to inverse transformer  1306 . 
     Inverse transformer  1306  generates an inverse transformation-applied prediction residual by applying inverse transformation on the inverse quantized coefficient generated by inverse quantizer  1305 . This inverse transformation-applied prediction residual does not need to completely coincide with the prediction residual outputted by transformer  1303 , since the inverse transformation-applied prediction residual is a prediction residual that is generated after the quantization. 
     Adder  1307  adds, to generate a reconstructed volume, (i) the inverse transformation-applied prediction residual generated by inverse transformer  1306  to (ii) a predicted volume that is generated through intra prediction or intra prediction, which will be described later, and is used to generate a pre-quantized prediction residual. This reconstructed volume is stored in reference volume memory  1308  or reference space memory  1310 . 
     Intra predictor  1309  generates a predicted volume of an encoding target volume using attribute information of a neighboring volume stored in reference volume memory  1308 . The attribute information includes color information or a reflectance of the voxels. Intra predictor  1309  generates a predicted value of color information or a reflectance of the encoding target volume; 
       FIG.  44    is a diagram for describing an operation of intra predictor  1309 . For example, intra predictor  1309  generates the predicted volume of the encoding target volume (volume idx=3) shown in  FIG.  44   , using a neighboring volume (volume idx=0). Volume idx here is identifier information that is appended to a volume in a space, and a different value is assigned to each volume. An order of assigning volume idx may be the same as an encoding order, and may also be different from the encoding order. For example, intra predictor  1309  uses an average value of color information of voxels included in volume idx=0, which is a neighboring volume, as the predicted value of the color information of the encoding target volume shown in  FIG.  44   . In this case, a prediction residual is generated by deducting the predicted value of the color information from the color information of each voxel included in the encoding target volume. The following processes are performed by transformer  1303  and subsequent processors with respect to this prediction residual. In this case, three-dimensional data encoding device  1300  appends, to the bitstream, neighboring volume information and prediction mode information. The neighboring volume information here is information indicating a neighboring volume used in the prediction, and indicates, for example, volume idx of the neighboring volume used in the prediction. The prediction mode information here indicates a mode used to generate the predicted volume. The mode is, for example, an average value mode in which the predicted value is generated using an average value of the voxels in the neighboring volume, or a median mode in which the predicted value is generated using the median of the voxels in the neighboring volume. 
     Intra predictor  1309  may generate the predicted volume using a plurality of neighboring volumes. For example, in the structure shown in  FIG.  44   , intra predictor  1309  generates predicted volume 0 using a volume with volume idx=0, and generates predicted volume 1 using a volume with volume idx=1. Intra predictor  1309  then generates an average of predicted volume 0 and predicted volume 1 as a final predicted volume. In this case, three-dimensional data encoding device  1300  may append, to the bitstream, a plurality of volumes idx of a plurality of volumes used to generate the predicted volume; 
       FIG.  45    is a diagram schematically showing the inter prediction process according to the present embodiment. Inter predictor  1311  encodes (inter predicts) a space (SPC) associated with certain time T_Cur using an encoded space associated with different time T_LX. In this case, inter predictor  1311  performs an encoding process by applying a rotation and translation process to the encoded space associated with different time T_LX. 
     Three-dimensional data encoding device  1300  appends, to the bitstream, RT information relating to a rotation and translation process suited to the space associated with different time T_LX. Different time T_LX is, for example, time T_L0 before certain time T_Cur. At this point, three-dimensional data encoding device  1300  may append, to the bitstream, RT information RT_L0 relating to a rotation and translation process suited to a space associated with time T_L0. 
     Alternatively, different time T_LX is, for example, time T_L1 after certain time T_Cur. At this point, three-dimensional data encoding device  1300  may append, to the bitstream, RT information RT_L1 relating to a rotation and translation process suited to a space associated with time T_L1. 
     Alternatively, inter predictor  1311  encodes (bidirectional prediction) with reference to the spaces associated with time T_L0 and time T_L1 that differ from each other. In this case, three-dimensional data encoding device  1300  may append, to the bitstream, both RT information RT_L0 and RT information RT_L1 relating to the rotation and translation process suited to the spaces thereof. 
     Note that T_L0 has been described as being before T_Cur and T_L1 as being after T_Cur, but are not necessarily limited thereto. For example, T_L0 and T_L1 may both be before T_Cur. T_L0 and T_L1 may also both be after T_Cur. 
     Three-dimensional data encoding device  1300  may append, to the bitstream, RT information relating to a rotation and translation process suited to spaces associated with different times, when encoding with reference to each of the spaces. For example, three-dimensional data encoding device  1300  manages a plurality of encoded spaces to be referred to, using two reference lists (list L0 and list L1). When a first reference space in list L0 is L0R0, a second reference space in list L0 is L0R1, a first reference space in list L0 is L1R0, and a second reference space in list L1 is L1R1, three-dimensional data encoding device  1300  appends, to the bitstream, RT information RT_L0R0 of L0R0, RT information RT_L0R1 of L0R1, RT information RT_L1R0 of L1R0, and RT information RT_L1R1 of L1R1. For example, three-dimensional data encoding device  1300  appends these pieces of RT information to a header and the like of the bitstream. 
     Three-dimensional data encoding device  1300  determines whether to apply rotation and translation per reference space, when encoding with reference to reference spaces associated with different times. In this case, three-dimensional data encoding device  1300  may append, to header information and the like of the bitstream, information (RT flag, etc.) indicating whether rotation and translation are applied per reference space. For example, three-dimensional data encoding device  1300  calculates the RT information and an Iterative Closest Point (ICP) error value, using an ICP algorithm per reference space to be referred to from the encoding target space. Three-dimensional data encoding device  1300  determines that rotation and translation do not need to be performed and sets the RT flag to OFF, when the ICP error value is lower than or equal to a predetermined fixed value. In contrast, three-dimensional data encoding device  1300  sets the RT flag to ON and appends the RT information to the bitstream, when the ICP error value exceeds the above fixed value; 
       FIG.  46    is a diagram showing an example syntax to be appended to a header of the RT information and the RT flag. Note that a bit count assigned to each syntax may be decided based on a range of this syntax. For example, when eight reference spaces are included in reference list L0, 3 bits may be assigned to MaxRefSpc_l0. The bit count to be assigned may be variable in accordance with a value each syntax can be, and may also be fixed regardless of the value each syntax can be. When the bit count to be assigned is fixed, three-dimensional data encoding device  1300  may append this fixed bit count to other header information. 
     MaxRefSpc_l0 shown in  FIG.  46    indicates a number of reference spaces included in reference list L0. RT_flag_l0[i] is an RT flag of reference space i in reference list L0. When RT_flag_l0[i] is 1, rotation and translation are applied to reference space i. When RT_flag_l0[i] is 0, rotation and translation are not applied to reference space i. 
     R_l0[i] and T_l0[i] are RT information of reference space i in reference list L0. R_l0[i] is rotation information of reference space i in reference list L0. The rotation information indicates contents of the applied rotation process, and is, for example, a rotation matrix or a quaternion. T_l0[i] is translation information of reference space i in reference list L0. The translation information indicates contents of the applied translation process, and is, for example, a translation vector. 
     MaxRefSpc_l1 indicates a number of reference spaces included in reference list L1. RT_flag_l1[i] is an RT flag of reference space i in reference list L1. When RT_flag_l1[i] is 1, rotation and translation are applied to reference space i. When RT_flag_l1[i] is 0, rotation and translation are not applied to reference space i. 
     R_l1[i] and T_l1[i] are RT information of reference space i in reference list L1. R_l1[i] is rotation information of reference space i in reference list L1 .The rotation information indicates contents of the applied rotation process, and is, for example, a rotation matrix or a quaternion. T_l1[i] is translation information of reference space i in reference list L1. The translation information indicates contents of the applied translation process, and is, for example, a translation vector. 
     Inter predictor  1311  generates the predicted volume of the encoding target volume using information on an encoded reference space stored in reference space memory  1310 . As stated above, before generating the predicted volume of the encoding target volume, inter predictor  1311  calculates RT information at an encoding target space and a reference space using an ICP algorithm, in order to approach an overall positional relationship between the encoding target space and the reference space. Inter predictor  1311  then obtains reference space B by applying a rotation and translation process to the reference space using the calculated RT information. Subsequently, inter predictor  1311  generates the predicted volume of the encoding target volume in the encoding target space using information in reference space B. Three-dimensional data encoding device  1300  appends, to header information and the like of the encoding target space, the RT information used to obtain reference space B. 
     In this manner, inter predictor  1311  is capable of improving precision of the predicted volume by generating the predicted volume using the information of the reference space, after approaching the overall positional relationship between the encoding target space and the reference space, by applying a rotation and translation process to the reference space. It is possible to reduce the encoding amount since it is possible to limit the prediction residual. Note that an example has been described in which ICP is performed using the encoding target space and the reference space, but is not necessarily limited thereto. For example, inter predictor  1311  may calculate the RT information by performing ICP using at least one of (i) an encoding target space in which a voxel or point cloud count is pruned, or (ii) a reference space in which a voxel or point cloud count is pruned, in order to reduce the processing amount. 
     When the ICP error value obtained as a result of the ICP is smaller than a predetermined first threshold, i.e., when for example the positional relationship between the encoding target space and the reference space is similar, inter predictor  1311  determines that a rotation and translation process is not necessary, and the rotation and translation process does not need to be performed. In this case, three-dimensional data encoding device  1300  may control the overhead by not appending the RT information to the bitstream. 
     When the ICP error value is greater than a predetermined second threshold, inter predictor  1311  determines that a shape change between the spaces is large, and intra prediction may be applied on all volumes of the encoding target space. Hereinafter, spaces to which intra prediction is applied will be referred to as intra spaces. The second threshold is greater than the above first threshold. The present embodiment is not limited to ICP, and any type of method may be used as long as the method calculates the RT information using two voxel sets or two point cloud sets. 
     When attribute information, e.g. shape or color information, is included in the three-dimensional data, inter predictor  1311  searches, for example, a volume whose attribute information, e.g. shape or color information, is the most similar to the encoding target volume in the reference space, as the predicted volume of the encoding target volume in the encoding target space. This reference space is, for example, a reference space on which the above rotation and translation process has been performed. Inter predictor  1311  generates the predicted volume using the volume (reference volume) obtained through the search.  FIG.  47    is a diagram for describing a generating operation of the predicted volume. When encoding the encoding target volume (volume idx=0) shown in  FIG.  47    using inter prediction, inter predictor  1311  searches a volume with a smallest prediction residual, which is the difference between the encoding target volume and the reference volume, while sequentially scanning the reference volume in the reference space. Inter predictor  1311  selects the volume with the smallest prediction residual as the predicted volume. The prediction residuals of the encoding target volume and the predicted volume are encoded through the processes performed by transformer  1303  and subsequent processors. The prediction residual here is a difference between the attribute information of the encoding target volume and the attribute information of the predicted volume. Three-dimensional data encoding device  1300  appends, to the header and the like of the bitstream, volume idx of the reference volume in the reference space, as the predicted volume. 
     In the example shown in  FIG.  47   , the reference volume with volume idx=4 of reference space L0R0 is selected as the predicted volume of the encoding target volume. The prediction residuals of the encoding target volume and the reference volume, and reference volume idx=4 are then encoded and appended to the bitstream. 
     Note that an example has been described in which the predicted volume of the attribute information is generated, but the same process may be applied to the predicted volume of the position information. 
     Prediction controller  1312  controls whether to encode the encoding target volume using intra prediction or inter prediction. A mode including intra prediction and inter prediction is referred to here as a prediction mode. For example, prediction controller  1312  calculates the prediction residual when the encoding target volume is predicted using intra prediction and the prediction residual when the encoding target volume is predicted using inter prediction as evaluation values, and selects the prediction mode whose evaluation value is smaller. Note that prediction controller  1312  may calculate an actual encoding amount by applying orthogonal transformation, quantization, and entropy encoding to the prediction residual of the intra prediction and the prediction residual of the inter prediction, and select a prediction mode using the calculated encoding amount as the evaluation value. Overhead information (reference volume idx information, etc.) aside from the prediction residual may be added to the evaluation value. Prediction controller  1312  may continuously select intra prediction when it has been decided in advance to encode the encoding target space using intra space. 
     Entropy encoder  1313  generates an encoded signal (encoded bitstream) by variable-length encoding the quantized coefficient, which is an input from quantizer  1304 . To be specific, entropy encoder  1313 , for example, binarizes the quantized coefficient and arithmetically encodes the obtained binary signal. 
     A three-dimensional data decoding device that decodes the encoded signal generated by three-dimensional data encoding device  1300  will be described next.  FIG.  48    is a block diagram of three-dimensional data decoding device  1400  according to the present embodiment. This three-dimensional data decoding device  1400  includes entropy decoder  1401 , inverse quantizer  1402 , inverse transformer  1403 , adder  1404 , reference volume memory  1405 , intra predictor  1406 , reference space memory  1407 , inter predictor  1408 , and prediction controller  1409 . 
     Entropy decoder  1401  variable-length decodes the encoded signal (encoded bitstream). For example, entropy decoder  1401  generates a binary signal by arithmetically decoding the encoded signal, and generates a quantized coefficient using the generated binary signal. 
     Inverse quantizer  1402  generates an inverse quantized coefficient by inverse quantizing the quantized coefficient inputted from entropy decoder  1401 , using a quantization parameter appended to the bitstream and the like. 
     Inverse transformer  1403  generates a prediction residual by inverse transforming the inverse quantized coefficient inputted from inverse quantizer  1402 . For example, inverse transformer  1403  generates the prediction residual by inverse orthogonally transforming the inverse quantized coefficient, based on information appended to the bitstream. 
     Adder  1404  adds, to generate a reconstructed volume, (i) the prediction residual generated by inverse transformer  1403  to (ii) a predicted volume generated through intra prediction or intra prediction. This reconstructed volume is outputted as decoded three-dimensional data and is stored in reference volume memory  1405  or reference space memory  1407 . 
     Intra predictor  1406  generates a predicted volume through intra prediction using a reference volume in reference volume memory  1405  and information appended to the bitstream. To be specific, intra predictor  1406  obtains neighboring volume information (e.g. volume idx) appended to the bitstream and prediction mode information, and generates the predicted volume through a mode indicated by the prediction mode information, using a neighboring volume indicated in the neighboring volume information. Note that the specifics of these processes are the same as the above-mentioned processes performed by intra predictor  1309 , except for which information appended to the bitstream is used. 
     Inter predictor  1408  generates a predicted volume through inter prediction using a reference space in reference space memory  1407  and information appended to the bitstream. To be specific, inter predictor  1408  applies a rotation and translation process to the reference space using the RT information per reference space appended to the bitstream, and generates the predicted volume using the rotated and translated reference space. Note that when an RT flag is present in the bitstream per reference space, inter predictor  1408  applies a rotation and translation process to the reference space in accordance with the RT flag. Note that the specifics of these processes are the same as the above-mentioned processes performed by inter predictor  1311 , except for which information appended to the bitstream is used. 
     Prediction controller  1409  controls whether to decode a decoding target volume using intra prediction or inter prediction. For example, prediction controller  1409  selects intra prediction or inter prediction in accordance with information that is appended to the bitstream and indicates the prediction mode to be used. Note that prediction controller  1409  may continuously select intra prediction when it has been decided in advance to decode the decoding target space using intra space. 
     Hereinafter, variations of the present embodiment will be described. In the present embodiment, an example has been described in which rotation and translation is applied in units of spaces, but rotation and translation may also be applied in smaller units. For example, three-dimensional data encoding device  1300  may divide a space into subspaces, and apply rotation and translation in units of subspaces. In this case, three-dimensional data encoding device  1300  generates RT information per subspace, and appends the generated RT information to a header and the like of the bitstream. Three-dimensional data encoding device  1300  may apply rotation and translation in units of volumes, which is an encoding unit. In this case, three-dimensional data encoding device  1300  generates RT information in units of encoded volumes, and appends the generated RT information to a header and the like of the bitstream. The above may also be combined. In other words, three-dimensional data encoding device  1300  may apply rotation and translation in large units and subsequently apply rotation and translation in small units. For example, three-dimensional data encoding device  1300  may apply rotation and translation in units of spaces, and may also apply different rotations and translations to each of a plurality of volumes included in the obtained spaces. 
     In the present embodiment, an example has been described in which rotation and translation is applied to the reference space, but is not necessarily limited thereto. For example, three-dimensional data encoding device  1300  may apply a scaling process and change a size of the three-dimensional data. Three-dimensional data encoding device  1300  may also apply one or two of the rotation, translation, and scaling. When applying the processes in multiple stages and different units as stated above, a type of the processes applied in each unit may differ. For example, rotation and translation may be applied in units of spaces, and translation may be applied in units of volumes. 
     Note that these variations are also applicable to three-dimensional data decoding device  1400 . 
     As stated above, three-dimensional data encoding device  1300  according to the present embodiment performs the following processes.  FIG.  48    is a flowchart of the inter prediction process performed by three-dimensional data encoding device  1300 . 
     Three-dimensional data encoding device  1300  generates predicted position information (e.g. predicted volume) using position information on three-dimensional points included in three-dimensional reference data (e.g. reference space) associated with a time different from a time associated with current three-dimensional data (e.g. encoding target space) (S 1301 ). To be specific, three-dimensional data encoding device  1300  generates the predicted position information by applying a rotation and translation process to the position information on the three-dimensional points included in the three-dimensional reference data. 
     Note that three-dimensional data encoding device  1300  may perform a rotation and translation process using a first unit (e.g. spaces), and may perform the generating of the predicted position information using a second unit (e.g. volumes) that is smaller than the first unit. For example, three-dimensional data encoding device  1300  searches a volume among a plurality of volumes included in the rotated and translated reference space, whose position information differs the least from the position information of the encoding target volume included in the encoding target space. Note that three-dimensional data encoding device  1300  may perform the rotation and translation process, and the generating of the predicted position information in the same unit. 
     Three-dimensional data encoding device  1300  may generate the predicted position information by applying (i) a first rotation and translation process to the position information on the three-dimensional points included in the three-dimensional reference data, and (ii) a second rotation and translation process to the position information on the three-dimensional points obtained through the first rotation and translation process, the first rotation and translation process using a first unit (e.g. spaces) and the second rotation and translation process using a second unit (e.g. volumes) that is smaller than the first unit. 
     For example, as illustrated in  FIG.  41   , the position information on the three-dimensional points and the predicted position information is represented using an octree structure. For example, the position information on the three-dimensional points and the predicted position information is expressed in a scan order that prioritizes a breadth over a depth in the octree structure. For example, the position information on the three-dimensional points and the predicted position information is expressed in a scan order that prioritizes a depth over a breadth in the octree structure. 
     As illustrated in  FIG.  46   , three-dimensional data encoding device  1300  encodes an RT flag that indicates whether to apply the rotation and translation process to the position information on the three-dimensional points included in the three-dimensional reference data. In other words, three-dimensional data encoding device  1300  generates the encoded signal (encoded bitstream) including the RT flag. Three-dimensional data encoding device  1300  encodes RT information that indicates contents of the rotation and translation process. In other words, three-dimensional data encoding device  1300  generates the encoded signal (encoded bitstream) including the RT information. Note that three-dimensional data encoding device  1300  may encode the RT information when the RT flag indicates to apply the rotation and translation process, and does not need to encode the RT information when the RT flag indicates not to apply the rotation and translation process. 
     The three-dimensional data includes, for example, the position information on the three-dimensional points and the attribute information (color information, etc.) of each three-dimensional point. Three-dimensional data encoding device  1300  generates predicted attribute information using the attribute information of the three-dimensional points included in the three-dimensional reference data (S 1302 ). 
     Three-dimensional data encoding device  1300  next encodes the position information on the three-dimensional points included in the current three-dimensional data, using the predicted position information. For example, as illustrated in  FIG.  38   , three-dimensional data encoding device  1300  calculates differential position information, the differential position information being a difference between the predicted position information and the position information on the three-dimensional points included in the current three-dimensional data (S 1303 ). 
     Three-dimensional data encoding device  1300  encodes the attribute information of the three-dimensional points included in the current three-dimensional data, using the predicted attribute information. For example, three-dimensional data encoding device  1300  calculates differential attribute information, the differential attribute information being a difference between the predicted attribute information and the attribute information on the three-dimensional points included in the current three-dimensional data (S 1304 ). Three-dimensional data encoding device  1300  next performs transformation and quantization on the calculated differential attribute information (S 1305 ). 
     Lastly, three-dimensional data encoding device  1300  encodes (e.g. entropy encodes) the differential position information and the quantized differential attribute information (S 1036 ). In other words, three-dimensional data encoding device  1300  generates the encoded signal (encoded bitstream) including the differential position information and the differential attribute information. 
     Note that when the attribute information is not included in the three-dimensional data, three-dimensional data encoding device  1300  does not need to perform steps S 1302 , S 1304 , and S 1305 . Three-dimensional data encoding device  1300  may also perform only one of the encoding of the position information on the three-dimensional points and the encoding of the attribute information of the three-dimensional points. 
     An order of the processes shown in  FIG.  49    is merely an example and is not limited thereto. For example, since the processes with respect to the position information (S 1301  and S 1303 ) and the processes with respect to the attribute information (S 1302 , S 1304 , and S 1305 ) are separate from one another, they may be performed in an order of choice, and a portion thereof may also be performed in parallel. 
     With the above, three-dimensional data encoding device  1300  according to the present embodiment generates predicted position information using position information on three-dimensional points included in three-dimensional reference data associated with a time different from a time associated with current three-dimensional data; and encodes differential position information, which is a difference between the predicted position information and the position information on the three-dimensional points included in the current three-dimensional data. This makes it possible to improve encoding efficiency since it is possible to reduce the amount of data of the encoded signal. 
     Three-dimensional data encoding device  1300  according to the present embodiment generates predicted attribute information using attribute information on three-dimensional points included in three-dimensional reference data; and encodes differential attribute information, which is a difference between the predicted attribute information and the attribute information on the three-dimensional points included in the current three-dimensional data. This makes it possible to improve encoding efficiency since it is possible to reduce the amount of data of the encoded signal. 
     For example, three-dimensional data encoding device  1300  includes a processor and memory. The processor uses the memory to perform the above processes; 
       FIG.  48    is a flowchart of the inter prediction process performed by three-dimensional data decoding device  1400 . 
     Three-dimensional data decoding device  1400  decodes (e.g. entropy decodes) the differential position information and the differential attribute information from the encoded signal (encoded bitstream) (S 1401 ). 
     Three-dimensional data decoding device  1400  decodes, from the encoded signal, an RT flag that indicates whether to apply the rotation and translation process to the position information on the three-dimensional points included in the three-dimensional reference data. Three-dimensional data decoding device  1400  encodes RT information that indicates contents of the rotation and translation process. Note that three-dimensional data decoding device  1400  may decode the RT information when the RT flag indicates to apply the rotation and translation process, and does not need to decode the RT information when the RT flag indicates not to apply the rotation and translation process. 
     Three-dimensional data decoding device  1400  next performs inverse transformation and inverse quantization on the decoded differential attribute information (S 1402 ). 
     Three-dimensional data decoding device  1400  next generates predicted position information (e.g. predicted volume) using the position information on the three-dimensional points included in the three-dimensional reference data (e.g. reference space) associated with a time different from a time associated with the current three-dimensional data (e.g. decoding target space) (S 1403 ). To be specific, three-dimensional data decoding device  1400  generates the predicted position information by applying a rotation and translation process to the position information on the three-dimensional points included in the three-dimensional reference data. 
     More specifically, when the RT flag indicates to apply the rotation and translation process, three-dimensional data decoding device  1400  applies the rotation and translation process on the position information on the three-dimensional points included in the three-dimensional reference data indicated in the RT information. In contrast, when the RT flag indicates not to apply the rotation and translation process, three-dimensional data decoding device  1400  does not apply the rotation and translation process on the position information on the three-dimensional points included in the three-dimensional reference data. 
     Note that three-dimensional data decoding device  1400  may perform the rotation and translation process using a first unit (e.g. spaces), and may perform the generating of the predicted position information using a second unit (e.g. volumes) that is smaller than the first unit. Note that three-dimensional data decoding device  1400  may perform the rotation and translation process, and the generating of the predicted position information in the same unit. 
     Three-dimensional data decoding device  1400  may generate the predicted position information by applying (i) a first rotation and translation process to the position information on the three-dimensional points included in the three-dimensional reference data, and (ii) a second rotation and translation process to the position information on the three-dimensional points obtained through the first rotation and translation process, the first rotation and translation process using a first unit (e.g. spaces) and the second rotation and translation process using a second unit (e.g. volumes) that is smaller than the first unit. 
     For example, as illustrated in  FIG.  41   , the position information on the three-dimensional points and the predicted position information is represented using an octree structure. For example, the position information on the three-dimensional points and the predicted position information is expressed in a scan order that prioritizes a breadth over a depth in the octree structure. For example, the position information on the three-dimensional points and the predicted position information is expressed in a scan order that prioritizes a depth over a breadth in the octree structure. 
     Three-dimensional data decoding device  1400  generates predicted attribute information using the attribute information of the three-dimensional points included in the three-dimensional reference data (S 1404 ). 
     Three-dimensional data decoding device  1400  next restores the position information on the three-dimensional points included in the current three-dimensional data, by decoding encoded position information included in an encoded signal, using the predicted position information. The encoded position information here is the differential position information. Three-dimensional data decoding device  1400  restores the position information on the three-dimensional points included in the current three-dimensional data, by adding the differential position information to the predicted position information (S 1405 ). 
     Three-dimensional data decoding device  1400  restores the attribute information of the three-dimensional points included in the current three-dimensional data, by decoding encoded attribute information included in an encoded signal, using the predicted attribute information. The encoded attribute information here is the differential position information. Three-dimensional data decoding device  1400  restores the attribute information on the three-dimensional points included in the current three-dimensional data, by adding the differential attribute information to the predicted attribute information (S 1406 ). 
     Note that when the attribute information is not included in the three-dimensional data, three-dimensional data decoding device  1400  does not need to perform steps S 1402 , S 1404 , and S 1406 . Three-dimensional data decoding device  1400  may also perform only one of the decoding of the position information on the three-dimensional points and the decoding of the attribute information of the three-dimensional points. 
     An order of the processes shown in  FIG.  50    is merely an example and is not limited thereto. For example, since the processes with respect to the position information (S 1403  and S 1405 ) and the processes with respect to the attribute information (S 1402 , S 1404 , and S 1406 ) are separate from one another, they may be performed in an order of choice, and a portion thereof may also be performed in parallel. 
     Embodiment 8 
     In the present embodiment, a representation means of three-dimensional points (point cloud) in encoding of three-dimensional data will be described; 
       FIG.  51    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.  51    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.  52    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.  53    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.  53   . 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.  54    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.  55    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 sub coordinates (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.  56    is a diagram showing an example syntax of the submap. NumOfPoint shown in  FIG.  56    indicates a total number of point clouds included in the submap. sub_coordinate_x, sub_coordinate_y, and sub_coordinate_z are the subcoordinate information. sub_coordinate_x indicates an x-coordinate of the subcoordinates. sub_coordinate_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_coordinate_ 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.  57    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.  58    is a diagram showing an example syntax of the submap when performing this switching. coding_type shown in  FIG.  58    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.  59    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.  60    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.  61    to  FIG.  63    are diagrams schematically showing operations of variations of the switching process of the encoding type. 
     As illustrated in  FIG.  61   , 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.  62   , 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.  63   , 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.  64    is a diagram for describing an operation in this case. For example, in the example shown in  FIG.  64   , 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.  65    to  FIG.  67    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.  65   , the subcoordinates may be coordinates in a center of the current space. As illustrated in  FIG.  66   , 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.  67   , 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.  68    is a diagram showing an example syntax of a volume when applying octree encoding. The syntax shown in  FIG.  68    is basically the same as the syntax shown in  FIG.  58   , 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_coordinate_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 sub coordinate 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.  59   ). 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.  60   ). 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 9 
     In the present embodiment, a method for encoding a tree structure such as an octree structure will be described. 
     It is possible to improve efficiency by identifying an important area and preferentially decoding three-dimensional data of the important area; 
       FIG.  69    is a diagram showing an example of an important area in a three-dimensional map. The important area includes, for example, at least a fixed number of three-dimensional points, among three-dimensional points in the three-dimensional map, having a high feature quantity. The important area may also include, for example, a fixed number of three-dimensional points necessary when, for example, a vehicle-mounted client performs self-location estimation. Alternatively, the important area may also be a face in a three-dimensional model of a person. Such an important area can be defined per application type, and may be switched in accordance therewith. 
     In the present embodiment, occupancy encoding and location encoding are used as a method for representing an octree structure and the like. A bit sequence obtained through occupancy encoding is referred to as occupancy code. A bit sequence obtained through location encoding is referred to as location code; 
       FIG.  70    is a diagram showing an example of an occupancy code.  FIG.  70    shows an example of the occupancy code of a quadtree structure. In  FIG.  70   , occupancy code is assigned to each node. Each piece of occupancy code indicates whether a three-dimensional point is included in a child node or a leaf of a node. In the case of a quadtree, for example, information, which indicates whether four child nodes or leaves included in each node include three-dimensional points, is expressed with a 4-bit occupancy code. In the case of an octree, information, which indicates whether eight child nodes or leaves included in each node include three-dimensional points, is expressed with an 8-bit occupancy code. Note that an example of a quadtree structure is described here in order to simplify the description, but the same is applicable to an octree structure. As illustrated in  FIG.  70   , for example, the occupancy code is a bit sequence in which the nodes and leaves have been scanned breadth-first, as described in  FIG.  40   , etc. In the occupancy code, since a plurality of pieces of three-dimensional point information are decoded in a fixed order, it is not possible to preferentially decode a piece of three-dimensional point information of choice. Note that the occupancy code may also be a bit sequence in which the nodes and leaves have been scanned depth-first, as described in  FIG.  40   , etc. 
     Hereinafter, location encoding will be described. It is possible to directly decode important portions in the octree structure by using the location code. It is also possible to efficiently encode the important three-dimensional points in deeper levels; 
       FIG.  71    is a diagram for describing location encoding and shows an example of a quadtree structure. In the example shown in  FIG.  71   , three-dimensional points A-I are represented with a quadtree structure. Three-dimensional points A and C are important three-dimensional points included in the important area; 
       FIG.  72    is a diagram showing occupancy codes and location codes expressing important three-dimensional points A and C in the quadtree structure shown in  FIG.  71   . 
     In the location encoding, an index of each node present on a path up until a leaf to which a current three-dimensional point belongs that is an encoding target three-dimensional point, and an index of each leaf in the tree structure are encoded. The index here is a numerical value assigned to each node and each leaf. In other words, the index is an identifier for identifying child nodes of a current node. In the case of the quadtree as shown in  FIG.  71   , indexes between 0 and 3 are shown. 
     In the quadtree structure shown in  FIG.  71   , for example, leaf A is represented as 0→2→1→0→1→2→1 when leaf A is the current three-dimensional point. Since a maximum value of each index in the case of  FIG.  71    is  4  (representable as 2-bit value), a bit count necessary for the location code of leaf A is 7×2 bits=14 bits. Similarly, a bit count necessary when leaf C is the encoding target is 14 bits. Note that in the case of an octree, it is possible to calculate a bit count necessary for 3 bits×leaf depth, since the maximum value of each index is 8 (representable as 3-bit value). Note that the three-dimensional data encoding device may reduce a data amount through entropy encoding after binarizing each index. 
     As illustrated in  FIG.  72   , in the occupancy code, it is necessary to decode all nodes of upper levels of leaves A and C in order to decode leaves A and C. On the other hand, it is possible to only decode data of leaves A and C in the location code. As illustrated in  FIG.  72   , this makes it possible to reduce bit count more than with the occupancy code by using the location code. 
     As illustrated in  FIG.  72   , it is possible to further reduce a code amount by performing dictionary compression such as LZ77 on a portion or all of the location code. 
     An example in which location encoding is applied to three-dimensional points (point cloud) obtained through LiDAR will be described next.  FIG.  73    is a diagram showing the example of the three-dimensional points obtained through LiDAR. The three-dimensional points obtained through LiDAR are sparsely disposed. In other words, when expressing these three-dimensional points with an occupancy code, a number of zero values is high. High three-dimensional precision is required for these three-dimensional points. In other words, the hierarchy of the octree structure becomes deeper; 
       FIG.  74    is a diagram showing an example of such a sparse and deep octree structure. An occupancy code of the octree structure shown in  FIG.  74    is a 136-bit value(=8 bits×17 nodes). Since the octree structure has a depth of 6 and six three-dimensional points, the location code is 3 bits×6×6=108 bits. In other words, the location code is capable of reducing 20% of a code amount of the occupancy code. In this manner, it is possible to reduce the code amount by applying location encoding to the sparse and deep octree structure. 
     Hereinafter, the code amounts of the occupancy code and the location code will be described. When the octree structure has a depth of 10, a maximum number of three-dimensional points is 8 10 =1,073,741,824. Bit count L o  of the occupancy code of the octree structure is expressed below. 
         L   o =8+8 2 + . . . +8 10 =127,133,512 bits 
     As such, a bit count of one three-dimensional point is 1.143 bits. Note that in the occupancy code, this bit count does not change even if the total number of three-dimensional points included in the octree structure changes. 
     On the other hand, in the location code, a bit count of one three-dimensional point is directly influenced by the depth of the octree structure. To be specific, a bit count of the location code of one three-dimensional point is 3 bits×depth of 10=30 bits. 
     As such, bit count L l  of the location code of the octree structure is expressed below. 
         L   l =30× N  
 
     N here is the total number of three-dimensional points included in the octree structure. 
     As such, in the case of N&lt;L o /30=40,904,450.4, i.e., when the total number of three-dimensional points is lower than 40,904,450, the code amount of the location code is smaller than the code amount of the occupancy code (L l &lt;L o ). 
     In this manner, the code amount of the location code is lower than the code amount of the occupancy code in the case of a low number of three-dimensional points, and the code amount of the location code is higher than the code amount of the occupancy code in the case of a high number of three-dimensional points. 
     As such, the three-dimensional data encoding device may switch between using location encoding or occupancy encoding in accordance with the total number of inputted three-dimensional points. In this case, the three-dimensional data encoding device may append, to header information and the like of the bitstream, information indicating whether the location encoding or the occupancy encoding has been performed. 
     Hereinafter, hybrid encoding, which is a combination of the location encoding and the occupancy encoding, will be described. When encoding a dense important area, hybrid encoding, which is a combination of the location encoding and the occupancy encoding, is effective.  FIG.  75    is a diagram showing this example. In the example shown in  FIG.  75   , the important three-dimensional points are disposed densely. In this case, the three-dimensional data encoding device performs location encoding on the upper levels at a shallow depth and uses occupancy encoding for the lower levels. To be specific, location encoding is used up until a deepest common node and occupancy encoding is used from the deepest common node up until the deepest level. The deepest common node here is the deepest node among nodes that are the common ancestors of the plurality of important three-dimensional points. 
     Hybrid encoding that prioritizes compression efficiency will be described next. The three-dimensional data encoding device may switch between location encoding or occupancy encoding in accordance with a predetermined rule during encoding of the octree; 
       FIG.  76    is a diagram showing an example of this rule. The three-dimensional data encoding device first checks a percentage of nodes including three-dimensional points at each level (depth). When the percentage is higher than a predetermined threshold value, the three-dimensional data encoding device occupancy encodes several nodes of upper levels of the current level. For example, the three-dimensional data encoding device applies occupancy encoding from the current level to levels up until the deepest common node. 
     For example, in the example of  FIG.  76   , the percentage of nodes including three-dimensional points in a third level is higher than the predetermined threshold value. As such, the three-dimensional data encoding device applies occupancy encoding from the third level up until the second level including the deepest common node, and applies location encoding to the other levels, i.e., the first level and the fourth level. 
     A method for calculating the above threshold value will be described. One level of the octree structure includes one root node and eight child nodes. As such, in the occupancy encoding, 8 bits are necessary for encoding one level of the octree structure. On the other hand, in the location encoding, 3 bits are necessary per child node including a three-dimensional point. As such, when a total number of nodes including three-dimensional points is higher than 2, occupancy encoding is more effective than location encoding. In other words, in this case, the threshold value is 2. 
     Hereinafter, an example structure of a bitstream generated through the above-mentioned location encoding, occupancy encoding, or hybrid encoding will be described; 
       FIG.  77    is a diagram showing an example of a bitstream generated through location encoding. As illustrated in  FIG.  77   , the bitstream generated through location encoding includes a header and pieces of location code. Each piece of location code corresponds to one three-dimensional point. 
     This structure enables the three-dimensional data decoding device to individually decode a plurality of three-dimensional points will high precision. Note that  FIG.  77    shows an example of a bitstream in the case of a quadtree structure. In the case of an octree structure, each index can take a value between 0 and 7. 
     The three-dimensional data encoding device may entropy encode an index sequence expressing one three-dimensional point after binarizing the index sequence. For example, when the index sequence is 0121, the three-dimensional data encoding device may binarize 0121 into 00011001 and perform arithmetic encoding on this bit sequence; 
       FIG.  78    is a diagram showing an example of a bitstream generated through hybrid encoding when the bitstream includes important three-dimensional points. As illustrated in  FIG.  78   , location code of upper levels, occupancy code of important three-dimensional points of lower levels, and occupancy code of non-important three-dimensional points of lower levels are disposed in this order. Note that a location code length shown in  FIG.  78    expresses a code amount of subsequent location code. An occupancy code amount expresses a code amount of subsequent occupancy code. 
     This structure enables the three-dimensional data decoding device to select a decoding plan in accordance with the type of application. 
     Encoded data of the important three-dimensional points is stored around a head of the bitstream, and encoded data of the non-important three-dimensional points not included in the important area is stored behind the encoded data of the important three-dimensional points; 
       FIG.  79    is a diagram showing a tree structure expressed with the occupancy code of the important three-dimensional points shown in  FIG.  78   .  FIG.  80    is a diagram showing a tree structure expressed with the occupancy code of the non-important three-dimensional points shown in  FIG.  78   . As illustrated in  FIG.  79   , information relating to the non-important three-dimensional points is excluded in the occupancy code of the important three-dimensional points. To be specific, since node  0  and node  3  at a depth of 5 do not include important three-dimensional points, value 0 is assigned indicating that node  0  and node  3  do not include three-dimensional points. 
     On the other hand, as illustrated in  FIG.  80   , information relating to the important three-dimensional points is excluded in the occupancy code of the non-important three-dimensional points. To be specific, since node  1  at a depth of 5 does not include non-important three-dimensional points, value 0 is assigned indicating that node  1  does not include a three-dimensional point. 
     In this manner, the three-dimensional data encoding device divides the original tree structure into a first tree structure including the important three-dimensional points and a second tree structure including the non-important three-dimensional points, and separately occupancy encodes the first tree structure and the second tree structure. This enables the three-dimensional data decoding device to preferentially decode the important three-dimensional points. 
     An example structure of a bitstream generated through hybrid encoding emphasizing efficiency will be described next.  FIG.  81    is a diagram showing the example structure of the bitstream generated through hybrid encoding emphasizing efficiency. As illustrated in  FIG.  81   , a subtree root location, occupancy code amount, and occupancy code are disposed per subtree in this order. The subtree root location shown in  FIG.  81    is the location code of the root of the subtree. 
     In the above structure, the following holds true when only one of location encoding or occupancy encoding is applied to the octree structure. 
     When the length of the location code of the root of the subtree is identical to the depth of the octree structure, the subtree does not include any child nodes. In other words, location encoding is applied to the entire tree structure. 
     When the root of the subtree is identical to the root of the octree structure, occupancy encoding is applied to the entire tree structure. 
     For example, the three-dimensional data decoding device is capable of discerning whether the bitstream includes location code or occupancy code, based on the above rule. 
     The bitstream may include encoding mode information indicating which of location encoding, occupancy encoding, and hybrid encoding is used.  FIG.  82    is a diagram showing an example of a bitstream in this case. As illustrated in  FIG.  82   , for example, 2-bit encoding mode information indicating the encoding mode is appended to the bitstream. 
     (1) “THREE-DIMENSIONAL POINT COUNT” in the location encoding expresses a total number of subsequent three-dimensional points. (2) “OCCUPANCY CODE AMOUNT” in the occupancy encoding expresses a code amount of subsequent occupancy code. (3) “IMPORTANT SUBTREE COUNT” in the hybrid encoding (important three-dimensional points) expresses a total number of subtrees including important three-dimensional points. (4) “OCCUPANCY SUBTREE COUNT” in the hybrid encoding (emphasis on efficiency) expresses a total number of occupancy encoded subtrees. 
     An example syntax used for switching between applying occupancy encoding or location encoding will be described next.  FIG.  83    is a diagram showing this example syntax. 
     isleaf shown in  FIG.  83    is a flag indicating whether the current node is a leaf. isleaf=1 indicates that the current node is a leaf, and isleaf=0 indicates that the current node is not a leaf. 
     When the current node is a leaf, point_flag is appended to the bitstream. point_flag is a flag indicating whether the current node (leaf) includes a three-dimensional point. point_flag=1 indicates that the current node includes a three-dimensional point, and point_flag=0 indicates that the current node does not include a three-dimensional point. 
     When the current node is not a leaf, coding_type is appended to the bitstream. coding_type is encoding type information indicating which encoding type has been applied. coding_type=00 indicates that location encoding has been applied, coding_type=01 indicates that occupancy encoding has been applied, and coding_type=10 or 11 indicates that another encoding method has been applied. 
     When the encoding type is location encoding, numPoint, num_idx[i], and idx[i][j] are appended to the bitstream. 
     numPoint indicates a total number of three-dimensional points on which to perform location encoding. num_idx[i] indicates a total number (depth) of indexes from the current node up to three-dimensional point i. When the three-dimensional points on which location encoding is to be performed are all at the same depth, each num_idx[i] has the same value. As such, num_idx may be defined as a common value before the for statement (for (i=0;i&lt;numPoint;i++){) shown in  FIG.  83   . 
     idx[i][j] indicates a value of a j-th index among indexes from the current node up to three-dimensional point i. In the case of an octree, a bit count of idx[i][j] is 3 bits. 
     Note that, as stated above, the index is an identifier for the identifying child nodes of the current node. In the case of an octree, idx[i][j] indicates a value between 0 and 7. In the case of an octree, there are eight child nodes which respectively correspond to eight subblocks obtained by spatially dividing a current block corresponding to the current node into eight. As such, idx[i][j] may be information indicating a three-dimensional position of the subblock corresponding to a child node. For example, idx[i][j] may be 3-bit information in total includes three pieces of 1-bit information each indicating a position of each of x, y, and z of the subblock. 
     When the encoding type is occupancy encoding, occupancy_code is appended to the bitstream. occupancy_code is the occupancy code of the current node. In the case of an octree, occupancy_code is an 8-bit bit sequence such as bit sequence “00101000”. 
     When a value of an (i+1)-th bit of occupancy_code is 1, processing of the child node begins. In other words, the child node is set as the next current node, and a bit sequence is recursively generated. 
     In the present embodiment, an example is shown in which ends of the octree are expressed by appending leaf information (isleaf, point_flag) to the bitstream, but the present embodiment is not necessarily limited thereto. For example, the three-dimensional data encoding device may append, to a header portion of a start-node (root), a maximum depth from the start-node of the occupancy code up to ends (leaves) including three-dimensional points. The three-dimensional data encoding device may recursively convert information on the child nodes while increasing the depth from the start-node, and may determine as to having arrived at the leaves when the depth becomes the maximum depth. The three-dimensional data encoding device may also append information indicating the maximum depth to the first node where the coding type has become occupancy encoding, and may also append this information to the start-node (root) of the octree. 
     As stated above, the three-dimensional data encoding device may append, to the bitstream, information for switching between occupancy encoding and location encoding as header information of each node. 
     The three-dimensional data encoding device may entropy encode coding_type, numPoint, num_idx, idx, and occupancy_code of each node generated using the above method. For example, the three-dimensional data encoding device arithmetically encodes each value after binarizing each value. 
     In the above syntax, an example is shown of when a depth-first bit sequence of the octree structure is used as the occupancy code, but the present embodiment is not necessarily limited thereto. The three-dimensional data encoding device may use a breadth-first bit sequence of the octree structure as the occupancy code. The three-dimensional data encoding device may append, to the bitstream, information for switching between occupancy encoding and location encoding as header information of each node, also when using a breadth-first bit sequence. 
     In the present embodiment, an example has been shown of an octree structure, but the present embodiment is not necessarily limited thereto, and the above method may be applied to an N-ary (N is an integer of 2 or higher) structure such as a quadtree or a hextree, or another tree structure. 
     Hereinafter, a flow example of an encoding process for switching between applying occupancy encoding or location encoding will be described.  FIG.  84    is a flowchart of the encoding process according to the present embodiment. 
     The three-dimensional data encoding device first represents a plurality of three-dimensional points included in three-dimensional data using an octree structure (S 1601 ). The three-dimensional data encoding device next sets a root in the octree structure as a current node (S 1602 ). The three-dimensional data encoding device next generates a bit sequence of the octree structure by performing a node encoding process on the current node (S 1603 ). The three-dimensional data encoding device next generates a bit sequence by entropy encoding the generated bit sequence (S 1604 ); 
       FIG.  85    is a flowchart of the node encoding process (S 1603 ). The three-dimensional data encoding device first determines whether the current node is a leaf (S 1611 ). When the current node is not a leaf (NO in S 1611 ), the three-dimensional data encoding device sets a leaf flag (isleaf) to 0, and appends the leaf flag to the bit sequence (S 1612 ). 
     The three-dimensional data encoding device next determines whether a total number of child nodes including three-dimensional points is higher than a predetermined threshold value (S 1613 ). Note that three-dimensional data encoding device may append this threshold value to the bit sequence. 
     When the total number of child nodes including three-dimensional points is higher than the predetermined threshold value (YES in S 1613 ), the three-dimensional data encoding device sets the encoding type (coding_type) to occupancy encoding, and appends the encoding type to the bit sequence (S 1614 ). 
     The three-dimensional data encoding device next configures occupancy encoding information, and appends the occupancy encoding information to the bit sequence. To be specific, the three-dimensional data encoding device generates an occupancy code for the current node, and appends the occupancy code to the bit sequence (S 1615 ). 
     The three-dimensional data encoding device next sets the next current node based on the occupancy code (S 1616 ). To be specific, the three-dimensional data encoding device sets the next current node from an unprocessed child node whose occupancy code is “1”. 
     The three-dimensional data encoding device performs the node encoding process on the newly-set current node (S 1617 ). In other words, the process shown in  FIG.  85    is performed on the newly-set current node. 
     When all child nodes have not been processed yet (NO in S 1618 ), the processes from step S 1616  are performed again. On the other hand, when all of the child nodes have been processed (YES in S 1618 ), the three-dimensional data encoding device ends the node encoding process. 
     In step S 1613 , when the total number of child nodes including three-dimensional points is lower than or equal to the predetermined threshold value (NO in S 1613 ), the three-dimensional data encoding device sets the encoding type to location encoding, and appends the encoding type to the bit sequence (S 1619 ). 
     The three-dimensional data encoding device next configures location encoding information, and appends the location encoding information to the bit sequence. To be specific, the three-dimensional data encoding device next generates a location code, and appends the location code to the bit sequence (S 1620 ). The location code includes numPoint, num_idx, and idx. 
     In step S 1611 , when the current node is a leaf (YES in S 1611 ), the three-dimensional data encoding device sets the leaf flag to 1, and appends the leaf flag to the bit sequence (S 1621 ). The three-dimensional data encoding device configures a point flag (point_flag) that is information indicating whether the leaf includes a three-dimensional point, and appends the point flag to the bit sequence (S 1622 ). 
     A flow example of a decoding process for switching between applying occupancy encoding or location encoding will be described next.  FIG.  85    is a flowchart of the decoding process according to the present embodiment. 
     The three-dimensional data encoding device generates a bit sequence by entropy decoding the bitstream (S 1631 ). The three-dimensional data decoding device next restores the octree structure by performing a node decoding process on the obtained bit sequence (S 1632 ). The three-dimensional data decoding device next generates the three-dimensional points from the restores octree structure (S 1633 ); 
       FIG.  87    is a flowchart of the node decoding process (S 1632 ). The three-dimensional data decoding device first obtains (decodes) the leaf flag (isleaf) from the bit sequence (S 1641 ). The three-dimensional data decoding device next determines whether the current node is a leaf based on the leaf flag (S 1642 ). 
     When the current node is not a leaf (NO in S 1642 ), the three-dimensional data decoding device obtains the encoding type (coding_type) from the bit sequence (S 1643 ). The three-dimensional data decoding device determines whether the encoding type is occupancy encoding (S 1644 ). 
     When the encoding type is occupancy encoding (YES in S 1644 ), the three-dimensional data decoding device obtains the occupancy encoding information from the bit sequence. To be specific, the three-dimensional data decoding device obtains the occupancy code from the bit sequence (S 1645 ). 
     The three-dimensional data decoding device next sets the next current node based on the occupancy code (S 1646 ). To be specific, the three-dimensional data decoding device sets the next current node from an unprocessed child node whose occupancy code is “1”. 
     The three-dimensional data decoding device next performs the node decoding process on the newly-set current node (S 1647 ). In other words, the process shown in  FIG.  87    is performed on the newly-set current node. 
     When all child nodes have not been processed yet (NO in S 1648 ), the processes from step S 1646  are performed again. On the other hand, when all of the child nodes have been processed (YES in S 1648 ), the three-dimensional data decoding device ends the node decoding process. 
     In step  1644 , when the encoding type is location encoding (NO in S 1644 ), the three-dimensional data decoding device obtains the location encoding information from the bit sequence. To be specific, the three-dimensional data decoding device obtains the location code from the bit sequence (S 1649 ). The location code includes numPoint, num_idx, and idx. 
     In step S 1642 , when the current node is a leaf (YES in S 1642 ), the three-dimensional data decoding device obtains, from the bit sequence, the point flag (point_flag) that is the information indicating whether the leaf includes a three-dimensional point (S 1650 ). 
     Note that in the present embodiment, an example has been shown in which the encoding type is switched per node, but the present embodiment is not necessarily limited thereto. The encoding type may be fixed per volume, space, or world unit. In this case, the three-dimensional data encoding device may append encoding type information to header information of the volume, space, or world. 
     As stated above, the three-dimensional data encoding device according to the present embodiment: generates first information in which an N-ary (N is an integer of 2 or higher) tree structure of a plurality of three-dimensional points included in three-dimensional data is expressed using a first formula (location encoding); and generates a bitstream including the first information. The first information includes pieces of three-dimensional point information (location code) each associated with a corresponding one of the plurality of three-dimensional points. The pieces of three-dimensional point information each include indexes (idx) each associated with a corresponding one of a plurality of levels in the N-ary tree structure. The indexes each indicate a subblock, among N subblocks belonging to a corresponding one of the plurality of levels, to which a corresponding one of the plurality of three-dimensional points belongs. In other words, the pieces of three-dimensional point information each indicate a path until the corresponding one of the plurality of three-dimensional points in the N-ary tree structure. The indexes each indicate a child node, among N child nodes belonging to a corresponding layer (node), included on the path. 
     This enables the three-dimensional data encoding method to generate a bitstream from which the three-dimensional points can be selectively decoded. 
     For example, the pieces of three-dimensional point information (location code) each include information (num_idx) indicating a total number of the indexes included in the piece of three-dimensional point information. In other words, the information indicates a depth (layer count) until a corresponding three-dimensional point in the N-ary tree structure. 
     For example, the first information includes information (numPoint) indicating a total number of the pieces of three-dimensional point information included in the first information. In other words, the information indicates a total number of three-dimensional points included in the N-ary tree structure. 
     For example, N is 8, and the indexes are each a 3-bit value. 
     For example, in the three-dimensional data encoding device, a first encoding mode is used for generating the first information, and a second encoding mode is used for (i) generating second information (occupancy code) in which the N-ary tree structure is expressed using a second formula (occupancy encoding) and (ii) generating a bitstream including the second information. The second information includes pieces of 1-bit information each of which (i) is associated with a corresponding one of a plurality of subblocks belonging to the plurality of levels in the N-ary tree structure and (ii) indicates whether a three-dimensional point is present in the corresponding one of the plurality of subblocks. 
     For example, the three-dimensional data encoding device uses the first encoding mode when a total number of the plurality of three-dimensional points is lower than or equal to a predetermined threshold value, and the second encoding mode may be used when the total number of the plurality of three-dimensional points is higher than the predetermined threshold value. This enables the three-dimensional data encoding method to reduce a code amount of the bitstream. 
     For example, the first information and the second information each include information (encoding mode information) indicating whether the N-ary tree structure is expressed using the first formula or the second formula. 
     For example, as illustrated in  FIG.  75    and the like, the three-dimensional data encoding device uses the first encoding mode for one portion of the N-ary tree structure and the second encoding mode for another portion of the N-ary tree structure. 
     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 obtains, from a bitstream, first information (location code) in which an N-ary (N is an integer of 2 or higher) tree structure of a plurality of three-dimensional points included in three-dimensional data is expressed using a first formula (location encoding). The first information includes pieces of three-dimensional point information (location code) each associated with a corresponding one of the plurality of three-dimensional points. The pieces of three-dimensional point information each include indexes (idx) each associated with a corresponding one of a plurality of levels in the N-ary tree structure. The indexes each indicate a subblock, among N subblocks belonging to a corresponding one of the plurality of levels, to which a corresponding one of the plurality of three-dimensional points belongs. 
     In other words, the pieces of three-dimensional point information each indicate a path until the corresponding one of the plurality of three-dimensional points in the N-ary tree structure. The indexes each indicate a child node, among N child nodes belonging to a corresponding layer (node), included on the path. 
     The three-dimensional data decoding method further restores, using a corresponding one of the pieces of three-dimensional point information, a three-dimensional point associated with the corresponding one of the pieces of three-dimensional point information. 
     This enables the three-dimensional data decoding device to selectively generate the three-dimensional points from the bitstream. 
     For example, the pieces of three-dimensional point information (location code) each include information (num_idx) indicating a total number of the indexes included in the piece of three-dimensional point information. In other words, the information indicates a depth (layer count) until a corresponding three-dimensional point in the N-ary tree structure. 
     For example, the first information includes information (numPoint) indicating a total number of the pieces of three-dimensional point information included in the first information. In other words, the information indicates a total number of three-dimensional points included in the N-ary tree structure. 
     For example, N is 8, and the indexes are each a 3-bit value. 
     For example, the three-dimensional data decoding device further obtains, from a bitstream, second information (occupancy code) in which an N-ary tree structure is expressed using a second formula (occupancy encoding). The three-dimensional data decoding device restores the plurality of three-dimensional points using the second information. The second information includes pieces of 1-bit information each of which (i) is associated with a corresponding one of a plurality of subblocks belonging to the plurality of levels in the N-ary tree structure and (ii) indicates whether a three-dimensional point is present in the corresponding one of the plurality of subblocks. 
     For example, the first information and the second information each include information (encoding mode information) indicating whether the N-ary tree structure is expressed using the first formula or the second formula. 
     For example, as illustrated in  FIG.  75    and the like, one portion of the N-ary tree structure is expressed using the first formula and another portion of the N-ary tree structure is expressed using the second formula. 
     For example, the three-dimensional data decoding device includes a processor and memory, the processor using the memory to perform the above processes. 
     Embodiment 10 
     In the present embodiment, another example of the method of encoding a tree structure such as an octree structure will be described.  FIG.  88    is a diagram illustrating an example of a tree structure according to the present embodiment. Specifically,  FIG.  88    shows an example of a quadtree structure. 
     A leaf including a three-dimensional point is referred to as a valid leaf, and a leaf including no three-dimensional point is referred to as an invalid leaf. A branch having the number of valid leaves greater than or equal to a threshold value is referred to as a dense branch. A branch having the number of valid leaves less than the threshold value is referred to as a sparse branch. 
     A three-dimensional data encoding device calculates the number of three-dimensional points (i.e., the number of valid leaves) included in each branch in a layer of a tree structure.  FIG.  88    shows an example in which a threshold value is 5. In this example, two branches are present in layer  1 . Since the left branch includes seven three-dimensional points, the left branch is determined as a dense branch. Since the right branch includes two three-dimensional points, the right branch is determined as a sparse branch; 
       FIG.  89    is a graph showing an example of the number of valid leaves (3D points) of each branch in layer  5 . The horizontal axis of  FIG.  89    indicates an index that is an identification number of the branch in layer  5 . As clearly shown in  FIG.  89   , specific branches include many three-dimensional points, compared to other branches. Occupancy encoding is more effective for such dense branches than for sparse branches. 
     The following describes how occupancy encoding and location encoding are applied.  FIG.  90    is a diagram illustrating a relationship between encoding schemes to be applied and the number of three-dimensional points (the number of valid leaves) included in each branch in layer  5 . As illustrated in  FIG.  90   , the three-dimensional data encoding device applies the occupancy encoding to dense branches, and applies the location encoding to sparse branches. As a result, it is possible to improve the coding efficiency; 
       FIG.  91    is a diagram illustrating an example of a dense branch area in LiDAR data. As illustrated in  FIG.  91   , a three-dimensional point density calculated from the number of three-dimensional points included in each branch varies from area to area. 
     Separating dense three-dimensional points (branch) and sparse three-dimensional points (branch) brings the following advantage. A three-dimensional point density is higher with a decreasing distance to a LiDAR sensor. Consequently, separating branches in accordance with sparseness and denseness enables division in a distance direction. Such division is effective for specific applications. Using a method other than the occupancy encoding is effective for sparse branches. 
     In the present embodiment, the three-dimensional data encoding device separates an inputted three-dimensional point cloud into two or more three-dimensional point sub-clouds, and applies a different encoding method to each of the two or more three-dimensional point sub-clouds. 
     For example, the three-dimensional data encoding device separates an inputted three-dimensional point cloud into three-dimensional point sub-cloud A (dense three-dimensional point cloud: dense cloud) including a dense branch, and three-dimensional point sub-cloud B (sparse three-dimensional point cloud: sparse cloud).  FIG.  92    is a diagram illustrating an example of three-dimensional point sub-cloud A (dense three-dimensional point cloud) including a dense branch which is separated from the tree structure illustrated in  FIG.  88   .  FIG.  93    is a diagram illustrating an example of three-dimensional point sub-cloud B (sparse three-dimensional point cloud) including a sparse branch which is separated from the tree structure illustrated in  FIG.  88   . 
     Next, the three-dimensional data encoding device encodes three-dimensional point sub-cloud A using the occupancy encoding, and encodes three-dimensional point sub-cloud B using the location encoding. 
     It should be noted that although the example has been described above in which different encoding schemes (the occupancy encoding and the location encoding) are applied as different encoding methods, for example, the three-dimensional data encoding device may apply the same encoding scheme to three-dimensional point sub-cloud A and three-dimensional point sub-cloud B, and may use different parameters in encoding three-dimensional point sub-cloud A and three-dimensional point sub-cloud B. 
     The following describes a procedure for a three-dimensional data encoding process performed by the three-dimensional data encoding device.  FIG.  94    is a flowchart of a three-dimensional data encoding process performed by the three-dimensional data encoding device according to the present embodiment. 
     First, the three-dimensional data encoding device separates an inputted three-dimensional point cloud into three-dimensional point sub-clouds (S 1701 ). The three-dimensional data encoding device may perform this separation automatically or based on information inputted by a user. For example, the user may specify a range of three-dimensional point sub-clouds. As for an example of automatic separation, for example, when input data is LiDAR data, the three-dimensional data encoding device performs the separation using distance information indicating a distance to each point cloud. Specifically, the three-dimensional data encoding device separates point clouds within a certain range from a measurement point, and point clouds outside the certain range. In addition, the three-dimensional data encoding device may perform the separation using information indicating, for example, important areas and unimportant areas. 
     Next, the three-dimensional data encoding device generates encoded data (encoded bitstream) by encoding three-dimensional point sub-cloud A using method A (S 1702 ). Besides, the three-dimensional data encoding device generates encoded data by encoding three-dimensional point sub-cloud B using method B (S 1703 ). It should be noted that the three-dimensional data encoding device may encode three-dimensional point sub-cloud B using method A. In this case, the three-dimensional data encoding device encodes three-dimensional point sub-cloud B using a parameter different from an encoding parameter used in encoding three-dimensional point sub-cloud A. For example, this parameter may be a quantization parameter. For example, the three-dimensional data encoding device encodes three-dimensional point sub-cloud B using a quantization parameter greater than a quantization parameter used in encoding three-dimensional point sub-cloud A. In this case, the three-dimensional data encoding device may append information indicating a quantization parameter used in encoding each of three-dimensional point sub-clouds, to a header of encoded data of the three-dimensional point sub-cloud. 
     Then, the three-dimensional data encoding device generates a bitstream by combining the encoded data obtained in step S 1702  and the encoded data obtained in step S 1703  (S 1704 ). 
     Moreover, the three-dimensional data encoding device may encode, as header information of the bitstream, information for decoding each three-dimensional point sub-cloud. For example, the three-dimensional data encoding device may encode information as described below. 
     The header information may include information indicating the number of encoded three-dimensional sub-points. In this example, this information indicates 2. 
     The header information may include information indicating the number of three-dimensional points included in each three-dimensional point sub-cloud, and encoding methods. In this example, this information indicates the number of three-dimensional points included in three-dimensional point sub-cloud A, the encoding method (method A) applied to three-dimensional point sub-cloud A, the number of three-dimensional points included in three-dimensional point sub-cloud B, and the encoding method (method B) applied to three-dimensional point sub-cloud B. 
     The header information may include information for identifying the start position or end position of encoded data of each three-dimensional point sub-cloud. 
     Moreover, the three-dimensional data encoding device may encode three-dimensional point sub-cloud A and three-dimensional point sub-cloud B in parallel. Alternatively, the three-dimensional data encoding device may encode three-dimensional point sub-cloud A and three-dimensional point sub-cloud B in sequence. 
     A method of separation into three-dimensional point sub-clouds is not limited to the above method. For example, the three-dimensional data encoding device changes a separation method, performs encoding using each of separation methods, and calculates the coding efficiency of encoded data obtained using each separation method. Subsequently, the three-dimensional data encoding device selects a separation method having the highest coding efficiency from the separation methods. For example, the three-dimensional data encoding device may (i) separate three-dimensional point clouds in each of layers, (ii) calculate coding efficiency in each of the cases, (iii) select a separation method (i.e., a layer in which separation is performed) having the highest coding efficiency from separation methods, (iv) generate three-dimensional point sub-clouds using the selected separation method, and (v) perform encoding. 
     Moreover, when combining encoded data, the three-dimensional data encoding device may place encoding information of a more important three-dimensional point sub-cloud in a position closer to the head of a bitstream. Since this enables a three-dimensional data decoding device to obtain important information by only decoding the head of the bitstream, the three-dimensional data decoding device can obtain the important information quickly. 
     The following describes a procedure for a three-dimensional data decoding process performed by the three-dimensional data decoding device.  FIG.  95    is a flowchart of a three-dimensional data decoding process performed by the three-dimensional data decoding device according to the present embodiment. 
     First, for example, the three-dimensional data decoding device obtains a bitstream generated by the above three-dimensional data encoding device. Next, the three-dimensional data decoding device separates, from the obtained bitstream, encoded data of three-dimensional point sub-cloud A and encoded data of three-dimensional point sub-cloud B (S 1711 ). Specifically, the three-dimensional data decoding device decodes, from header information of the bitstream, information for decoding each three-dimensional point sub-cloud, and separates encoded data of each three-dimensional point sub-cloud using the information. 
     Then, the three-dimensional data decoding device obtains three-dimensional point sub-cloud A by decoding the encoded data of three-dimensional point sub-cloud A using method A (S 1712 ). In addition, the three-dimensional data decoding device obtains three-dimensional point sub-cloud B by decoding the encoded data of three-dimensional point sub-cloud B using method B (S 1713 ). After that, the three-dimensional data decoding device combines three-dimensional point sub-cloud A and three-dimensional point sub-cloud B (S 1714 ). 
     It should be noted that the three-dimensional data decoding device may decode three-dimensional point sub-cloud A and three-dimensional point sub-cloud B in parallel. Alternatively, the three-dimensional data decoding device may decode three-dimensional point sub-cloud A and three-dimensional point sub-cloud B in sequence. 
     Moreover, the three-dimensional data decoding device may decode a necessary three-dimensional point sub-cloud. For example, the three-dimensional data decoding device may decode three-dimensional point sub-cloud A and need not decode three-dimensional point sub-cloud B. For example, when three-dimensional point sub-cloud A is a three-dimensional point cloud included in an important area of LiDAR data, the three-dimensional data decoding device decodes the three-dimensional point cloud included in the important area. Self-location estimation etc. in a vehicle or the like is performed using the three-dimensional point cloud included in the important area. 
     The following describes a specific example of an encoding process according to the present embodiment.  FIG.  96    is a flowchart of a three-dimensional data encoding process performed by the three-dimensional data encoding device according to the present embodiment. 
     First, the three-dimensional data encoding device separates inputted three-dimensional points into a sparse three-dimensional point cloud and a dense three-dimensional point cloud (S 1721 ). Specifically, the three-dimensional data encoding device counts the number of valid leaves of a branch in a layer of an octree structure. The three-dimensional data encoding device sets each branch as a dense branch or a sparse branch in accordance with the number of valid leaves of the branch. Subsequently, the three-dimensional data encoding device generates a three-dimensional point sub-cloud (a dense three-dimensional point cloud) obtained by gathering dense branches, and a three-dimensional point sub-cloud (a sparse three-dimensional point cloud) obtained by gathering sparse branches. 
     Next, the three-dimensional data encoding device generates encoded data by encoding the sparse three-dimensional point cloud (S 1722 ). For example, the three-dimensional data encoding device encodes a sparse three-dimensional point cloud using the location encoding. 
     Furthermore, the three-dimensional data encoding device generates encoded data by encoding the dense three-dimensional point cloud (S 1723 ). For example, the three-dimensional data encoding device encodes a dense three-dimensional point cloud using the occupancy encoding. 
     Then, the three-dimensional data encoding device generates a bitstream by combining the encoded data of the sparse three-dimensional point cloud obtained in step S 1722  and the encoded data of the dense three-dimensional point cloud obtained in step S 1723  (S 1724 ). 
     Moreover, the three-dimensional data encoding device may encode, as header information of the bitstream, information for decoding the sparse three-dimensional point cloud and the dense three-dimensional point cloud. For example, the three-dimensional data encoding device may encode information as described below. 
     The header information may include information indicating the number of encoded three-dimensional point sub-clouds. In this example, this information indicates 2. 
     The header information may include information indicating the number of three-dimensional points included in each three-dimensional point sub-cloud, and encoding methods. In this example, this information indicates the number of three-dimensional points included in the sparse three-dimensional point cloud, the encoding method (location encoding) applied to the sparse three-dimensional point cloud, the number of three-dimensional points included in the dense three-dimensional point cloud, and the encoding method (occupancy encoding) applied to the dense three-dimensional point cloud. 
     The header information may include information for identifying the start position or end position of encoded data of each three-dimensional point sub-cloud. In this example, this information indicates at least one of the start position and end position of the encoded data of the sparse three-dimensional point cloud or the start position and end position of the encoded data of the dense three-dimensional point cloud. 
     Moreover, the three-dimensional data encoding device may encode the sparse three-dimensional point cloud and the dense three-dimensional point cloud in parallel. Alternatively, the three-dimensional data encoding device may encode the sparse three-dimensional point cloud and the dense three-dimensional point cloud in sequence. 
     The following describes a specific example of a three-dimensional data decoding process.  FIG.  97    is a flowchart of a three-dimensional data decoding process performed by the three-dimensional data decoding device according to the present embodiment. 
     First, for example, the three-dimensional data decoding device obtains a bitstream generated by the above three-dimensional data encoding device. Next, the three-dimensional data decoding device separates, from the obtained bitstream, encoded data of a sparse three-dimensional point cloud and encoded data of a dense three-dimensional point cloud (S 1731 ). Specifically, the three-dimensional data decoding device decodes, from header information of the bitstream, information for decoding each three-dimensional point sub-cloud, and separates encoded data of each three-dimensional point sub-cloud using the information. In this example, the three-dimensional data decoding device separates, from the bitstream, the encoded data of the sparse three-dimensional point cloud and the encoded data of the dense three-dimensional point cloud using the header information. 
     Then, the three-dimensional data decoding device obtains the sparse three-dimensional point cloud by decoding the encoded data of the sparse three-dimensional point cloud (S 1732 ). For example, the three-dimensional data decoding device decodes the sparse three-dimensional point cloud using location decoding for decoding encoded data obtained as a result of the location encoding. 
     In addition, the three-dimensional data decoding device obtains the dense three-dimensional point cloud by decoding the encoded data of the dense three-dimensional point cloud (S 1733 ). For example, the three-dimensional data decoding device decodes the dense three-dimensional point cloud using occupancy decoding for decoding encoded data obtained as a result of the occupancy encoding. 
     After that, the three-dimensional data decoding device combines the sparse three-dimensional point cloud obtained in step S 1732  and the dense three-dimensional point cloud obtained in step S 1733  (S 1734 ). 
     It should be noted that the three-dimensional data decoding device may decode the sparse three-dimensional point cloud and the dense three-dimensional point cloud in parallel. Alternatively, the three-dimensional data decoding device may decode the sparse three-dimensional point cloud and the dense three-dimensional point cloud in sequence. 
     Moreover, the three-dimensional data decoding device may decode part of necessary three-dimensional point sub-clouds. For example, the three-dimensional data decoding device may decode a dense three-dimensional point cloud and need not decode a sparse three-dimensional point cloud. For example, when a dense three-dimensional point cloud is a three-dimensional point cloud included in an important area of LiDAR data, the three-dimensional data decoding device decodes the three-dimensional point cloud included in the important area. Self-location estimation etc. in a vehicle or the like is performed using the three-dimensional point cloud included in the important area; 
       FIG.  98    is a flowchart of an encoding process according to the present embodiment. First, the three-dimensional data encoding separates an inputted three-dimensional point cloud into a sparse three-dimensional point cloud and a dense three-dimensional point cloud (S 1741 ). 
     Next, the three-dimensional data encoding device generates encoded data by encoding the dense three-dimensional point cloud (S 1742 ). Then, the three-dimensional data encoding device generates encoded data by encoding the sparse three-dimensional point cloud (S 1743 ). Finally, the three-dimensional data encoding device generates a bitstream by combining the encoded data of the sparse three-dimensional point cloud obtained in step S 1742  and the encoded data of the dense three-dimensional point cloud obtained in step S 1743  (S 1744 ); 
       FIG.  99    is a flowchart of a decoding process according to the present embodiment. First, the three-dimensional data decoding device extracts, from a bitstream, encoded data of a sparse three-dimensional point cloud and encoded data of a dense three-dimensional (S 1751 ). Next, the three-dimensional data decoding device obtains decoded data of the dense three-dimensional point cloud by decoding the encoded data of the dense three-dimensional point cloud (S 1752 ). Then, the three-dimensional data decoding device obtains decoded data of the sparse three-dimensional point cloud by decoding the encoded data of the sparse three-dimensional point cloud (S 1753 ). Finally, the three-dimensional data decoding device generates a three-dimensional point cloud by combining the decoded data of the dense three-dimensional point cloud obtained in step S 1752  and the decoded data of the sparse three-dimensional point cloud obtained in step S 1753  (S 1754 ). 
     It should be noted that the three-dimensional data encoding device and the three-dimensional data decoding device may encode and decode any one of a dense three-dimensional point cloud and a sparse three-dimensional point cloud first. In addition, encoding processes or decoding processes may be performed in parallel using processors etc. 
     Moreover, the three-dimensional data encoding device may encode one of a dense three-dimensional point cloud and a sparse three-dimensional point cloud. For example, when a dense three-dimensional point cloud includes important information, the three-dimensional data encoding device extracts the dense three-dimensional point cloud and a sparse three-dimensional point cloud from an inputted three-dimensional point cloud, and encode the dense three-dimensional point cloud but does not encode the sparse three-dimensional point cloud. This enables the three-dimensional data encoding device to append the important information to a stream while reducing an amount of bit. For example, when, between a server and a client, the client sends to the server a transmission request for three-dimensional point cloud information about the surroundings of the client, the server encodes important information about the surroundings of the client as a dense three-dimensional point cloud and transmits the encoded important information to the client. This enables the server to transmit the information requested by the client while reducing a network bandwidth. 
     Moreover, the three-dimensional data decoding device may decode one of a dense three-dimensional point cloud and a sparse three-dimensional point cloud. For example, when a dense three-dimensional point cloud includes important information, the three-dimensional data decoding device decodes the dense three-dimensional point cloud but does not decode a sparse three-dimensional point cloud. This enables the three-dimensional data decoding device to obtain necessary information while reducing a processing load of the decoding process; 
       FIG.  100    is a flowchart of the process of separating three-dimensional points (S 1741 ) illustrated in  FIG.  98   . First, the three-dimensional data encoding device sets layer L and threshold value TH (S 1761 ). It should be noted that the three-dimensional data encoding device may append information indicating set layer L and threshold value TH, to a bitstream. In other words, the three-dimensional data encoding device may generate a bitstream including information indicating set layer L and threshold value TH. 
     Next, the three-dimensional data encoding device moves a target position from a root of an octree to a lead branch in layer L. In other words, the three-dimensional data encoding device selects the lead branch in layer L as a current branch (S 1762 ). 
     Then, the three-dimensional data encoding device counts the number of valid leaves of the current branch in layer L (S 1763 ). When the number of the valid leaves of the current branch is greater than threshold value TH (YES in S 1764 ), the three-dimensional data encoding device registers the current branch as a dense branch with a dense three-dimensional point cloud (S 1765 ). In contrast, when the number of the valid leaves of the current branch is less than threshold value TH (NO in S 1764 ), the three-dimensional data encoding device registers the current branch as a sparse branch with a sparse three-dimensional point cloud (S 1766 ). 
     When processing of all branches in layer L is not completed (NO in S 1767 ), the three-dimensional data encoding device moves the target position to the next branch in layer L. In other words, the three-dimensional data encoding device selects the next branch in layer L as a current branch (S 1768 ). And then, the three-dimensional data encoding device performs step S 1763  and the subsequent steps on the selected next current branch. 
     The above-described process is repeated until the processing of all the branches in layer L is completed (YES in S 1767 ). 
     It should be noted that although layer L and threshold value TH are preset in the above description, the present embodiment is not necessarily limited to this. For example, the three-dimensional data encoding device sets different combinations of layer L and threshold value TH, generates a dense three-dimensional point cloud and a sparse three-dimensional point cloud using each of the combinations, and encodes the dense three-dimensional point cloud and the sparse three-dimensional point cloud. The three-dimensional data encoding device finally encodes the dense three-dimensional point cloud and the sparse three-dimensional point cloud using, among the combinations, a combination of layer L and threshold value TH having the highest coding efficiency for encoded data generated. This makes it possible to improve the coding efficiency. Moreover, for example, the three-dimensional data encoding device may calculate layer L and threshold value TH. For example, the three-dimensional data encoding device may set, to layer L, a value half as much as the maximum value of layers included in a tree structure. Furthermore, the three-dimensional data encoding device may set, to threshold value TH, a value half as much as a total number of three-dimensional points included in the tree structure. 
     In the above description, the example has been shown in which the inputted three-dimensional point cloud is separated into two types of three-dimensional point cloud, that is, the dense three-dimensional point cloud and the sparse three-dimensional point cloud. The three-dimensional data encoding device, however, may separate the inputted three-dimensional point cloud into at least three types of three-dimensional point cloud. For example, when the number of valid leaves of a current branch is greater than or equal to first threshold value TH 1 , the three-dimensional data encoding device classifies the current branch into a first dense three-dimensional point cloud, and when the number of the valid leaves of the current branch is less than first threshold value TH 1  and greater than or equal to second threshold value TH 2 , the three-dimensional data encoding device classifies the current branch into a second dense three-dimensional point cloud. When the number of the valid leaves of the current branch is less than second threshold value TH 2  and greater than or equal to third threshold value TH 3 , the three-dimensional data encoding device classifies the current branch into a first sparse three-dimensional point cloud, and when the number of the valid leaves of the current branch is less than third threshold value TH 3 , the three-dimensional data encoding device classifies the current branch into a second sparse three-dimensional point cloud. 
     The following describes an example of a syntax of encoded data of a three-dimensional point cloud according to the present embodiment.  FIG.  101    is a diagram illustrating an example of this syntax. pc_header( ) is, for example, header information of inputted three-dimensional points. 
     num_sub_pc illustrated in  FIG.  101    indicates the number of three-dimensional point sub-clouds. numPoint[i] indicates the number of three-dimensional points included in the i-th three-dimensional point sub-cloud. coding_type[i] is coding type information indicating a coding type (an encoding scheme) applied to the i-th three-dimensional point sub-cloud. For example, coding_type=00 indicates that the location encoding has been applied. coding_type=01 indicates that the occupancy encoding has been applied. coding_type=10 or 11 indicates that another encoding scheme has been applied. 
     data_sub_cloud( ) is encoded data of the i-th three-dimensional point sub-cloud. coding_type_00_data is encoded data to which a coding type of 00 indicated by coding_type has been applied, and is encoded data to which the location encoding has been applied, for example. coding_type_01_data is encoded data to which a coding type of 01 indicated by coding_type has been applied, and is encoded data to which the occupancy encoding has been applied, for example. 
     end_of data is end information indicating the end of encoded data. For example, a constant bit sequence not used for encoded data is assigned to end_of data. This enables the three-dimensional data decoding device to, for example, skip decoding of encoded data that need not be decoded, by searching a bitstream for a bit sequence of end_of data. 
     It should be noted that the three-dimensional data encoding device may entropy encode the encoded data generated by the above-described method. For example, the three-dimensional data encoding device binarizes each value and performs arithmetic coding on the binarized value. 
     Although the example of the quadtree structure or the octree structure has been shown in the present embodiment, the present embodiment is not necessarily limited to this. The above-described method may be applied to an N-ary (N is an integer greater than or equal to 2) tree, such as a binary tree and a hexadecatree, or another tree structure. 
     Variation 
     In the above example, as illustrated in  FIG.  92    and  FIG.  93   , the tree structure is encoded that includes the dense branch and the upper layer (the tree structure from the root of the whole tree structure to the root of the dense branch), and the tree structure is encoded that includes the sparse branch and the upper layer (the tree structure from the root of the whole tree structure to the root of the sparse branch). In the present variation, the three-dimensional data encoding device separates a dense branch and a sparse branch, and encodes the dense branch and the sparse branch. In other words, a tree structure to be encoded does not include a tree structure of an upper layer. For example, the three-dimensional data encoding device applies the occupancy encoding to a dense branch, and applies the location encoding to a sparse branch; 
       FIG.  102    is a diagram illustrating an example of a dense branch separated from the tree structure illustrated in  FIG.  88   .  FIG.  103    is a diagram illustrating an example of a sparse branch separated from the tree structure illustrated in  FIG.  88   . In the present variation, the tree structures illustrated in FIG. 102  and  FIG.  103    are encoded. 
     The three-dimensional data encoding device encodes information indicating a position of a branch instead of encoding a tree structure of an upper layer. For example, this information indicates a position of a root of a branch. 
     For example, the three-dimensional data encoding device encodes, as encoded data of a dense branch, layer information indicating a layer in which the dense branch is generated, and branch information indicating what number branch in the layer the dense branch is. This enables the three-dimensional data decoding device to decode the layer information and the branch information from a bitstream, and grasp which three-dimensional point cloud of what number branch in which layer the decoded dense branch is. Likewise, the three-dimensional data encoding device encodes, as encoded data of a sparse branch, layer information indicating a layer in which the sparse branch is generated, and branch information indicating what number branch in the layer the sparse branch is present, using these layer information and branch information. 
     This enables the three-dimensional data decoding device to decode the layer information and the branch information from a bitstream, and grasp which three-dimensional point cloud of what number branch in which layer the decoded sparse branch is, using these layer information and branch information. Accordingly, since it is possible to reduce overhead resulting from encoding information of a layer higher than the dense branch or the sparse branch, it is possible to improve the coding efficiency. 
     It should be noted that branch information may indicate a value assigned to each branch in a layer indicated by layer information. Moreover, branch information may indicate a value assigned to each node from a root of an octree as a starting point. In this case, layer information need not be encoded. Furthermore, the three-dimensional data encoding device may generate dense branches and sparse branches; 
       FIG.  104    is a flowchart of an encoding process according to the present variation. First, the three-dimensional data encoding device generates one or more sparse branches and one or more dense branches from an inputted three-dimensional point cloud (S 1771 ). 
     Next, the three-dimensional data encoding device generates encoded data by encoding each of the one or more dense branches (S 1772 ). Then, the three-dimensional data encoding device determines whether encoding of all the dense branches generated in step S 1771  is completed (S 1774 ). 
     When the encoding of all the dense branches is not completed (NO in S 1773 ), the three-dimensional data encoding device selects the next dense branch (S 1774 ) and generates encoded data by encoding the selected dense branch (S 1772 ). 
     On the other hand, when the encoding of all the dense branches is completed (YES in S 1773 ), the three-dimensional data encoding device generates encoded data by encoding each of the one or more sparse branches (S 1775 ). Next, the three-dimensional data encoding device determines whether encoding of all the sparse branches generated in step S 1771  is completed (S 1776 ). 
     When the encoding of all the sparse branches is not completed (NO in S 1776 ), the three-dimensional data encoding device selects the next sparse branch (S 1777 ) and generates encoded data by encoding the selected sparse branch (S 1775 ). 
     On the other hand, when the encoding of all the sparse branches is completed (YES in S 1776 ), the three-dimensional data encoding device combines the encoded data generated in steps  51772  and  51775  to generate a bitstream (S 1778 ); 
       FIG.  105    is a flowchart of a decoding process according to the present variation. First, the three-dimensional data decoding device extracts one or more encoded data items of respective dense branches, and one or more encoded data items of respective sparse branches, from a bitstream (S 1781 ). Next, the three-dimensional data decoding device obtains decoded data of each of the dense branches by decoding the encoded data of the dense branch (S 1782 ). 
     Then, the three-dimensional data decoding device determines whether decoding of the encoded data items of all the dense branches extracted in step S 1781  is completed (S 1783 ). When the decoding of the encoded data items of all the dense branches is not completed (NO in S 1783 ), the three-dimensional data decoding device selects the encoded data of the next dense branch (S 1784 ) and obtains decoded data of the dense branch by decoding the selected encoded data of the dense branch (S 1782 ). 
     On the other hand, when the decoding of the encoded data items of all the dense branches is completed (YES in S 1783 ), the three-dimensional data decoding device obtains decoded data of each of the sparse branches by decoding the encoded data of the sparse branch (S 1785 ). 
     After that, the three-dimensional data decoding device determines whether decoding of the encoded data items of all the sparse branches extracted in step S 1781  is completed (S 1786 ). When the decoding of the encoded data items of all the sparse branches is not completed (NO in S 1786 ), the three-dimensional data decoding device selects the encoded data of the next sparse branch (S 1787 ) and obtains decoded data of the sparse branch by decoding the selected encoded data of the sparse branch (S 1785 ). 
     On the other hand, when the decoding of the encoded data items of all the sparse branches is completed (YES in S 1786 ), the three-dimensional data decoding device combines the decoded data obtained in steps S 1782  and S 1785  to generate a three-dimensional point cloud (S 1788 ). 
     It should be noted that the three-dimensional data encoding device and the three-dimensional data decoding device may encode and decode any one of a dense branch and a sparse branch first. In addition, encoding processes or decoding processes may be performed in parallel using processors etc. 
     Moreover, the three-dimensional data encoding device may encode one of a dense branch and a sparse branch. In addition, the three-dimensional data encoding device may encode part of dense branches. For example, when a specific dense branch includes important information, the three-dimensional data encoding device extracts dense branches and sparse branches from an inputted three-dimensional point cloud, and encodes the dense branch including the important information but does not encode the other dense branches and sparse branches. This enables the three-dimensional data encoding device to append the important information to a stream while reducing an amount of bit. For example, when, between a server and a client, the client sends to the server a transmission request for three-dimensional point cloud information about the surroundings of the client, the server encodes important information about the surroundings of the client as a dense branch and transmits the important information to the client. This enables the server to transmit the information requested by the client while reducing a network bandwidth. 
     Moreover, the three-dimensional data decoding device may decode one of a dense branch and a sparse branch. In addition, the three-dimensional data decoding device may decode part of dense branches. For example, when a specific dense branch includes important information, the three-dimensional data decoding device decodes the specific dense branch but does not decode other dense branches and sparse branches. This enables the three-dimensional data decoding device to obtain necessary information while reducing a processing load of the decoding process; 
       FIG.  106    is a flowchart of the process of separating three-dimensional points (S 1771 ) illustrated in  FIG.  104   . First, the three-dimensional data encoding device sets layer L and threshold value TH (S 1761 ). It should be noted that the three-dimensional data encoding device may append information indicating set layer L and threshold value TH, to a bitstream. 
     Next, the three-dimensional data encoding device selects a lead branch in layer L as a current branch (S 1762 ). Then, the three-dimensional data encoding device counts the number of valid leaves of the current branch in layer L (S 1763 ). When the number of the valid leaves of the current branch is greater than threshold value TH (YES in S 1764 ), the three-dimensional data encoding device sets the current branch as a dense branch, and appends layer information and branch information to a bitstream (S 1765 A). On the other hand, when the number of the valid leaves of the current branch is less than threshold value TH (NO in S 1764 ), the three-dimensional data encoding device sets the current branch as a sparse branch, and appends layer information and branch information to a bitstream (S 1766 A). 
     When processing of all branches in layer L is not completed (NO in S 1767 ), the three-dimensional data encoding device selects the next branch in layer L as a current branch (S 1768 ). And then, the three-dimensional data encoding device performs step S 1763  and the subsequent steps on the selected next current branch. The above-described process is repeated until the processing of all the branches in layer L is completed (YES in S 1767 ). 
     It should be noted that although layer L and threshold value TH are preset in the above description, the present disclosure is not necessarily limited to this. For example, the three-dimensional data encoding device sets different combinations of layer L and threshold value TH, generates a dense branch and a sparse branch using each of the combinations, and encodes the dense branch and the sparse branch. The three-dimensional data encoding device finally encodes the dense branch and the sparse branch using, among the combinations, a combination of layer L and threshold value TH having the highest coding efficiency for encoded data generated. This makes it possible to improve the coding efficiency. Moreover, for example, the three-dimensional data encoding device may calculate layer L and threshold value TH. For example, the three-dimensional data encoding device may set, to layer L, a value half as much as the maximum value of layers included in a tree structure. Furthermore, the three-dimensional data encoding device may set, to threshold value TH, a value half as much as a total number of three-dimensional points included in the tree structure. 
     The following describes an example of a syntax of encoded data of a three-dimensional point cloud according to the present variation.  FIG.  107    is a diagram illustrating an example of this syntax. The example of the syntax illustrated in  FIG.  107    is obtained by appending layer_id[i] that is layer information and branch_id[i] that is branch information, to the example of the syntax illustrated in  FIG.  101   . 
     layer_id[i] indicates a layer number of the i-th three-dimensional point sub-cloud. branch_id[i] indicates a branch number in layer_id[i] of the i-th three-dimensional point sub-cloud. 
     layer_id[i] and branch_id[i] are layer information and branch information that indicate, for example, a position of a branch in an octree. For example, layer_id[i]=2 and branch_id[i]=5 indicate that the i-th branch is the fifth branch in layer 2. 
     It should be noted that the three-dimensional data encoding device may entropy encode the encoded data generated by the above-described method. For example, the three-dimensional data encoding device binarizes each value and performs arithmetic coding on the binarized value. 
     Although the example of the quadtree structure or the octree structure has been given in the present variation, the present disclosure is not necessarily limited to this. The above-described method may be applied to an N-ary (N is an integer greater than or equal to 2) tree, such as a binary tree and a hexadecatree, or another tree structure. 
     As stated above, the three-dimensional data encoding device according to the present embodiment performs the process illustrated in  FIG.  108   . 
     First, the three-dimensional data encoding device generates an N-ary (N is an integer greater than or equal to 2) tree structure of three-dimensional points included in three-dimensional data (S 1801 ). 
     Next, the three-dimensional data encoding device generates first encoded data by encoding, using a first encoding process, a first branch having, as a root, a first node included in a first layer that is one of layers included in the N-ary tree structure (S 1802 ). 
     In addition, the three-dimensional data encoding device generates second encoded data by encoding, using a second encoding process different from the first encoding process, a second branch having, as a root, a second node that is included in the first layer and different from the first node (S 1803 ). 
     Then, the three-dimensional data encoding device generates a bitstream including the first encoded data and the second encoded data (S 1804 ). 
     Since this enables the three-dimensional data encoding device to apply an encoding process suitable for each branch included in the N-ary tree structure, it is possible to improve the coding efficiency. 
     For example, the number of three-dimensional points included in the first branch is less than a predetermined threshold value, and the number of three-dimensional points included in the second branch is greater than the threshold value. In other words, when the number of three-dimensional points included in a current branch is less than a threshold value, the three-dimensional data encoding device sets the current branch as the first branch, and when the number of three-dimensional points included in the current branch is greater than the threshold value, the three-dimensional data encoding device sets the current branch as the second branch. 
     For example, the first encoded data includes first information indicating that a first N-ary tree structure of first three-dimensional points included in the first branch is expressed using a first formula. The second encoded data includes second information indicating that a second N-ary tree structure of second three-dimensional points included in the second branch is expressed using a second formula. In other words, the first encoding process and the second encoding process differ in encoding scheme. 
     For example, the location encoding is used in the first encoding process, and the occupancy encoding is used in the second encoding process. In other words, the first information includes pieces of three-dimensional point information each of which is associated with a corresponding one of the first three-dimensional points. Each of the pieces of three-dimensional point information includes an index associated with each of layers in the first N-ary tree structure. Each of the indexes indicates, among N sub-blocks belonging to a corresponding one of the layers, a sub-block to which a corresponding one of the first three-dimensional points belongs. The second information includes pieces of 1-bit information each of which is associated with a corresponding one of sub-blocks belonging to layers in the second N-ary tree structure, and indicates whether a three-dimensional point is present in the corresponding sub-block. 
     For example, a quantization parameter used in the second encoding process is different from a quantization parameter used in the first encoding process. In other words, the first encoding process and the second encoding process are identical in encoding scheme, but differ in parameter for use. 
     For example, as illustrated in  FIG.  92    and  FIG.  93   , in the encoding of the first branch, the three-dimensional data encoding device encodes, using the first encoding process, the tree structure including the first branch and the tree structure from the root of the N-ary tree structure to the first node, and in the encoding of the second branch, the three-dimensional data encoding device encodes, using the second encoding process, the tree structure including the second branch and the tree structure from the root of the N-ary tree structure to the second node. 
     For example, the first encoded data includes encoded data of the first branch, and third information indicating a position of the first node in the N-ary tree structure. The second encoded data includes encoded data of the second branch, and fourth information indicating a position of the second node in the N-ary tree structure. 
     For example, the third information includes information (layer information) indicating the first layer, and information (branch information) indicating which one of nodes included in the first layer the first node is. The fourth information includes the information (layer information) indicating the first layer, and information (branch information) indicating which one of nodes included in the first layer the second node is. 
     For example, the first encoded data includes information (numPoint) indicating the number of three-dimensional points included in the first branch, and the second encoded data includes information (numPoint) indicating the number of three-dimensional points included in the second branch. 
     For example, the three-dimensional data encoding device includes a processor and memory, and the processor performs the above process using the memory. 
     The three-dimensional data decoding device according to the present embodiment performs the process illustrated in  FIG.  109   . 
     First, the three-dimensional data decoding device obtains, from a bitstream, first encoded data obtained by encoding a first branch having, as a root, a first node included in a first layer that is one of layers included in an N-ary (N is an integer greater than or equal to 2) tree structure of three-dimensional points, and second encoded data obtained by encoding a second branch having, as a root, a second node that is included in the first layer and different from the first node (S 1811 ). 
     Next, the three-dimensional data decoding device generates first decoded data of the first branch by decoding the first encoded data using a first decoding process (S 1812 ). 
     In addition, the three-dimensional data decoding device generates second decoded data of the second branch by decoding the second encoded data using a second decoding process different from the first decoding process (S 1813 ). 
     Then, the three-dimensional data decoding device restores three-dimensional points using the first decoded data and the second decoded data (S 1814 ). For example, these three-dimensional points include three-dimensional points indicated by the first decoded data, and three-dimensional points indicated by the second decoded data. 
     This enables the three-dimensional data decoding device to decode the bitstream for which the coding efficiency is improved. 
     For example, the number of three-dimensional points included in the first branch is less than a predetermined threshold value, and the number of three-dimensional points included in the second branch is greater than the threshold value. 
     For example, the first encoded data includes first information indicating that a first N-ary tree structure of first three-dimensional points included in the first branch is expressed using a first formula. The second encoded data includes second information indicating that a second N-ary tree structure of second three-dimensional points included in the second branch is expressed using a second formula. In other words, the first decoding process and the second decoding process differ in encoding scheme (decoding scheme). 
     For example, the location encoding is used for the first encoded data, and the occupancy encoding is used for the second encoded data. In other words, the first information includes pieces of three-dimensional point information each of which is associated with a corresponding one of the first three-dimensional points. Each of the pieces of three-dimensional point information includes an index associated with each of layers in the first N-ary tree structure. Each of the indexes indicates, among N sub-blocks belonging to a corresponding one of the layers, a sub-block to which a corresponding one of the first three-dimensional points belongs. The second information includes pieces of 1-bit information each of which is associated with a corresponding one of sub-blocks belonging to layers in the second N-ary tree structure, and indicates whether a three-dimensional point is present in the corresponding sub-block. 
     For example, a quantization parameter used in the second decoding process is different from a quantization parameter used in the first decoding process. In other words, the first decoding process and the second decoding process are identical in encoding scheme (decoding scheme), but differ in parameter for use. 
     For example, as illustrated in  FIG.  92    and  FIG.  93   , in the decoding of the first branch, the three-dimensional data decoding device decodes, using the first decoding process, the tree structure including the first branch and the tree structure from the root of the N-ary tree structure to the first node, and in the decoding of the second branch, the three-dimensional data decoding device decodes, using the second decoding process, the tree structure including the second branch and the tree structure from the root of the N-ary tree structure to the second node. 
     For example, the first encoded data includes encoded data of the first branch, and third information indicating a position of the first node in the N-ary tree structure. The second encoded data includes encoded data of the second branch, and fourth information indicating a position of the second node in the N-ary tree structure. 
     For example, the third information includes information (layer information) indicating the first layer, and information (branch information) indicating which one of nodes included in the first layer the first node is. The fourth information includes the information (layer information) indicating the first layer, and information (branch information) indicating which one of nodes included in the first layer the second node is. 
     For example, the first encoded data includes information (numPoint) indicating the number of three-dimensional points included in the first branch, and the second encoded data includes information (numPoint) indicating the number of three-dimensional points included in the second branch. 
     For example, the three-dimensional data decoding device includes a processor and memory, and the processor performs the above process using the memory. 
     Embodiment 11 
     In the present embodiment, adaptive entropy encoding (arithmetic coding) performed on occupancy codes of an octree will be described; 
       FIG.  110    is a diagram illustrating an example of a quadtree structure.  FIG.  111    is a diagram illustrating occupancy codes of the tree structure illustrated in  FIG.  110   .  FIG.  112    is a diagram schematically illustrating an operation performed by a three-dimensional data encoding device according to the present embodiment. 
     The three-dimensional data encoding device according to the present embodiment entropy encodes an 8-bit occupancy code in an octree. The three-dimensional data encoding device also updates a coding table in an entropy encoding process for occupancy code. Additionally, the three-dimensional data encoding device does not use a single coding table but uses an adaptive coding table in order to use similarity information of three-dimensional points. In other words, the three-dimensional data encoding device uses coding tables. 
     Similarity information is, for example, geometry information of a three-dimensional point, structure information of an octree, or attribute information of a three-dimensional point. 
     It should be noted that although the quadtree is shown as the example in  FIG.  110    to  FIG.  112   , the same method may be applied to an N-ary tree such as a binary tree, an octree, and a hexadecatree. For example, the three-dimensional data encoding device entropy encodes an 8-bit occupancy code in the case of an octree, a 4-bit occupancy code in the case of a quadtree, and a 16-bit occupancy code in the case of a hexadecatree, using an adaptive table (also referred to as a coding table). 
     The following describes an adaptive entropy encoding process using geometry information of a three-dimensional point. 
     When local geometries of two nodes in a tree structure are similar to each other, there is a chance that occupancy states (i.e., states each indicating whether a three-dimensional point is included) of child nodes are similar to each other. As a result, the three-dimensional data encoding device performs grouping using a local geometry of a parent node. This enables the three-dimensional data encoding device to group together the occupancy states of the child nodes, and use a different coding table for each group. Accordingly, it is possible to improve the entropy encoding efficiency; 
       FIG.  113    is a diagram illustrating an example of geometry information. Geometry information includes information indicating whether each of neighboring nodes of a current node is occupied (i.e., includes a three-dimensional point). For example, the three-dimensional data encoding device calculates a local geometry of the current node using information indicating whether a neighboring node includes a three-dimensional point (is occupied or non-occupied). A neighboring node is, for example, a node spatially located around a current node, or a node located in the same position in a different time as the current node or spatially located around the position. 
     In  FIG.  113   , a hatched cube indicates a current node. A white cube is a neighboring node, and indicates a node including a three-dimensional point. In  FIG.  113   , the geometry pattern indicated in (2) is obtained by rotating the geometry pattern indicated in (1). Accordingly, the three-dimensional data encoding device determines that these geometry patterns have a high geometry similarity, and entropy encodes the geometry patterns using the same coding table. In addition, the three-dimensional data encoding device determines that the geometry patterns indicated in (3) and (4) have a low geometry similarity, and entropy encodes the geometry patterns using other coding tables; 
       FIG.  114    is a diagram illustrating an example of occupancy codes of current nodes in the geometry patterns of (1) to (4) illustrated in  FIG.  113   , and coding tables used for entropy encoding. As illustrated above, the three-dimensional data encoding device determines that the geometry patterns of (1) and (2) are included in the same geometry group, and uses same coding table A for the geometry patterns of (1) and (2). The three-dimensional data encoding device uses coding table B and coding table C for the geometry patterns of (3) and (4), respectively. 
     As illustrated in  FIG.  114   , there is a case in which the occupancy codes of the current nodes in the geometry patterns of (1) and (2) included in the same geometry group are identical to each other. 
     Next, the following describes an adaptive entropy encoding process using structure information of a tree structure. For example, structure information includes information indicating a layer to which a current node belongs; 
       FIG.  115    is a diagram illustrating an example of a tree structure. Generally speaking, a local shape of an object depends on a search criterion. For example, a tree structure tends to be sparser in a lower layer than in an upper layer. Accordingly, the three-dimensional data encoding device uses different coding tables for upper layers and lower layers as illustrated in  FIG.  115   , which makes it possible to improve the entropy encoding efficiency. 
     In other words, when the three-dimensional data encoding device encodes an occupancy code of each layer, the three-dimensional data encoding device may use a different coding table for each layer. For example, when the three-dimensional data encoding device encodes an occupancy code of layer N (N=0 to 6), the three-dimensional data encoding device may perform entropy encoding on the tree structure illustrated in  FIG.  115    using a coding table for layer N. Since this enables the three-dimensional data encoding device to select a coding table in accordance with an appearance pattern of an occupancy code of each layer, the three-dimensional data encoding device can improve the coding efficiency. 
     Moreover, as illustrated in  FIG.  115   , the three-dimensional data encoding device may use coding table A for the occupancy codes of layer 0 to layer 2, and may use coding table B for the occupancy codes of layer 3 to layer 6. Since this enables the three-dimensional data encoding device to select a coding table in accordance with an appearance pattern of the occupancy code for each group of layers, the three-dimensional data encoding device can improve the coding efficiency. The three-dimensional data encoding device may append information of the coding table used for each layer, to a header of a bitstream. Alternatively, the coding table used for each layer may be predefined by standards etc. 
     Next, the following describes an adaptive entropy encoding process using attribute information (property information) of a three-dimensional point. For example, attribute information includes information about an object including a current node, or information about a normal vector of the current node. 
     It is possible to group together three-dimensional points having a similar geometry, using pieces of attribute information of the three-dimensional points. For example, a normal vector indicating a direction of each of the three-dimensional points may be used as common attribute information of the three-dimensional points. It is possible to find a geometry relating to a similar occupancy code in a tree structure by using the normal vector. 
     Moreover, a color or a degree of reflection (reflectance) may be used as attribute information. For example, the three-dimensional data encoding device groups together three-dimensional points having a similar geometry, using the colors or reflectances of the three-dimensional points, and performs a process such as switching between coding tables for each of the groups; 
       FIG.  116    is a diagram for describing switching between coding tables based on a normal vector. As illustrated in  FIG.  116   , when normal vector groups to which normal vectors of current nodes belong are different, different coding tables are used. For example, a normal vector included in a predetermined range is categorized into one normal vector group. 
     When objects belong in different categories, there is a high possibility that occupancy codes are different. Accordingly, the three-dimensional data encoding device may select a coding table in accordance with a category of an object to which a current node belongs.  FIG.  117    is a diagram for describing switching between coding tables based on a category of an object. As illustrated in  FIG.  117   , when objects belong in different categories, different coding tables are used. 
     The following describes an example of a structure of a bitstream according to the present embodiment.  FIG.  118    is a diagram illustrating an example of a structure of a bitstream generated by the three-dimensional data encoding device according to the present embodiment. As illustrated in  FIG.  118   , the bitstream includes a coding table group, table indexes, and encoded occupancy codes. The coding table group includes coding tables. 
     A table index indicates a coding table used for entropy encoding of a subsequent encoded occupancy code. An encoded occupancy code is an occupancy code that has been entropy encoded. As illustrated in  FIG.  118   , the bitstream also includes combinations of a table index and an encoded occupancy code. 
     For example, in the example illustrated in  FIG.  118   , encoded occupancy code  0  is data that has been entropy encoded using a context model (also referred to as a context) indicated by table index  0 . Encoded occupancy code  1  is data that has been entropy encoded using a context indicated by table index  1 . A context for encoding encoded occupancy code  0  may be predefined by standards etc., and a three-dimensional data decoding device may use this context when decoding encoded occupancy code  0 . Since this eliminates the need for appending the table index to the bitstream, it is possible to reduce overhead. 
     Moreover, the three-dimensional data encoding device may append, in the header, information for resetting each context. 
     The three-dimensional data encoding device determines a coding table using geometry information, structure information, or attribute information of a current node, and encodes an occupancy code using the determined coding table. The three-dimensional data encoding device appends a result of the encoding and information (e.g., a table index) of the coding table used for the encoding to a bitstream, and transmits the bitstream to the three-dimensional data decoding device. This enables the three-dimensional data decoding device to decode the occupancy code using the information of the coding table appended to the header. 
     Moreover, the three-dimensional data encoding device need not append information of a coding table used for encoding to a bitstream, and the three-dimensional data decoding device may determine a coding table using geometry information, structure information, or attribute information of a current node that has been decoded, using the same method as the three-dimensional data encoding device, and decode an occupancy code using the determined coding table. Since this eliminates the need for appending the information of the coding table to the bitstream, it is possible to reduce overhead; 
       FIG.  119    and  FIG.  120    each are a diagram illustrating an example of a coding table. As illustrated in  FIG.  119    and  FIG.  120   , one coding table shows, for each value of an 8-bit occupancy code, a context model and a context model type associated with the value. 
     As with the coding table illustrated in  FIG.  119   , the same context model (context) may be applied to occupancy codes. In addition, a different context model may be assigned to each occupancy code. Since this enables assignment of a context model in accordance with a probability of appearance of an occupancy code, it is possible to improve the coding efficiency. 
     A context model type indicates, for example, whether a context model is a context model that updates a probability table in accordance with an appearance frequency of an occupancy code, or is a context model having a fixed probability table. 
     Next, the following gives another example of a bitstream and a coding table.  FIG.  121    is a diagram illustrating a variation of a structure of a bitstream. As illustrated in  FIG.  121   , the bitstream includes a coding table group and an encoded occupancy code. The coding table group includes coding tables; 
       FIG.  122    and  FIG.  123    each are a diagram illustrating an example of a coding table. As illustrated in  FIG.  122    and  FIG.  123   , one coding table shows, for each  1  bit included in an occupancy code, a context model and a context model type associated with the 1 bit; 
       FIG.  124    is a diagram illustrating an example of a relationship between an occupancy code and bit numbers of the occupancy code. 
     As stated above, the three-dimensional data encoding device may handle an occupancy code as binary data, assign a different context model for each bit, and entropy encode the occupancy code. Since this enables assignment of a context model in accordance with a probability of appearance of each bit of the occupancy code, it is possible to improve the coding efficiency. 
     Specifically, each bit of the occupancy code corresponds to a sub-block obtained by dividing a spatial block corresponding to a current node. Accordingly, when sub-blocks in the same spatial position in a block have the same tendency, it is possible to improve the coding efficiency. For example, when a ground surface or a road surface crosses through a block, in an octree, four lower blocks include three-dimensional points, and four upper blocks include no three-dimensional point. Additionally, the same pattern appears in blocks horizontally arranged. Accordingly, it is possible to improve the coding efficiency by switching between contexts for each bit as described above. 
     A context model that updates a probability table in accordance with an appearance frequency of each bit of an occupancy code may also be used. In addition, a context model having a fixed probability table may be used. 
     Next, the following describes procedures for a three-dimensional data encoding process and a three-dimensional data decoding process according to the present embodiment; 
       FIG.  125    is a flowchart of a three-dimensional data encoding process including an adaptive entropy encoding process using geometry information. 
     In a decomposition process, an octree is generated from an initial bounding box of three-dimensional points. A bounding box is divided in accordance with the position of a three-dimensional point in the bounding box. Specifically, a non-empty sub-space is further divided. Next, information indicating whether a sub-space includes a three-dimensional point is encoded into an occupancy code. It should be noted that the same process is performed in the processes illustrated in  FIG.  127    and  FIG.  129   . 
     First, the three-dimensional data encoding device obtains inputted three-dimensional points (S 1901 ). Next, the three-dimensional data encoding device determines whether a decomposition process per unit length is completed (S 1902 ). 
     When the decomposition process per unit length is not completed (NO in S 1902 ), the three-dimensional data encoding device generates an octree by performing the decomposition process on a current node (S 1903 ). 
     Then, the three-dimensional data encoding device obtains geometry information (S 1904 ), and selects a coding table based on the obtained geometry information (S 1905 ). Here, as stated above, the geometry information is information indicating, for example, a geometry of occupancy states of neighboring blocks of a current node. 
     After that, the three-dimensional data encoding device entropy encodes an occupancy code of the current node using the selected coding table (S 1906 ). 
     Steps S 1903  to S 1906  are repeated until the decomposition process per unit length is completed. When the decomposition process per unit length is completed (YES in S 1902 ), the three-dimensional data encoding device outputs a bitstream including generated information (S 1907 ). 
     The three-dimensional data encoding device determines a coding table using geometry information, structure information, or attribute information of a current node, and encodes a bit sequence of an occupancy code using the determined coding table. The three-dimensional data encoding device appends a result of the encoding and information (e.g., a table index) of the coding table used for the encoding to a bitstream, and transmits the bitstream to the three-dimensional data decoding device. This enables the three-dimensional data decoding device to decode the occupancy code using the information of the coding table appended to the header. 
     Moreover, the three-dimensional data encoding device need not append information of a coding table used for encoding to a bitstream, and the three-dimensional data decoding device may determine a coding table using geometry information, structure information, or attribute information of a current node that has been decoded, using the same method as the three-dimensional data encoding device, and decode an occupancy code using the determined coding table. Since this eliminates the need for appending the information of the coding table to the bitstream, it is possible to reduce overhead; 
       FIG.  126    is a flowchart of a three-dimensional data decoding process including an adaptive entropy decoding process using geometry information. 
     A decomposition process included in the decoding process is similar to the decomposition process included in the above-described encoding process, they differ in the following point. The three-dimensional data decoding device divides an initial bounding box using a decoded occupancy code. When the three-dimensional data decoding device completes a process per unit length, the three-dimensional data decoding device stores the position of a bounding box as the position of a three-dimensional point. It should be noted that the same process is performed in the processes illustrated in  FIG.  128    and  FIG.  130   . 
     First, the three-dimensional data decoding device obtains an inputted bitstream (S 1911 ). Next, the three-dimensional data decoding device determines whether a decomposition process per unit length is completed (S 1912 ). 
     When the decomposition process per unit length is not completed (NO in S 1912 ), the three-dimensional data decoding device generates an octree by performing the decomposition process on a current node (S 1913 ). 
     Then, the three-dimensional data decoding device obtains geometry information (S 1914 ), and selects a coding table based on the obtained geometry information (S 1915 ). Here, as stated above, the geometry information is information indicating, for example, a geometry of occupancy states of neighboring blocks of a current node. 
     After that, the three-dimensional data decoding device entropy decodes an occupancy code of the current node using the selected coding table (S 1916 ). 
     Steps S 1913  to S 1916  are repeated until the decomposition process per unit length is completed. When the decomposition process per unit length is completed (YES in S 1912 ), the three-dimensional data decoding device outputs three-dimensional points (S 1917 ); 
       FIG.  127    is a flowchart of a three-dimensional data encoding process including an adaptive entropy encoding process using structure information. 
     First, the three-dimensional data encoding device obtains inputted three-dimensional points (S 1921 ). Next, the three-dimensional data encoding device determines whether a decomposition process per unit length is completed (S 1922 ). 
     When the decomposition process per unit length is not completed (NO in S 1922 ), the three-dimensional data encoding device generates an octree by performing the decomposition process on a current node (S 1923 ). 
     Then, the three-dimensional data encoding device obtains structure information (S 1924 ), and selects a coding table based on the obtained structure information (S 1925 ). Here, as stated above, the structure information is information indicating, for example, a layer to which a current node belongs. 
     After that, the three-dimensional data encoding device entropy encodes an occupancy code of the current node using the selected coding table (S 1926 ). 
     Steps S 1923  to S 1926  are repeated until the decomposition process per unit length is completed. When the decomposition process per unit length is completed (YES in S 1922 ), the three-dimensional data encoding device outputs a bitstream including generated information (S 1927 ); 
       FIG.  128    is a flowchart of a three-dimensional data decoding process including an adaptive entropy decoding process using structure information. 
     First, the three-dimensional data decoding device obtains an inputted bitstream (S 1931 ). Next, the three-dimensional data decoding device determines whether a decomposition process per unit length is completed (S 1932 ). 
     When the decomposition process per unit length is not completed (NO in S 1932 ), the three-dimensional data decoding device generates an octree by performing the decomposition process on a current node (S 1933 ). 
     Then, the three-dimensional data decoding device obtains structure information (S 1934 ), and selects a coding table based on the obtained structure information (S 1935 ). Here, as stated above, the structure information is information indicating, for example, a layer to which a current node belongs. 
     After that, the three-dimensional data decoding device entropy decodes an occupancy code of the current node using the selected coding table (S 1936 ). 
     Steps S 1933  to S 1936  are repeated until the decomposition process per unit length is completed. When the decomposition process per unit length is completed (YES in S 1932 ), the three-dimensional data decoding device outputs three-dimensional points (S 1937 ); 
       FIG.  129    is a flowchart of a three-dimensional data encoding process including an adaptive entropy encoding process using attribute information. 
     First, the three-dimensional data encoding device obtains inputted three-dimensional points (S 1941 ). Next, the three-dimensional data encoding device determines whether a decomposition process per unit length is completed (S 1942 ). 
     When the decomposition process per unit length is not completed (NO in S 1942 ), the three-dimensional data encoding device generates an octree by performing the decomposition process on a current node (S 1943 ). 
     Then, the three-dimensional data encoding device obtains attribute information (S 1944 ), and selects a coding table based on the obtained attribute information (S 1945 ). Here, as stated above, the attribute information is information indicating, for example, a normal vector of a current node. 
     After that, the three-dimensional data encoding device entropy encodes an occupancy code of the current node using the selected coding table (S 1946 ). 
     Steps S 1943  to S 1946  are repeated until the decomposition process per unit length is completed. When the decomposition process per unit length is completed (YES in S 1942 ), the three-dimensional data encoding device outputs a bitstream including generated information (S 1947 ); 
       FIG.  130    is a flowchart of a three-dimensional data decoding process including an adaptive entropy decoding process using attribute information. 
     First, the three-dimensional data decoding device obtains an inputted bitstream (S 1951 ). Next, the three-dimensional data decoding device determines whether a decomposition process per unit length is completed (S 1952 ). 
     When the decomposition process per unit length is not completed (NO in S 1952 ), the three-dimensional data decoding device generates an octree by performing the decomposition process on a current node (S 1953 ). 
     Then, the three-dimensional data encoding device obtains attribute information (S 1954 ), and selects a coding table based on the obtained attribute information (S 1955 ). Here, as stated above, the attribute information is information indicating, for example, a normal vector of a current node. 
     After that, the three-dimensional data decoding device entropy decodes an occupancy code of the current node using the selected coding table (S 1956 ). 
     Steps S 1953  to S 1956  are repeated until the decomposition process per unit length is completed. When the decomposition process per unit length is completed (YES in S 1952 ), the three-dimensional data decoding device outputs three-dimensional points (S 1957 ); 
       FIG.  131    is a flowchart of the process of selecting a coding table using geometry information (S 1905 ). 
     The three-dimensional data encoding device may select a coding table to be used for entropy encoding of an occupancy code, using, as geometry information, information of a geometry group of a tree structure, for example. Here, information of a geometry group is information indicating a geometry group including a geometry pattern of a current node. 
     As illustrated in  FIG.  131   , when a geometry group indicated by geometry information is geometry group  0  (YES in S 1961 ), the three-dimensional data encoding device selects coding table  0  (S 1962 ). When the geometry group indicated by the geometry information is geometry group  1  (YES in S 1963 ), the three-dimensional data encoding device selects coding table  1  (S 1964 ). In any other case (NO in S 1963 ), the three-dimensional data encoding device selects coding table  2  (S 1965 ). 
     It should be noted that a method of selecting a coding table is not limited to the above. For example, when a geometry group indicated by geometry information is geometry group  2 , the three-dimensional data encoding device may further select a coding table according to a value of the geometry group, such as using coding table  2 . 
     For example, a geometry group is determined using occupancy information indicating whether a node neighboring a current node includes a point cloud. Geometry patterns that become the same shape by transform such as rotation being applied to may be included in the same geometry group. The three-dimensional data encoding device may select a geometry group using occupancy information of a node that neighbors a current node or is located around the current node, and belongs to the same layer as the current node. In addition, the three-dimensional data encoding device may select a geometry group using occupancy information of a node that belongs to a layer different from that of a current node. For example, the three-dimensional data encoding device may select a geometry group using occupancy information of a parent node, a node neighboring the parent node, or a node located around the parent node. 
     It should be noted that the same applies to the process of selecting a coding table using geometry information (S 1915 ) in the three-dimensional data decoding device; 
       FIG.  132    is a flowchart of the process of selecting a coding table using structure information (S 1925 ). The three-dimensional data encoding device may select a coding table to be used for entropy encoding of an occupancy code, using, as structure information, layer information of a tree structure, for example. Here, the layer information indicates, for example, a layer to which a current node belongs. 
     As illustrated in  FIG.  132   , when a current node belongs to layer  0  (YES in S 1971 ), the three-dimensional data encoding device selects coding table  0  (S 1972 ). When the current node belongs to layer  1  (YES in S 1973 ), the three-dimensional data encoding device selects coding table  1  (S 1974 ). In any other case (NO in S 1973 ), the three-dimensional data encoding device selects coding table  2  (S 1975 ). 
     It should be noted that a method of selecting a coding table is not limited to the above. For example, when a current node belongs to layer  2 , the three-dimensional data encoding device may further select a coding table in accordance with the layer to which the current node belongs, such as using coding table  2 . 
     The same applies to the process of selecting a coding table using structure information (S 1935 ) in the three-dimensional data decoding device;  FIG.  133    is a flowchart of the process of selecting a coding table using attribute information (S 1945 ). 
     The three-dimensional data encoding device may select a coding table to be used for entropy encoding of an occupancy code, using, as attribute information, information about an object to which a current node belongs or information about a normal vector of the current node. 
     As illustrated in  FIG.  133   , when a normal vector of a current node belongs to normal vector group  0  (YES in S 1981 ), the three-dimensional data encoding device selects coding table  0  (S 1982 ). When the normal vector of the current node belongs to normal vector group  1  (YES in S 1983 ), the three-dimensional data encoding device selects coding table  1  (S 1984 ). In any other case (NO in S 1983 ), the three-dimensional data encoding device selects coding table  2  (S 1985 ). 
     It should be noted that a method of selecting a coding table is not limited to the above. For example, when a normal vector of a current node belongs to normal vector group  2 , the three-dimensional data encoding device may further select a coding table in accordance with a normal vector group to which the normal vector of the current belongs, such as using coding table  2 . 
     For example, the three-dimensional data encoding device selects a normal vector group using information about a normal vector of a current node. For example, the three-dimensional data encoding device determines, as the same normal vector group, normal vectors having a distance between normal vectors that is less than or equal to a predetermined threshold value. 
     The information about the object to which the current node belongs may be information about, for example, a person, a vehicle, or a building. 
     The following describes configurations of three-dimensional data encoding device  1900  and three-dimensional data decoding device  1910  according to the present embodiment.  FIG.  134    is a block diagram of three-dimensional data encoding device  1900  according to the present embodiment. Three-dimensional data encoding device  1900  illustrated in  FIG.  134    includes octree generator  1901 , similarity information calculator  1902 , coding table selector  1903 , and entropy encoder  1904 . 
     Octree generator  1901  generates, for example, an octree from inputted three-dimensional points, and generates an occupancy code for each node included in the octree. Similarity information calculator  1902  obtains, for example, similarity information that is geometry information, structure information, or attribute information of a current node. Coding table selector  1903  selects a context to be used for entropy encoding of an occupancy code, according to the similarity information of the current node. Entropy encoder  1904  generates a bitstream by entropy encoding the occupancy code using the selected context. It should be noted that entropy encoder  1904  may append, to the bitstream, information indicating the selected context; 
       FIG.  135    is a block diagram of three-dimensional data decoding device  1910  according to the present embodiment. Three-dimensional data decoding device  1910  illustrated in  FIG.  135    includes octree generator  1911 , similarity information calculator  1912 , coding table selector  1913 , and entropy decoder  1914 . 
     Octree generator  1911  generates an octree in order from, for example, a lower layer to an upper layer using information obtained from entropy decoder  1914 . Similarity information calculator  1912  obtains similarity information that is geometry information, structure information, or attribute information of a current node. Coding table selector  1913  selects a context to be used for entropy encoding of an occupancy code, according to the similarity information of the current node. Entropy decoder  1914  generates three-dimensional points by entropy decoding the occupancy code using the selected context. It should be noted that entropy decoder  1914  may obtain, by performing decoding, information of the selected context appended to a bitstream, and use the context indicated by the information. 
     As illustrated in  FIG.  122    to  FIG.  124    above, the contexts are provided to the respective bits of the occupancy code. In other words, the three-dimensional data encoding device entropy encodes a bit sequence representing an N-ary (N is an integer greater than or equal to 2) tree structure of three-dimensional points included in three-dimensional data, using a coding table selected from coding tables. The bit sequence includes N-bit information for each node in the N-ary tree structure. The N-bit information includes N pieces of 1-bit information each indicating whether a three-dimensional point is present in a corresponding one of N child nodes of a corresponding node. In each of the coding tables, a context is provided to each bit of the N-bit information. The three-dimensional data encoding device entropy encodes each bit of the N-bit information using the context provided to the bit in the selected coding table. 
     This enables the three-dimensional data encoding device to improve the coding efficiency by selecting a context for each bit. 
     For example, in the entropy encoding, the three-dimensional data encoding device selects a coding table to be used from coding tables, based on whether a three-dimensional point is present in each of neighboring nodes of a current node. This enables the three-dimensional data encoding device to improve the coding efficiency by selecting a coding table based on whether the three-dimensional point is present in the neighboring node. 
     For example, in the entropy encoding, the three-dimensional data encoding device (i) selects a coding table based on an arrangement pattern indicating an arranged position of a neighboring node in which a three-dimensional point is present, among neighboring nodes, and (ii) selects the same coding table for arrangement patterns that become identical by rotation, among arrangement patterns. This enables the three-dimensional data encoding device to reduce an increase in the number of coding tables. 
     For example, in the entropy encoding, the three-dimensional data encoding device selects a coding table to be used from coding tables, based on a layer to which a current node belongs. This enables the three-dimensional data encoding device to improve the coding efficiency by selecting a coding table based on the layer to which the current node belongs. 
     For example, in the entropy encoding, the three-dimensional data encoding device selects a coding table to be used from coding tables, based on a normal vector of a current node. This enables the three-dimensional data encoding device to improve the coding efficiency by selecting a coding table based on the normal vector. 
     For example, the three-dimensional data encoding device includes a processor and memory, and the processor performs the above process using the memory. 
     The three-dimensional data decoding device entropy decodes a bit sequence representing an N-ary (N is an integer greater than or equal to 2) tree structure of three-dimensional points included in three-dimensional data, using a coding table selected from coding tables. The bit sequence includes N-bit information for each node in the N-ary tree structure. The N-bit information includes N pieces of 1-bit information each indicating whether a three-dimensional point is present in a corresponding one of N child nodes of a corresponding node. In each of the coding tables, a context is provided to each bit of the N-bit information. The three-dimensional data decoding device entropy decodes each bit of the N-bit information using the context provided to the bit in the selected coding table. 
     This enables the three-dimensional data decoding device to improve the coding efficiency by selecting a context for each bit. 
     For example, in the entropy decoding, the three-dimensional data decoding device selects a coding table to be used from coding tables, based on whether a three-dimensional point is present in each of neighboring nodes of a current node. This enables the three-dimensional data decoding device to improve the coding efficiency by selecting a coding table based on whether the three-dimensional point is present in the neighboring node. 
     For example, in the entropy decoding, the three-dimensional data decoding device (i) selects a coding table based on an arrangement pattern indicating an arranged position of a neighboring node in which a three-dimensional point is present, among neighboring nodes, and (ii) selects the same coding table for arrangement patterns that become identical by rotation, among arrangement patterns. This enables the three-dimensional data decoding device to reduce an increase in the number of coding tables. 
     For example, in the entropy decoding, the three-dimensional data decoding device selects a coding table to be used from coding tables, based on a layer to which a current node belongs. This enables the three-dimensional data decoding device to improve the coding efficiency by selecting a coding table based on the layer to which the current node belongs. 
     For example, in the entropy decoding, the three-dimensional data decoding device selects a coding table to be used from coding tables, based on a normal vector of a current node. This enables the three-dimensional data decoding device to improve the coding efficiency by selecting a coding table based on the normal vector. 
     For example, the three-dimensional data decoding device includes a processor and memory, and the processor performs the above process using the memory. 
     Embodiment 12 
     In the present embodiment, a method of controlling reference when an occupancy code is encoded will be described. It should be noted that although the following mainly describes an operation of a three-dimensional data encoding device, a three-dimensional data decoding device may perform the same process; 
       FIG.  136    and  FIG.  137    each are a diagram illustrating a reference relationship according to the present embodiment. Specifically,  FIG.  136    is a diagram illustrating a reference relationship in an octree structure, and  FIG.  137    is a diagram illustrating a reference relationship in a spatial region. 
     In the present embodiment, when the three-dimensional data encoding device encodes encoding information of a current node to be encoded (hereinafter referred to as a current node), the three-dimensional data encoding device refers to encoding information of each node in a parent node to which the current node belongs. In this regard, however, the three-dimensional data encoding device does not refer to encoding information of each node in another node (hereinafter referred to as a parent neighbor node) that is in the same layer as the parent node. In other words, the three-dimensional data encoding device disables or prohibits reference to a parent neighbor node. 
     It should be noted that the three-dimensional data encoding device may permit reference to encoding information of a parent node (hereinafter also referred to as a grandparent node) of the parent node. In other words, the three-dimensional data encoding device may encode the encoding information of the current node by reference to the encoding information of each of the grandparent node and the parent node to which the current node belongs. 
     Here, encoding information is, for example, an occupancy code. When the three-dimensional data encoding device encodes the occupancy code of the current node, the three-dimensional data encoding device refers to information (hereinafter referred to as occupancy information) indicating whether a point cloud is included in each node in the parent node to which the current node belongs. To put it in another way, when the three-dimensional data encoding device encodes the occupancy code of the current node, the three-dimensional data encoding device refers to an occupancy code of the parent node. On the other hand, the three-dimensional data encoding device does not refer to occupancy information of each node in a parent neighbor node. In other words, the three-dimensional data encoding device does not refer to an occupancy code of the parent neighbor node. Moreover, the three-dimensional data encoding device may refer to occupancy information of each node in the grandparent node. In other words, the three-dimensional data encoding device may refer to the occupancy information of each of the parent node and the parent neighbor node. 
     For example, when the three-dimensional data encoding device encodes the occupancy code of the current node, the three-dimensional data encoding device selects a coding table to be used for entropy encoding of the occupancy code of the current node, using the occupancy code of the grandparent node or the parent node to which the current node belongs. It should be noted that the details will be described later. At this time, the three-dimensional data encoding device need not refer to the occupancy code of the parent neighbor node. Since this enables the three-dimensional data encoding device to, when encoding the occupancy code of the current node, appropriately select a coding table according to information of the occupancy code of the parent node or the grandparent node, the three-dimensional data encoding device can improve the coding efficiency. Moreover, by not referring to the parent neighbor node, the three-dimensional data encoding device can suppress a process of checking the information of the parent neighbor node and reduce a memory capacity for storing the information. Furthermore, scanning the occupancy code of each node of the octree in a depth-first order makes encoding easy. 
     The following describes an example of selecting a coding table using an occupancy code of a parent node.  FIG.  138    is a diagram illustrating an example of a current node and neighboring reference nodes.  FIG.  139    is a diagram illustrating a relationship between a parent node and nodes.  FIG.  140    is a diagram illustrating an example of an occupancy code of the parent node. Here, a neighboring reference node is a node referred to when a current node is encoded, among nodes spatially neighboring the current node. In the example shown in  FIG.  138   , the neighboring nodes belong to the same layer as the current node. Moreover, node X neighboring the current node in the x direction, node Y neighboring the current block in the y direction, and node Z neighboring the current block in the z direction are used as the reference neighboring nodes. In other words, one neighboring node is set as a reference neighboring node in each of the x, y, and z directions. 
     It should be noted that the node numbers shown in  FIG.  139    are one example, and a relationship between node numbers and node positions is not limited to the relationship shown in  FIG.  139   . Although node  0  is assigned to the lowest-order bit and node  7  is assigned to the highest-order bit in  FIG.  140   , assignments may be made in reverse order. In addition, each node may be assigned to any bit. 
     The three-dimensional data encoding device determines a coding table to be used when the three-dimensional data encoding device entropy encodes an occupancy code of a current node, using the following equation, for example. 
       CodingTable=(Flag X&lt;&lt; 2)+(Flag Y&lt;&lt; 1)+(Flag Z ) 
     Here, CodingTable indicates a coding table for an occupancy code of a current node, and indicates one of values ranging from 0 to 7. FlagX is occupancy information of neighboring node X. FlagX indicates 1 when neighboring node X includes a point cloud (is occupied), and indicates 0 when it does not. FlagY is occupancy information of neighboring node Y. FlagY indicates 1 when neighboring node Y includes a point cloud (is occupied), and indicates 0 when it does not. FlagZ is occupancy information of neighboring node Z. FlagZ indicates 1 when neighboring node Z includes a point cloud (is occupied), and indicates 0 when it does not. 
     It should be noted that since information indicating whether a neighboring node is occupied is included in an occupancy code of a parent node, the three-dimensional data encoding device may select a coding table using a value indicated by the occupancy code of the parent node. 
     From the foregoing, the three-dimensional data encoding device can improve the coding efficiency by selecting a coding table using the information indicating whether the neighboring node of the current node includes a point cloud. 
     Moreover, as illustrated in  FIG.  138   , the three-dimensional data encoding device may select a neighboring reference node according to a spatial position of the current node in the parent node. In other words, the three-dimensional data encoding device may select a neighboring node to be referred to from the neighboring nodes, according to the spatial position of the current node in the parent node. 
     Next, the following describes examples of configurations of the three-dimensional data encoding device and the three-dimensional data decoding device.  FIG.  141    is a block diagram of three-dimensional data encoding device  2100  according to the present embodiment. Three-dimensional data encoding device  2100  illustrated in  FIG.  141    includes octree generator  2101 , geometry information calculator  2102 , coding table selector  2103 , and entropy encoder  2104 . 
     Octree generator  2101  generates, for example, an octree from inputted three-dimensional points (a point cloud), and generates an occupancy code for each node included in the octree. Geometry information calculator  2102  obtains occupancy information indicating whether a neighboring reference node of a current node is occupied. For example, geometry information calculator  2102  obtains the occupancy information of the neighboring reference node from an occupancy code of a parent node to which the current node belongs. It should be noted that, as illustrated in  FIG.  138   , geometry information calculator  2102  may select a neighboring reference node according to a position of the current node in the parent node. In addition, geometry information calculator  2102  does not refer to occupancy information of each node in a parent neighbor node. 
     Coding table selector  2103  selects a coding table to be used for entropy encoding of an occupancy code of the current node, using the occupancy information of the neighboring reference node calculated by geometry information calculator  2102 . Entropy encoder  2104  generates a bitstream by entropy encoding the occupancy code using the selected coding table. It should be noted that entropy encoder  2104  may append, to the bitstream, information indicating the selected coding table; 
       FIG.  142    is a block diagram of three-dimensional data decoding device  2110  according to the present embodiment. Three-dimensional data decoding device  2110  illustrated in  FIG.  142    includes octree generator  2111 , geometry information calculator  2112 , coding table selector  2113 , and entropy decoder  2114 . 
     Octree generator  2111  generates an octree of a space (nodes) using header information of a bitstream etc. Octree generator  2111  generates an octree by, for example, generating a large space (a root node) using the size of a space along the x-axis, y-axis, and z-axis directions appended to the header information, and generating eight small spaces A (nodes A 0  to A 7 ) by dividing the space into two along each of the x-axis, y-axis, and z-axis directions. Nodes A 0  to A 7  are set as a current node in sequence. 
     Geometry information calculator  2112  obtains occupancy information indicating whether a neighboring reference node of a current node is occupied. For example, geometry information calculator  2112  obtains the occupancy information of the neighboring reference node from an occupancy code of a parent node to which the current node belongs. It should be noted that, as illustrated in  FIG.  138   , geometry information calculator  2112  may select a neighboring reference node according to a position of the current node in the parent node. In addition, geometry information calculator  2112  does not refer to occupancy information of each node in a parent neighboring node. 
     Coding table selector  2113  selects a coding table (a decoding table) to be used for entropy decoding of the occupancy code of the current node, using the occupancy information of the neighboring reference node calculated by geometry information calculator  2112 . Entropy decoder  2114  generates three-dimensional points by entropy decoding the occupancy code using the selected coding table. It should be noted that coding table selector  2113  may obtain, by performing decoding, information of the selected coding table appended to the bitstream, and entropy decoder  2114  may use a coding table indicated by the obtained information. 
     Each bit of the occupancy code (8 bits) included in the bitstream indicates whether a corresponding one of eight small spaces A (nodes A 0  to A 7 ) includes a point cloud. Furthermore, the three-dimensional data decoding device generates an octree by dividing small space node A 0  into eight small spaces B (nodes B 0  to B 7 ), and obtains information indicating whether each node of small space B includes a point cloud, by decoding the occupancy code. In this manner, the three-dimensional data decoding device decodes the occupancy code of each node while generating an octree by dividing a large space into small spaces. 
     The following describes procedures for processes performed by the three-dimensional data encoding device and the three-dimensional data decoding device.  FIG.  143    is a flowchart of a three-dimensional data encoding process in the three-dimensional data encoding device. First, the three-dimensional data encoding device determines (defines) a space (a current node) including part or whole of an inputted three-dimensional point cloud (S 2101 ). Next, the three-dimensional data encoding device generates eight small spaces (nodes) by dividing the current node into eight (S 2102 ). Then, the three-dimensional data encoding device generates an occupancy code for the current node according to whether each node includes a point cloud (S 2103 ). 
     After that, the three-dimensional data encoding device calculates (obtains) occupancy information of a neighboring reference node of the current node from an occupancy code of a parent node of the current node (S 2104 ). Next, the three-dimensional data encoding device selects a coding table to be used for entropy encoding, based on the calculated occupancy information of the neighboring reference node of the current node (S 2105 ). Then, the three-dimensional data encoding device entropy encodes the occupancy code of the current node using the selected coding table (S 2106 ). 
     Finally, the three-dimensional data encoding device repeats a process of dividing each node into eight and encoding an occupancy code of the node, until the node cannot be divided (S 2107 ). In other words, steps S 2102  to S 2106  are recursively repeated; 
       FIG.  144    is a flowchart of a three-dimensional data decoding process in the three-dimensional data decoding device. First, the three-dimensional data decoding device determines (defines) a space (a current node) to be decoded, using header information of a bitstream (S 2111 ). Next, the three-dimensional data decoding device generates eight small spaces (nodes) by dividing the current node into eight (S 2112 ). Then, the three-dimensional data decoding device calculates (obtains) occupancy information of a neighboring reference node of the current node from an occupancy code of a parent node of the current node (S 2113 ). 
     After that, the three-dimensional data decoding device selects a coding table to be used for entropy decoding, based on the occupancy information of the neighboring reference node (S 2114 ). Next, the three-dimensional data decoding device entropy decodes the occupancy code of the current node using the selected coding table (S 2115 ). 
     Finally, the three-dimensional data decoding device repeats a process of dividing each node into eight and decoding an occupancy code of the node, until the node cannot be divided (S 2116 ). In other words, steps S 2112  to S 2115  are recursively repeated. 
     Next, the following describes an example of selecting a coding table.  FIG.  145    is a diagram illustrating an example of selecting a coding table. For example, as in coding table  0  shown in  FIG.  145   , the same context mode may be applied to occupancy codes. Moreover, a different context model may be assigned to each occupancy code. Since this enables assignment of a context model in accordance with a probability of appearance of an occupancy code, it is possible to improve the coding efficiency. Furthermore, a context mode that updates a probability table in accordance with an appearance frequency of an occupancy code may be used. Alternatively, a context model having a fixed probability table may be used. 
     It should be noted that although the coding tables illustrated in  FIG.  119    and  FIG.  120    are used in the example shown in  FIG.  145   , the coding tables illustrated in  FIG.  122    and  FIG.  123    may be used instead. 
     Hereinafter, Variation 1 of the present embodiment will be described.  FIG.  146    is a diagram illustrating a reference relationship in the present variation. Although the three-dimensional data encoding device does not refer to the occupancy code of the parent neighbor node in the above-described embodiment, the three-dimensional data encoding device may switch whether to refer to an occupancy code of a parent neighbor node, according to a specific condition. 
     For example, when the three-dimensional data encoding device encodes an octree while scanning the octree breadth-first, the three-dimensional data encoding device encodes an occupancy code of a current node by reference to occupancy information of a node in a parent neighbor node. In contrast, when the three-dimensional data encoding device encodes the octree while scanning the octree depth-first, the three-dimensional data encoding device prohibits reference to the occupancy information of the node in the parent neighbor node. By appropriately selecting a referable node according to the scan order (encoding order) of nodes of the octree in the above manner, it is possible to improve the coding efficiency and reduce the processing load. 
     It should be noted that the three-dimensional data encoding device may append, to a header of a bitstream, information indicating, for example, whether an octree is encoded breadth-first or depth-first.  FIG.  147    is a diagram illustrating an example of a syntax of the header information in this case. octree_scan_order shown in  FIG.  147    is encoding order information (an encoding order flag) indicating an encoding order for an octree. For example, when octree_scan_order is 0, breadth-first is indicated, and when octree_scan_order is 1, depth-first is indicated. Since this enables the three-dimensional data decoding device to determine whether a bitstream has been encoded breadth-first or depth-first by reference to octree_scan_order, the three-dimensional data decoding device can appropriately decode the bitstream 
     Moreover, the three-dimensional data encoding device may append, to header information of a bitstream, information indicating whether to prohibit reference to a parent neighbor node.  FIG.  148    is a diagram illustrating an example of a syntax of the header information in this case. limit_refer_flag is prohibition switch information (a prohibition switch flag) indicating whether to prohibit reference to a parent neighbor node. For example, when limit_refer_flag is 1, prohibition of reference to the parent neighbor node is indicated, and when limit_refer_flag is 0, no reference limitation (permission of reference to the parent neighbor node) is indicated. 
     In other words, the three-dimensional data encoding device determines whether to prohibit the reference to the parent neighbor node, and selects whether to prohibit or permit the reference to the parent neighbor node, based on a result of the above determination. In addition, the three-dimensional data encoding device generates a bitstream including prohibition switch information that indicates the result of the determination and indicates whether to prohibit the reference to the parent neighbor node. 
     The three-dimensional data decoding device obtains, from a bitstream, prohibition switch information indicating whether to prohibit reference to a parent neighbor node, and selects whether to prohibit or permit the reference to the parent neighbor node, based on the prohibition switch information. 
     This enables the three-dimensional data encoding device to control the reference to the parent neighbor node and generate the bitstream. That also enables the three-dimensional data decoding device to obtain, from the header of the bitstream, the information indicating whether to prohibit the reference to the parent neighbor node. 
     Although the process of encoding an occupancy code has been described as an example of an encoding process in which reference to a parent neighbor node is prohibited in the present embodiment, the present disclosure is not necessarily limited to this. For example, the same method can be applied when other information of a node of an octree is encoded. For example, the method of the present embodiment may be applied when other attribute information, such as a color, a normal vector, or a degree of reflection, added to a node is encoded. Additionally, the same method can be applied when a coding table or a predicted value is encoded. 
     Hereinafter, Variation 2 of the present embodiment will be described. In the above description, as illustrated in  FIG.  138   , the example in which the three reference neighboring nodes are used is given, but four or more reference neighboring nodes may be used.  FIG.  149    is a diagram illustrating an example of a current node and neighboring reference nodes. 
     For example, the three-dimensional data encoding device calculates a coding table to be used when the three-dimensional data encoding device entropy encodes an occupancy code of the current node shown in  FIG.  149   , using the following equation. 
       CodingTable=(Flag X 0&lt;&lt;3)+(Flag X 1&lt;&lt;2)+(Flag Y&lt;&lt; 1)+(Flag Z ) 
     Here, CodingTable indicates a coding table for an occupancy code of a current node, and indicates one of values ranging from 0 to 15. FlagXN is occupancy information of neighboring node XN (N=0. . 1). FlaxXN indicates 1 when neighboring node XN includes a point cloud (is occupied), and indicates 0 when it does not. FlagY is occupancy information of neighboring node Y. FlagY indicates 1 when neighboring node Y includes a point cloud (is occupied), and indicates 0 when it does not. FlagZ is occupancy information of neighboring node Z. FlagZ indicates 1 when neighboring node Z includes a point cloud (is occupied), and indicates 0 when it does not. 
     At this time, when a neighboring node, for example, neighboring node X 0  in  FIG.  149   , is unreferable (prohibited from being referred to), the three-dimensional data encoding device may use, as a substitute value, a fixed value such as 1 (occupied) or 0 (unoccupied); 
       FIG.  150    is a diagram illustrating an example of a current node and neighboring reference nodes. As illustrated in  FIG.  150   , when a neighboring node is unreferable (prohibited from being referred to), occupancy information of the neighboring node may be calculated by reference to an occupancy code of a grandparent node of the current node. For example, the three-dimensional data encoding device may calculate FlagX 0  in the above equation using occupancy information of neighboring node GO instead of neighboring node X 0  illustrated in  FIG.  150   , and may determine a value of a coding table using calculated FlagX 0 . It should be noted that neighboring node G 0  illustrated in  FIG.  150    is a neighboring node occupancy or unoccupancy of which can be determined using the occupancy code of the grandparent node. Neighboring node X 1  is a neighboring node occupancy or unoccupancy of which can be determined using an occupancy code of a parent node. 
     Hereinafter, Variation 3 of the present embodiment will be described.  FIG.  151    and  FIG.  152    each are a diagram illustrating a reference relationship according to the present variation. Specifically,  FIG.  151    is a diagram illustrating a reference relationship in an octree structure, and  FIG.  152    is a diagram illustrating a reference relationship in a spatial region. 
     In the present variation, when the three-dimensional data encoding device encodes encoding information of a current node to be encoded (hereinafter referred to as current node  2 ), the three-dimensional data encoding device refers to encoding information of each node in a parent node to which current node  2  belongs. In other words, the three-dimensional data encoding device permits reference to information (e.g., occupancy information) of a child node of a first node, among neighboring nodes, that has the same parent node as a current node. For example, when the three-dimensional data encoding device encodes an occupancy code of current node  2  illustrated in  FIG.  151   , the three-dimensional data encoding device refers to an occupancy code of a node in the parent node to which current node  2  belongs, for example, the current node illustrated in  FIG.  151   . As illustrated in  FIG.  152   , the occupancy code of the current node illustrated in  FIG.  151    indicates, for example, whether each node in the current node neighboring current node  2  is occupied. Accordingly, since the three-dimensional data encoding device can select a coding table for the occupancy code of current node  2  in accordance with a more particular shape of the current node, the three-dimensional data encoding device can improve the coding efficiency. 
     The three-dimensional data encoding device may calculate a coding table to be used when the three-dimensional data encoding device entropy encodes the occupancy code of current node  2 , using the following equation, for example. 
       CodingTable=(Flag X 1&lt;&lt;5)+(Flag X 2&lt;&lt;4)+(Flag X 3&lt;&lt;3)+(Flag X 4&lt;&lt;2)+(Flag Y&lt;&lt; 1)+(Flag Z ) 
     Here, CodingTable indicates a coding table for an occupancy code of current node  2 , and indicates one of values ranging from 0 to 63. FlagXN is occupancy information of neighboring node XN (N=1.. 4). FlagXN indicates 1 when neighboring node XN includes a point cloud (is occupied), and indicates 0 when it does not. FlagY is occupancy information of neighboring node Y. FlagY indicates 1 when neighboring node Y includes a point cloud (is occupied), and indicates 0 when it does not. FlagZ is occupancy information of neighboring node Z. FlagZ indicates  1  when neighboring node Z includes a point cloud (is occupied), and indicates 0 when it does not. 
     It should be noted that the three-dimensional data encoding device may change a method of calculating a coding table, according to a node position of current node  2  in the parent node. 
     When reference to a parent neighbor node is not prohibited, the three-dimensional data encoding device may refer to encoding information of each node in the parent neighbor node. For example, when the reference to the parent neighbor node is not prohibited, reference to information (e.g., occupancy information) of a child node of a third node having a different parent node from that of a current node. In the example illustrated in  FIG.  150   , for example, the three-dimensional data encoding device obtains occupancy information of a child node of neighboring node X 0  by reference to an occupancy code of neighboring node X 0  having a different parent node from that of the current node. The three-dimensional data encoding device selects a coding table to be used for entropy encoding of an occupancy code of the current node, based on the obtained occupancy information of the child node of neighboring node X 0 . 
     As stated above, the three-dimensional data encoding device according to the present embodiment encodes information (e.g., an occupancy code) of a current node included in an N-ary tree structure of three-dimensional points included in three-dimensional data, where N is an integer greater than or equal to 2. As illustrated in  FIG.  136    and  FIG.  137   , in the encoding, the three-dimensional data encoding device permits reference to information (e.g., occupancy information) of a first node included in neighboring nodes spatially neighboring the current node, and prohibits reference to information of a second node included in the neighboring nodes, the first node having a same parent node as the current node, the second node having a different parent node from the parent node of the current node. To put it another way, in the encoding, the three-dimensional data encoding device permits reference to information (e.g., an occupancy code) of the parent node, and prohibits reference to information (e.g., an occupancy code) of another node (a parent neighbor node) in the same layer as the parent node. 
     With this, the three-dimensional data encoding device can improve coding efficiency by reference to the information of the first node included in the neighboring nodes spatially neighboring the current node, the first node having the same parent node as the current node. Besides, the three-dimensional data encoding device can reduce a processing amount by not reference to the information of the second node included in the neighboring nodes, the second node having a different parent node from the parent node of the current node. In this manner, the three-dimensional data encoding device can not only improve the coding efficiency but also reduce the processing amount. 
     For example, the three-dimensional data encoding device further determines whether to prohibit the reference to the information of the second node. In the encoding, the three-dimensional data encoding device selects whether to prohibit or permit the reference to the information of the second node, based on a result of the determining. Moreover, the three-dimensional data encoding device generates a bit stream including prohibition switch information (e.g., limit_refer_flag shown in  FIG.  148   ) that indicates the result of the determining and indicates whether to prohibit the reference to the information of the second node. 
     With this, the three-dimensional data encoding device can select whether to prohibit the reference to the information of the second node. In addition, a three-dimensional data decoding device can appropriately perform a decoding process using the prohibition switch information. 
     For example, the information of the current node is information (e.g., an occupancy code) that indicates whether a three-dimensional point is present in each of child nodes belonging to the current node. The information of the first node is information (the occupancy information of the first node) that indicates whether a three-dimensional point is present in the first node. The information of the second node is information (the occupancy information of the second node) that indicates whether a three-dimensional point is present in the second node. 
     For example, in the encoding, the three-dimensional data encoding device selects a coding table based on whether the three-dimensional point is present in the first node, and entropy encodes the information (e.g., the occupancy code) of the current node using the coding table selected. 
     For example, as illustrated in  FIG.  151    and  FIG.  152   , in the encoding, the three-dimensional data encoding device permits reference to information (e.g., occupancy information) of a child node of the first node, the child node being included in the neighboring nodes. 
     With this, since the three-dimensional data encoding device enables reference to more detailed information of a neighboring node, the three-dimensional data encoding device can improve the coding efficiency. 
     For example, as illustrated in  FIG.  138   , in the encoding, the three-dimensional data encoding device selects a neighboring node to be referred to from the neighboring nodes according to a spatial position of the current node in the parent node. 
     With this, the three-dimensional data encoding device can refer to an appropriate neighboring node according to the spatial position of the current node in the parent node. 
     For example, the three-dimensional data encoding device includes a processor and memory, and the processor performs the above process using the memory. 
     The three-dimensional data decoding device according to the present embodiment decodes information (e.g., an occupancy code) of a current node included in an N-ary tree structure of three-dimensional points included in three-dimensional data, where N is an integer greater than or equal to 2. As illustrated in  FIG.  136    and  FIG.  137   , in the decoding, the three-dimensional data decoding device permits reference to information (e.g., occupancy information) of a first node included in neighboring nodes spatially neighboring the current node, and prohibits reference to information of a second node included in the neighboring nodes, the first node having a same parent node as the current node, the second node having a different parent node from the parent node of the current node. To put it another way, in the decoding, the three-dimensional data decoding device permits reference to information (e.g., an occupancy code) of the parent node, and prohibits reference to information (e.g., an occupancy code) of another node (a parent neighbor node) in the same layer as the parent node. 
     With this, the three-dimensional data decoding device can improve coding efficiency by reference to the information of the first node included in the neighboring nodes spatially neighboring the current node, the first node having the same parent node as the current node. Besides, the three-dimensional data decoding device can reduce a processing amount by not reference to the information of the second node included in the neighboring nodes, the second node having a different parent node from the parent node of the current node. In this manner, the three-dimensional data decoding device can not only improve the coding efficiency but also reduce the processing amount. 
     For example, the three-dimensional data decoding device further obtains, from a bitstream, prohibition switch information (e.g., limit_refer_flag shown in  FIG.  148   ) indicating whether to prohibit the reference to the information of the second node. In the decoding, the three-dimensional data decoding device selects whether to prohibit or permit the reference to the information of the second node, based on the prohibition switch information. 
     With this, the three-dimensional data decoding device can appropriately perform a decoding process using the prohibition switch information. 
     For example, the information of the current node is information (e.g., an occupancy code) that indicates whether a three-dimensional point is present in each of child nodes belonging to the current node. The information of the first node is information (the occupancy information of the first node) that indicates whether a three-dimensional point is present in the first node. The information of the second node is information (the occupancy information of the second node) that indicates whether a three-dimensional point is present in the second node. 
     For example, in the decoding, the three-dimensional data encoding device selects a coding table based on whether the three-dimensional point is present in the first node, and entropy decodes the information (e.g., the occupancy code) of the current node using the coding table selected. 
     For example, as illustrated in  FIG.  151    and  FIG.  152   , in the decoding, the three-dimensional data decoding device permits reference to information (e.g., occupancy information) of a child node of the first node, the child node being included in the neighboring nodes. 
     With this, since the three-dimensional data decoding device enables reference to more detailed information of a neighboring node, the three-dimensional data decoding device can improve the coding efficiency. 
     For example, as illustrated in  FIG.  138   , in the decoding, the three-dimensional data decoding device selects a neighboring node to be referred to from the neighboring nodes according to a spatial position of the current node in the parent node. 
     With this, the three-dimensional data decoding device can refer to an appropriate neighboring node according to the spatial position of the current node in the parent node. 
     For example, the three-dimensional data decoding device includes a processor and memory, and the processor performs the above process using the memory. 
     Embodiment 13 
     Although the following mainly describes an operation of a three-dimensional data encoding device, a three-dimensional data decoding device may perform the same process. 
     In the present embodiment, in the case where the three-dimensional data encoding device encodes an inputted three-dimensional point cloud (a point cloud) using an octree structure, when the three-dimensional data encoding device repeats division until each leaf included in an octree has a single three-dimensional point, and performs encoding, the three-dimensional data encoding device appends, to a bitstream, mode information indicating whether each leaf of an octree includes a single three-dimensional point or one or more three-dimensional points. In addition, when the mode information is true (each leaf of the octree includes a single three-dimensional point), the three-dimensional data encoding device does not encode leaf information about the leaf, and when the mode information is false (each leaf of the octree includes one or more three-dimensional points), the three-dimensional data encoding device encodes the leaf information. 
     Here, the leaf information includes, for example, information indicating how many three-dimensional points a leaf includes, information indicating relative coordinates etc. of a three-dimensional point included in a leaf as illustrated in  FIG.  61    to  FIG.  67   , or both. Accordingly, since it is unnecessary to encode the leaf information for each leaf of the octree when the leaf includes a single three-dimensional point, it is possible to improve coding efficiency. When each leaf of the octree includes one or more three-dimensional points, the three-dimensional data encoding device appropriately encodes and appends the leaf information to the bitstream. This enables the three-dimensional data decoding device to correctly restore the one or more three-dimensional points included in the leaf using the leaf information; 
       FIG.  153    is a diagram illustrating an example of a syntax of header information of a bitstream according to the present embodiment. This header information is, for example, WLD, SPC, or VLM. single_point_per_leaf shown in  FIG.  153    is information indicating whether each leaf of an octree includes a single three-dimensional point or one or more three-dimensional points. Here, “each leaf of an octree includes a single three-dimensional point” means that all of the leaves included in the octree each include a single three-dimensional point (i.e., there is no leaf including two or more three-dimensional points). It should be noted that the octree here is, for example, a unit in which mode information is appended, and corresponds to, for example, WLD, SPC, or VLM. 
     Furthermore, “each leaf of an octree includes one or more three-dimensional points” means that at least one of the leaves included in the octree includes two or more three-dimensional points. In other words, some of the leaves may include two or more three-dimensional points, and the remaining leaves may each include a single three-dimensional point. 
     For example, that a value of mode information is 1 indicates each leaf including a single three-dimensional point, and that a value of mode information is 0 indicates each leaf including one or more three-dimensional points. It should be noted that even when all of the leaves included in the octree each include a single three-dimensional point, the three-dimensional data encoding device may set mode information (single_point_per_leaf) to 0; 
       FIG.  154    is a diagram illustrating a configuration example of an octree when mode information indicates 1. As illustrated in  FIG.  154   , when the mode information indicates 1, each leaf includes a single three-dimensional point.  FIG.  155    is a diagram illustrating a configuration example of an octree when mode information indicates 0. As illustrated in  FIG.  155   , when the mode information indicates 0, each leaf includes a single three-dimensional point or two or more three-dimensional points. 
     It should be noted that when a leaf includes two or more three-dimensional points, for example, coordinates of the at two or more three-dimensional points included in the leaf are different from each other. Alternatively, the coordinates of the at two or more three-dimensional points included in the leaf are identical, and pieces of attribute information, such as a color or a degree of reflection, (i.e., types of information) are mutually different. Alternatively, both the coordinates of the two or more three-dimensional points included in the leaf and the pieces of attribute information may be mutually different. 
     Next, an example of a syntax of leaf information will be described. It should be noted that although the example in which the mode information is appended to the header of the bitstream has been given above, the mode information need not be appended to the header, and standards or a profile or level etc. of standards may specify whether each leaf of the octree includes a single three-dimensional point or one or more three-dimensional points. In this case, the three-dimensional data decoding device can correctly restore the bitstream by, for example, determining whether each leaf of the octree includes a single three-dimensional point or one or more three-dimensional points, by reference to standards information included in the bitstream; 
       FIG.  156    is a diagram illustrating an example of a syntax of information of each node included in an octree. isleaf shown in  FIG.  156    is a flag indicating whether a node is a leaf. That isleaf is 1 indicates that a node is a leaf. That isleaf is 0 indicates that a node is not a leaf. 
     It should be noted that information indicating whether a node is a leaf need not be appended to a header. In this case, the three-dimensional data decoding device determines whether a node is a leaf using another method. For example, the three-dimensional data decoding device may determine whether each node of the octree is divided into the smallest possible size, and may determine that a node is a leaf when determining that each node is divided into the smallest possible size. This eliminates the need for encoding the flag indicating whether the node is the leaf, which makes it possible to reduce the code amount of the header. 
     num_point_per_leaf shown in  FIG.  156    is leaf information and indicates the number of three-dimensional points included in a leaf. num_point_per_leaf is encoded when single_point_per_leaf=0, and is not encoded when single_point_per_leaf=1. 
     It should be noted that the three-dimensional data encoding device may entropy encode num_point_per_leaf. At this time, the three-dimensional data encoding device may also perform encoding while switching coding tables. For example, the three-dimensional data encoding device may perform arithmetic coding on the first bit of num_point_per_leaf using coding table A, and may perform arithmetic coding on the remaining bits using coding table B. 
     As stated above, the three-dimensional data encoding device may append, to the header of the bitstream, the mode information indicating whether each leaf of the octree includes a single three-dimensional point or one or more three-dimensional points, and may select whether to encode the leaf information (the information indicating the number of three-dimensional points included in the leaf) according to the value of the mode information. Besides, the three-dimensional data encoding device may encode, as the leaf information, positional information of the single or one or more three-dimensional points included in the leaf. 
     It should be noted that the three-dimensional data encoding device may entropy encode single_point_per_leaf, isleaf, and num_point_per_leaf generated by the above method. For example, the three-dimensional data encoding device binarizes each value and performs arithmetic coding on the binarized value. 
     Although the octree structure has been given as an example in the present embodiment, the present disclosure is not necessarily limited to this. The aforementioned procedure may be applied to an N-ary tree structure such as a quadtree and a hexadecatree. 
     Moreover, when the three-dimensional data encoding device encodes, as the leaf information, pieces of positional information of two or more three-dimensional points in the same leaf, the three-dimensional data encoding device may also encode pieces of attribute information (color, degree of reflectance, etc.) of the two or more three-dimensional points. In this case, the pieces of positional information of the two or more three-dimensional points and the pieces of attribute information of the same may be associated with each other. For example, when the three-dimensional data encoding device encodes, as the leaf information, pieces of positional information of points A and B in the same leaf, the three-dimensional data encoding device may encode pieces of attribute information of points A and B and append the pieces of attribute information to a bitstream. In other words, the leaf information may include the positional information of point A, the attribute information of point A, the positional information of point B, and the attribute information of point B. The pieces of positional information of points A and B may be associated with the pieces of attribute information. 
     Moreover, the three-dimensional data encoding device may round off at least M pieces of positional information of at least M three-dimensional points in the same leaf, and may encode the at least M pieces of positional information as N pieces of positional information of N three-dimensional points, where N is less than M. In this case, the three-dimensional data encoding device may round off at least M pieces of attribute information of the at least M three-dimensional points by, for example, averaging to generate N pieces of attribute information, and may encode the N pieces of attribute information generated. For example, the three-dimensional data encoding device may round off the pieces of positional information of points A and B in the same leaf to a piece of positional information of one point, and may encode the piece of positional information. In this case, the three-dimensional data encoding device may round off the pieces of attribute information of points A and B by, for example, averaging to calculate a piece of attribute information of one point, and may encode the piece of attribute information calculated. 
     The following describes procedures performed by the three-dimensional data encoding device and three-dimensional data decoding device according to the present embodiment.  FIG.  157    is a flowchart of a three-dimensional data encoding process performed by the three-dimensional data encoding device according to the present embodiment. First, the three-dimensional data encoding device determines whether to perform encoding so that each leaf of an octree includes a single three-dimensional point or to perform encoding so that each leaf of the octree includes one or more three-dimensional points (S 2201 ). For example, the three-dimensional data encoding device may determine whether to perform encoding so that each leaf of the octree includes a single three-dimensional point or to perform encoding so that each leaf of the octree includes one or more three-dimensional points, according to whether to lossless encode an inputted three-dimensional point cloud. For example, when the three-dimensional data encoding device lossless encodes the inputted three-dimensional point cloud, the three-dimensional data encoding device determines to perform encoding so that each leaf of the octree includes a single three-dimensional point. Alternatively, the three-dimensional data encoding device may determine whether to perform encoding so that each leaf of the octree includes a single three-dimensional point or to perform encoding so that each leaf of the octree includes one or more three-dimensional points, according to whether all the coordinates of the inputted three-dimensional points are mutually different and whether to perform encoding so that each of the three-dimensional points is included in a different leaf. For example, when the three-dimensional points include three-dimensional points having the same coordinates, the three-dimensional data encoding device may determine to perform encoding so that each leaf of the octree includes one or more three-dimensional points. 
     When the three-dimensional data encoding device determines to perform encoding so that each leaf of the octree includes a single three-dimensional point (YES in S 2201 ), the three-dimensional data encoding device sets mode information to a value indicating that each leaf of the octree includes a single three-dimensional point (single_point_per_leaf=1), and appends the mode information to a header (S 2202 ). 
     When the three-dimensional data encoding device determines to perform encoding so that each leaf of the octree includes one or more three-dimensional points (NO in S 2201 ), the three-dimensional data encoding device sets mode information to a value indicating that each leaf of the octree includes one or more three-dimensional points (single_point_per_leaf=0), and appends the mode information to a header (S 2203 ). 
     Next, the three-dimensional data encoding device generates an octree structure by dividing a root node into an octree (S 2204 ). At this time, when the mode information indicates that each leaf of the octree is to include a single three-dimensional point, the three-dimensional data encoding device generates an octree in which each leaf of the octree includes a single three-dimensional point, and when the mode information indicates that each leaf of the octree is to include one or more three-dimensional points, the three-dimensional data encoding device generates an octree in which each leaf of the octree includes one or more three-dimensional points. 
     Then, the three-dimensional data encoding device selects a current node to be processed and determines whether the current node is a leaf (S 2205 ). When the current node is the leaf (YES in S 2205 ) and the mode information indicates that each leaf of the octree is to include one or more three-dimensional points (single_point_per_leaf=0) (YES in S 2206 ), the three-dimensional data encoding device encodes leaf information indicating, for example, the number of three-dimensional points included in the leaf (S 2207 ). 
     In contrast, when the current node is the leaf (YES in S 2205 ) and the mode information indicates that each leaf of the octree is to include a single three-dimensional point (single_point_per_leaf=1) (NO in S 2206 ), the three-dimensional data encoding device does not encode leaf information indicating, for example, the number of three-dimensional points included in the leaf. 
     When the current node is the leaf (NO in S 2205 ), the three-dimensional data encoding device encodes an occupancy code of the current node (S 2208 ). 
     When processing of all nodes is not completed (NO in S 2209 ), the three-dimensional data encoding device selects the next current node and performs step S 2205  and the subsequent steps on the selected current node. When the processing of all the nodes is completed (YES in S 2209 ), the three-dimensional data encoding device ends the process; 
       FIG.  158    is a flowchart of a three-dimensional data decoding process performed by the three-dimensional data decoding device according to the present embodiment. First, the three-dimensional data decoding device decodes mode information (single_point_per_leaf) in the header of a bitstream (S 2211 ). 
     Next, the three-dimensional data decoding device generates an octree of a space (nodes) using, for example, header information included in the bitstream (S 2212 ). For example, the three-dimensional data decoding device generates a large space (a root node) using the size of a space along the x-axis, y-axis, and z-axis directions appended to the header information. Subsequently, the three-dimensional data decoding device generates an octree by generating eight small spaces (nodes A 0  to A 7 ) by dividing the space into two along each of the x-axis, y-axis, and z-axis directions. In a similar way, the three-dimensional data decoding device divides each of nodes A 0  to A 7  into eight small spaces. Furthermore, the three-dimensional data decoding device performs decoding of an occupancy code of each node and decoding of leaf information in sequence through the process illustrated in  FIG.  158   . 
     Specifically, the three-dimensional data decoding device selects a current node to be processed and determines whether the current node is a leaf (S 2213 ). When the current node is the leaf (YES in S 2213 ) and the mode information indicates that each leaf of the octree is to include one or more three-dimensional points (single_point_per_leaf=0) (YES in S 2214 ), the three-dimensional data decoding device decodes leaf information indicating, for example, the number of three-dimensional points included in the leaf (S 2215 ). 
     In contrast, when the current node is the leaf (YES in S 2213 ) and the mode information indicates that each leaf of the octree is to include a single three-dimensional point (single_point_per_leaf=1) (NO in S 2214 ), the three-dimensional data decoding device does not decode leaf information indicating, for example, the number of three-dimensional points included in the leaf. 
     When the current node is not the leaf (NO in S 2213 ), the three-dimensional data decoding device decodes an occupancy code of the current node (S 2216 ). 
     When processing of all nodes is not completed (NO in S 2217 ), the three-dimensional data decoding device selects the next current node and performs step S 2213  and the subsequent steps on the selected current node. When the processing of all the nodes is completed (YES in S 2217 ), the three-dimensional data decoding device ends the process. 
     The following describes configurations of the three-dimensional data encoding device and three-dimensional data decoding device according to the present embodiment.  FIG.  159    is a block diagram illustrating a configuration of three-dimensional data encoding device  2200  according to the present embodiment. Three-dimensional data encoding device  2200  illustrated in  FIG.  159    includes octree generator  2201 , mode determiner  2202 , and entropy encoder  2203 . 
     Octree generator  2201  generates, for example, an octree from inputted three-dimensional points (a point cloud), and generates a corresponding one of an occupancy code and leaf information for each node included in the octree. Mode determiner  2202  determines whether to perform encoding so that each leaf of the octree includes a single three-dimensional point or to perform encoding so that each leaf of the octree includes one or more three-dimensional points, and generates mode information indicating a result of the determination. In other words, mode determiner  2202  sets a value of single_point_per_leaf. 
     Entropy encoder  2203  encodes the leaf information according to the mode information to generate a bitstream. Additionally, entropy encoder  2203  appends the leaf information (single_point_per_leaf) to the bitstream; 
       FIG.  160    is a block diagram illustrating a configuration of three-dimensional data decoding device  2210  according to the present embodiment. Three-dimensional data decoding device  2210  illustrated in  FIG.  160    includes octree generator  2211 , mode information decoder  2212 , and entropy decoder  2213 . 
     Octree generator  2211  generates an octree of a space (nodes) using, for example, header information of a bitstream. For example, octree generator  2211  generates a large space (a root node) using the size of a space along the x-axis, y-axis, and z-axis directions appended to the header information, and generates an octree by generating eight small spaces (nodes A 0  to A 7 ) by dividing the space into two along each of the x-axis, y-axis, and z-axis directions. In a similar way, octree generator  2211  divides each of nodes A 0  to A 7  into eight small spaces. As stated above, octree generator  2211  repeats the generation of an octree. 
     Mode information decoder  2212  decodes mode information (single_point_per_leaf) from the header information of the bitstream. It should be noted that mode information decoder  2212  may be included in entropy decoder  2213 . 
     Entropy decoder  2213  decodes an occupancy code and leaf information according to the mode information decoded, and generates three-dimensional points using the occupancy code and the leaf information decoded. 
     As stated above, the three-dimensional data encoding device according to the present embodiment performs the process illustrated in  FIG.  161   . First, the three-dimensional data encoding device appends, to a bitstream, first information (mode information) indicating whether a leaf to be included in an N-ary tree structure of three-dimensional points included in three-dimensional data is to include a single three-dimensional point or two or more three-dimensional points, where N is an integer greater than or equal to 2 (S 2221 ). In other words, the three-dimensional data encoding device encodes the first information. 
     When the first information indicates that the leaf is to include a single three-dimensional point (YES in S 2222 ), the three-dimensional data encoding device generates an N-ary tree structure in which a leaf includes a single three-dimensional point (S 2223 ), and encodes the N-ary tree structure (S 2224 ). 
     In contrast, when the first information indicates that the leaf is to include two or more three-dimensional points, the three-dimensional data encoding device generates an N-ary tree structure in which a leaf includes two or more three-dimensional points (S 2225 ), and encodes the N-ary tree structure (S 2226 ). 
     With this, the three-dimensional data encoding device can selectively use the tree structure in which the leaf includes a single three-dimensional point, and the tree structure in which the leaf includes two or more three-dimensional points. Accordingly, the three-dimensional data encoding device can improve the coding efficiency. 
     For example, when the first information indicates that the leaf is to include two or more three-dimensional points, the three-dimensional data encoding device appends second information about the leaf (leaf information). When the first information indicates that the leaf is to include a single three-dimensional point, the three-dimensional data encoding device appends no second information to the bitstream. 
     With this, the three-dimensional data encoding device can improve the coding efficiency by appending no second information to the bitstream when the leaf is to include a single three-dimensional point. 
     For example, the second information indicates a total number of three-dimensional points included in the leaf. 
     For example, the first information is commonly used by leaves. For example, the first information is commonly used by all or part of leaves to be included in an N-ary tree structure. In other words, the first information indicates whether each of leaves to be included in the N-ary tree structure is to include a single three-dimensional point or two or more three-dimensional points. When the first information indicates that each of the leaves is to include a single three-dimensional point, the three-dimensional data encoding device generates an N-ary tree structure in which each of leaves includes a single three-dimensional point, and encodes the N-ary tree structure. When the first information indicates that each of the leaves is to include two or more three-dimensional points, the three-dimensional data encoding device generates an N-ary tree structure in which each of leaves includes two or more three-dimensional points, and encodes the N-ary tree structure. 
     With this, since it is possible to control the formats of the leaves using the single first information, the three-dimensional data encoding device can improve the coding efficiency. 
     For example, the two or more three-dimensional points included in the leaf have mutually different space coordinates. In other words, the second information may show the coordinates of each of the two or more three-dimensional points included in the leaf. 
     For example, the two or more three-dimensional points included in the leaf have same space coordinates and mutually different attribute information. In other words, the second information may show the attribute information of each of the two or more three-dimensional points included in the leaf. 
     For example, each of the two or more three-dimensional points included in the leaf has coordinate information and attribute information. In other words, the second information may show the coordinates and the attribute information of each of the two or more three-dimensional points included in the leaf. 
     For example, the three-dimensional data encoding device includes a processor and memory, and the processor performs the above process using the memory. 
     The three-dimensional data decoding device according to the present embodiment performs the process illustrated in  FIG.  162   . First, the three-dimensional data decoding device decodes, from a bitstream, first information (mode information) indicating whether a leaf to be included in an N-ary tree structure of three-dimensional points included in three-dimensional data is to include a single three-dimensional point or two or more three-dimensional points, where N is an integer greater than or equal to 2 (S 2231 ). In other words, the three-dimensional data decoding device obtains the first information from the bitstream. 
     When the first information indicates that the leaf is to include a single three-dimensional point (YES in S 2232 ), the three-dimensional data decoding device decodes an N-ary tree structure in which a leaf includes a single three-dimensional point (S 2233 ). In contrast, when the first information indicates that the leaf is to include two or more three-dimensional points (NO in S 2232 ), the three-dimensional data decoding device decodes an N-ary tree structure in which a leaf includes two or more three-dimensional points (S 2234 ). Here, the phrase “to decode an N-ary tree structure in which a leaf includes a single three-dimensional point” means to parse information included in a bitstream based on a rule created on, for example, a premise that a leaf is to include only a single three-dimensional point. Likewise, the phrase “to decode an N-ary tree structure in which a leaf includes two or more three-dimensional points” means to parse information included in a bitstream based on a rule created on, for example, a premise that a leaf is to include two or more three-dimensional points. 
     With this, the three-dimensional data decoding device can selectively use the tree structure in which the leaf includes a single three-dimensional point, and the tree structure in which the leaf includes two or more three-dimensional points. Accordingly, the three-dimensional data decoding device can improve the coding efficiency. 
     For example, when the first information indicates that the leaf is to include two or more three-dimensional points, the three-dimensional data decoding device decodes (obtains), from the bitstream, second information about the leaf (leaf information). When the first information indicates that the leaf is to include a single three-dimensional point, the three-dimensional data decoding device decodes (obtains) no leaf information. 
     With this, since the second information need not be appended to the bitstream when the leaf is to include a single three-dimensional point, it is possible to improve the coding efficiency. 
     For example, the second information indicates a total number of three-dimensional points included in the leaf. 
     For example, the first information is commonly used by leaves. For example, the first information is commonly used by all or part of leaves to be included in an N-ary tree structure. In other words, the first information indicates whether each of leaves to be included in the N-ary tree structure is to include a single three-dimensional point or two or more three-dimensional points. When the first information indicates that each of the leaves is to include a single three-dimensional point, the three-dimensional data decoding device generates an N-ary tree structure in which each of leaves includes a single three-dimensional point, and decodes the N-ary tree structure. When the first information indicates that each of the leaves is to include two or more three-dimensional points, the three-dimensional data decoding device generates an N-ary tree structure in which each of leaves includes two or more three-dimensional points, and decodes the N-ary tree structure. 
     With this, since it is possible to control the formats of the leaves using the single first information, the three-dimensional data decoding device can improve the coding efficiency. 
     For example, the two or more three-dimensional points included in the leaf have mutually different space coordinates. In other words, the second information may show the coordinates of each of the two or more three-dimensional points included in the leaf. 
     For example, the two or more three-dimensional points included in the leaf have same space coordinates and mutually different attribute information. In other words, the second information may show the attribute information of each of the two or more three-dimensional points included in the leaf. 
     For example, each of the two or more three-dimensional points included in the leaf has coordinate information and attribute information. In other words, the second information may show the coordinates and the attribute information of each of the two or more three-dimensional points included in the leaf. 
     For example, the three-dimensional data decoding device includes a processor and memory, and the processor performs the above process using the memory. 
     Embodiment 14 
     In the present embodiment, a three-dimensional data encoding device expresses an occupancy code using a 1-bit occupied position and a remaining bit, and encodes each of the 1-bit occupied position and the remaining bit using a different method. 
     A 1-bit occupied position indicates a bit position at which 1 appears first when each bit included in an occupancy code is scanned from the left. For example, a 1-bit occupied position takes a value from 0 to 7 for an octree, and takes a value from 0 to 15 for a hexadecatree. 
     A remaining bit indicates part of a bit sequence located on the right side of a 1-bit occupied position of an occupancy code. The remaining bit has the number of bits ranging from 0 to 7 according to the 1-bit occupied position; 
       FIG.  163    is a diagram illustrating examples of a 1-bit occupied position and a remaining bit generated from an occupancy code. In the example shown by (a) in  FIG.  163   , the occupancy code is 01000010. Since 1 appears first at the sixth bit when this occupancy code is scanned from the left, the 1-bit occupied position is 6 and the remaining bit is 000010. In the example shown by (b) in  FIG.  163   , the occupancy code is 00000010. Since 1 appears first at the first bit when this occupancy code is scanned from the left, the 1-bit occupied position is 1 and the remaining bit is 0. In the example shown by (c) in  FIG.  163   , the occupancy code is 00000001. Since 1 appears first at the zeroth bit when this occupancy code is scanned from the left, the 1-bit occupied position is 0 and the remaining bit is absent. 
     Hereinafter, an example of a method of encoding a 1-bit occupied position will be described. In the event of an octree, the three-dimensional data encoding device entropy encodes a 1-bit occupied position as a 3-bit value (0 to 7). The three-dimensional data encoding device performs, for example, arithmetic encoding on the 1-bit occupied position using one coding table. It should be noted that the three-dimensional data encoding device may perform binary encoding (binary arithmetic encoding) one bit at a time on the 1-bit occupied position that is a 3-bit bit sequence. The three-dimensional data encoding device may set a probability of occurrence of 0 and a probability of occurrence of 1 to 50% in a coding table in this case. For example, the three-dimensional data encoding device may apply a bypass mode in binary arithmetic encoding. 
     Next, an example of a method of encoding a remaining bit will be described. For example, regarding a remaining bit as a binary bit sequence, the three-dimensional data encoding device performs binary coding on bits in order from the left to the right. For example, when a remaining bit is 000010, the three-dimensional data encoding device may perform arithmetic encoding on values of 0 and 1 in order of 0→0→0→0→1→0. 
     For example, in the example shown by (a) in  FIG.  163   , the three-dimensional data encoding device performs arithmetic encoding on a value of 6 at the 1-bit occupied position. For example, the three-dimensional data encoding device may perform arithmetic encoding on a bit sequence of 110 indicating the value of 6, using the bypass mode. The three-dimensional data encoding device also performs arithmetic encoding on a bit sequence of 000010 of the remaining bit. 
     Moreover, in the example shown by (b) in  FIG.  163   , the three-dimensional data encoding device performs arithmetic encoding on a value of 1 at the 1-bit occupied position. For example, the three-dimensional data encoding device may perform arithmetic encoding on a bit sequence of 1 indicating the value of 1, using the bypass mode. The three-dimensional data encoding device also performs arithmetic encoding on a bit sequence of 0 of the remaining bit. 
     Furthermore, in the example shown by (c) in  FIG.  163   , the three-dimensional data encoding device performs arithmetic encoding on a value of 0 at the 1-bit occupied position. For example, the three-dimensional data encoding device may perform arithmetic encoding on a bit sequence of 0 indicating the value of 0, using the bypass mode. Since the remaining bit is absent, the three-dimensional data encoding device encodes no remaining bit. 
     It should be noted that a 1-bit occupied position may be defined as a bit position at which 1 appears first when each bit of an occupancy code is scanned from the right. In this case, a remaining bit indicates part of a bit sequence located on the left side of the 1-bit occupied position of the occupancy code. Also, in this case, the three-dimensional data encoding device may perform binary coding on the remaining bit in order from the right to the left. In addition, the three-dimensional data encoding device may encode a switch flag for switching between scanning each bit of the occupancy code from the right and scanning each bit of the occupancy code from the left. The three-dimensional data encoding device may encode the switch flag for each occupancy code. Accordingly, it is possible to change a scan order for each occupancy code. Additionally, the three-dimensional data encoding device may add the switch flag to the header of a world, the header of a space, or the header of a volume, etc. and change a scan order on a world, space, or volume basis. 
     It should be noted that the scan order may be a predetermined order. In addition, a bit position at which 0 appears first may be used instead of the bit position at which  1  appears first in the scan order. 
     Moreover, an occupancy code in which only a 1 bit among bits included in the occupancy code has a value of 1 is defined as a 1-bit occupied code. For example, in the event of the octree, the occupancy code “0010000” is a 1-bit occupied code, but the occupancy code “0010001” is not a 1-bit occupied code. 
     The three-dimensional data encoding device may determine whether a current occupancy code to be encoded is likely to be a 1-bit occupied code. Then, the three-dimensional data encoding device may encode the current occupancy code in a form of the 1-bit occupied position and a remaining bit (hereinafter referred to as occupied position encoding) when determining that the current occupancy code is likely to be the 1-bit occupied code, and may encode a value of the current occupancy code (hereinafter referred to as direct encoding) directly when determining that the current occupancy code is not likely to be the 1-bit occupied code. 
     For example, the three-dimensional data encoding device determines whether a current occupancy code is likely to be a 1-bit occupied code using a value of an occupancy code of a parent node of a current node. For example, the three-dimensional data encoding device determines whether the occupancy code of the parent node is a 1-bit occupied code; performs occupied position encoding on a occupancy code of a current node when determining that the occupancy code of the parent node is the 1-bit occupied code; and performs direct encoding on the occupancy code of the current node when determining that the occupancy code of the parent node is not the 1-bit occupied code. 
     Here, in the case where occupied position encoding is performed when the current occupancy code of the current node is likely to be a 1-bit occupied code, a value of each bit of the remaining bit tends to be 0. Accordingly, it is possible to improve the coding efficiency by performing binary arithmetic encoding on the remaining bit. In addition, the three-dimensional data encoding device can efficiently determine whether the current occupancy code is likely to be a 1-bit occupied code, based on whether the occupancy code of the parent node is a 1-bit occupied code. Additionally, in the event of not a breadth-first coding order but a depth-first coding order, it is possible to apply the same determination method by reference to the occupancy code of the parent node; 
       FIG.  164    is a diagram schematically illustrating the above-mentioned process. As illustrated in  FIG.  164   , when the occupancy code of the parent node is a 1-bit occupied code, the three-dimensional data encoding device performs occupied position encoding on the current node. Moreover, when the occupancy code of the parent node is a non-1-bit occupied code (not a 1-bit occupied code), the three-dimensional data encoding device performs direct encoding on the current node. 
     Next, an example of a syntax of information of a node will be described.  FIG.  165    is a diagram illustrating an example of a syntax of information of a node. 
     As illustrated in  FIG.  165   , the node information includes 1 bit_occupied_position and remaining_bit. 1 bit_occupied_position is the above-mentioned 1-bit occupied position and indicates a bit position at which 1 appears first when each bit of an occupancy code is scanned from the left. For example, the 1-bit occupied position takes a value from 0 to 7 for the octree, and takes a value from 0 to 15 for the hexadecatree. 
     remaining_bit is the above-mentioned remaining bit and indicates part of a bit sequence located on the right side of the 1-bit occupied position of the occupancy code. Since a remaining bit is absent when a 1-bit occupied position (1 bit_occupied_position) is 0, remaining_bit need not be encoded as illustrated in  FIG.  165   . Moreover, regarding remaining_bit as a binary bit sequence, the three-dimensional data encoding device may perform binary coding on bits in order from the left to the right. Furthermore, the three-dimensional data encoding device may perform arithmetic encoding on a decimal value calculated from the bit sequence of remaining_bit, using a coding table. For example, when a bit sequence of a remaining bit is 000010, the three-dimensional data encoding device may perform arithmetic encoding on a value of 2. 
     When an occupancy code (parent_occupancy_code) of a parent node is not a 1-bit occupied code, the three-dimensional data encoding device may perform direct encoding on the occupancy code. For example, the three-dimensional data encoding device may perform arithmetic encoding on an occupancy code using one coding table. 
     It should be noted that although the octree structure has been described as an example in the present embodiment, the present disclosure is not necessarily limited to this. The aforementioned procedure may be applied to an N-ary tree such as the quadtree and the hexadecatree, or other tree structures, where N is an integer greater than or equal to 2. For example, 1 bit_occupied_position takes a value from 0 to 3 for the quadtree, and 1_bit_occupied_position takes a value from 0 to 15 for the hexadecatree. The three-dimensional data encoding device may encode, as a 2-bit occupied position (2 bit_occupied_position), a position at which 1 appears second when a bit sequence scanned, in addition to a 1-bit occupied position; and may encode part of the bit sequence after the 2-bit occupied position as a remaining bit. Additionally, the three-dimensional data encoding device may encode, for example, as a N-bit occupied position (Nbit_occupied_position), a position at which 1 appears for the nth time when a bit sequence is scanned; and may encode part of the bit sequence after the N-bit occupied position as a remaining bit. 
     In the present embodiment, when an occupancy code of a current node is likely to be a 1-bit occupied code, the three-dimensional data encoding device performs occupied position encoding. In other words, the three-dimensional data encoding device performs arithmetic encoding on, as a 1-bit occupied position, a bit position including values each of which is 1 with a random probability, using, for example, coding table A; and performs arithmetic encoding on, as a remaining bit, a remaining bit sequence including values each of which tends to be 0, using, for example, coding table B. It is possible to improve the coding efficiency by representing the occupancy code in different forms and using different coding tables for arithmetic encoding in such a manner. For example, the three-dimensional data encoding device can perform arithmetic encoding on a bit sequence of a remaining bit while keeping a probability of occurrence of values of 0 high, using coding table B. Even when an original bit sequence of the remaining bit has a great length, the three-dimensional data encoding device can reduce the number of bits in encoded data as a result. 
     Each bit of a 1-bit occupied code tends to be a value of 1 with a random probability. As a result, the three-dimensional data encoding device may perform arithmetic encoding on the 1-bit occupied code using a bypass mode that skips calculating an occurrence probability by setting a probability of occurrence of 0 and a probability of occurrence of 1 to 50%. Accordingly, it is possible to reduce the amount of processing. 
     It should be note that a three-dimensional data decoding device may determine whether occupied position encoding or direct encoding has been performed, through the same process as the three-dimensional data encoding device. Alternatively, the three-dimensional data encoding device may generate a bitstream including information indicating whether occupied position encoding or direct encoding has been performed, and the three-dimensional data decoding device may determine whether occupied position encoding or direct encoding has been performed, based on the information included in the bitstream. In this case, the three-dimensional data encoding device may also refer not to an occupancy code of a parent node but to a current occupancy code, perform occupied position encoding when the current occupancy code is a 1-bit occupied code, and perform direct encoding when the current occupancy code is not the 1-bit occupied code. 
     Also, although an example in which occupied position encoding and direct encoding are switched on a node basis has been described in the present embodiment, the present disclosure is not limited to this. For example, the three-dimensional data encoding device may add, to the header of a world or the header of a space, etc., a flag indicating whether to perform occupied position encoding; and may select whether to perform occupied position encoding on a world or space etc. basis. For example, for a world or a space including many sparse three-dimensional point clouds, the three-dimensional data encoding device may set the flag to ON and perform occupied position encoding on all occupancy codes of the three-dimensional point clouds in the world or the space. In addition, for a world or a space including many dense three-dimensional point clouds, the three-dimensional data encoding device may set the flag to OFF and perform direct encoding on all occupancy codes of the three-dimensional data point clouds in the world or the space. This eliminates the need for determining selection for each node, and it is thus possible to reduce the amount of processing. 
     Since the three-dimensional data decoding device can decode the flag included in the header such as the world or the space to determine whether occupied position encoding or direct encoding has been performed on the occupancy code in the world or the space, the three-dimensional data decoding device can decode the occupancy code appropriately. 
     The three-dimensional data encoding device may perform occupied position encoding when an occupancy code of a current node is likely to be a N-bit occupied code in which the number of bits having a value of 1 included in the occupancy code is less than or equal to N (any integer), and may perform direct encoding when the occupancy code of the current node is not likely to be the N-bit occupied code. For example, the three-dimensional data encoding device may perform occupied position encoding when an occupancy code of a parent node is a N-bit occupied code, and may perform direct encoding when the occupancy code of the parent node is not the N-bit occupied code. 
     Hereinafter, a processing flow in the three-dimensional data encoding device will be described.  FIG.  166    is a flowchart of a three-dimensional data encoding process performed by the three-dimensional data encoding device according to the present embodiment. 
     First, the three-dimensional data encoding device determines whether an occupancy code of a parent node of a current node is a 1-bit occupied code (S 2301 ). When the occupancy code of the parent node is the 1-bit occupied code (YES in S 2301 ), the three-dimensional data encoding device performs occupied position encoding on a current occupancy code of the current node (S 2302 ). 
     Specifically, the three-dimensional data encoding device searches for a 1-bit occupied position in the current occupancy code (S 2304 ), and encodes the obtained 1-bit occupied position (S 2305 ). Then, the three-dimensional data encoding device calculates a remaining bit (S 2306 ) and encodes the obtained remaining bit (S 2307 ). 
     On the other hand, when the occupancy code of the parent node is not the 1-bit occupied code (NO in S 2301 ), the three-dimensional data encoding device performs direct encoding on the current occupancy code (S 2303 ). 
     It should be noted that the order of the steps included in the occupied position encoding step (S 2302 ) may be rearranged. For example, the three-dimensional data encoding device may search for a 1-bit occupied position (S 2304 ), calculate a remaining bit (S 2306 ), and then encode the 1-bit occupied position and the remaining bit (S 2305 , S 2307 ); 
       FIG.  167    is a flowchart illustrating a specific example of the occupied position encoding step (S 2302 ). First, the three-dimensional data encoding device calculates a 1-bit occupied position (S 2304 ). Specifically, the three-dimensional data encoding device sets variable a to 7 (S 2311 ). Next, the three-dimensional data encoding device sets occupancy code − 2   a  to variable Diff (S 2312 ). Then, the three-dimensional data encoding device determines whether Diff&gt;−1 is satisfied (S 2313 ). 
     When Diff&gt;−1 is not satisfied (NO in S 2313 ), the three-dimensional data encoding device sets a−1 to variable a (S 2314 ). When Diff&gt;−1 is satisfied (YES in S 2313 ), the three-dimensional data encoding device sets a to a 1-bit occupied position and Diff to a remaining bit (S 2315 ). 
     After that, the three-dimensional data encoding device encodes the calculated 1-bit occupied position (S 2305 ). 
     Next, the three-dimensional data encoding device calculates a remaining bit (S 2306 ) and performs binary coding on the remaining bit (S 2307 ). Specifically, the three-dimensional data encoding device sets 1-bit occupied position −1 to variable b (S 2321 ). Then, the three-dimensional data encoding device sets remaining bit −2 b  to variable Diff (S 2322 ). After that, the three-dimensional data encoding device determines whether Diff&gt;−1 is satisfied (S 2323 ). 
     When Diff&gt;−1 is satisfied (YES in S 2323 ), the three-dimensional data encoding device encodes “1” and sets Diff to the remaining bit (S 2324 ), and sets b−1 to variable b (S 2326 ). On the other hand, when Diff&gt;−1 is not satisfied (NO in S 2323 ), the three-dimensional data encoding device encodes “0” (S 2325 ) and sets b−1 to variable b (S 2326 ). 
     Finally, the three-dimensional data encoding device determines whether b&lt;0 is satisfied (S 2327 ). When b&lt;0 is not satisfied (NO in S 2327 ), the three-dimensional data encoding device performs step S 2322  and the subsequent steps again. When b&lt;0 is satisfied (YES in S 2327 ), the three-dimensional data encoding device completes the process. 
     Hereinafter, a processing flow in the three-dimensional data decoding device will be described.  FIG.  168    is a flowchart of a three-dimensional data decoding process performed by the three-dimensional data decoding device according to the present embodiment. 
     First, the three-dimensional data decoding device determines whether an occupancy code of a parent node is a 1-bit occupied code (S 2331 ). When the occupancy code of the parent node is the 1-bit occupied code (YES in S 2331 ), the three-dimensional data decoding device performs occupied position decoding for decoding encoded data encoded by occupied position encoding (S 2332 ). 
     Specifically, the three-dimensional data decoding device decodes a 1-bit occupied position from a bitstream (S 2334 ); calculates part of an occupancy code (from the left end of the occupancy code to the 1-bit occupied position), based on the 1-bit occupied position (S 2335 ); and updates the occupancy code while decoding a remaining bit (S 2336 ). 
     On the other hand, when the occupancy code of the parent node is not the 1-bit occupied code (NO in S 2331 ), the three-dimensional data decoding device decodes the occupancy code from the bitstream using direct decoding for decoding an encoded occupancy code encoded by direct encoding (S 2333 ). 
     It should be noted that the order of the steps included in the occupied position decoding step (S 2332 ) may be rearranged. For example, the three-dimensional data decoding device may decode a 1-bit occupied position (S 2334 ), then update an occupancy code while decoding a remaining bit (S 2336 ), and finally add an occupancy code calculated from the 1-bit occupied position to the updated occupancy code (S 2335 ); 
       FIG.  169    is a flowchart illustrating a specific example of the occupied position decoding step (S 2332 ). First, the three-dimensional data decoding device decodes a 1-bit occupied position from a bitstream (S 2334 ) and calculates part of an occupancy code using the 1-bit occupied position (S 2335 ). 
     Specifically, the three-dimensional data decoding device sets the 1-bit occupied position to variable a (S 2341 ). Next, the three-dimensional data decoding device sets 2 a  to an occupancy code (S 2342 ). 
     Then, the three-dimensional data decoding device updates the occupancy code while decoding a remaining bit (S 2336 ). Specifically, the three-dimensional data decoding device sets a−1 to variable b (S 2351 ). Next, the three-dimensional data decoding device decodes a 1 bit and sets the decoded 1 bit to variable c (S 2352 ). Then, the three-dimensional data decoding device determines whether c==1 is satisfied (S 2353 ). 
     When c==1 is satisfied (YES in S 2353 ), the three-dimensional data decoding device adds 2 b  to the occupancy code (S 2354 ) and sets b−1 to variable b (S 2355 ). When c==1 is not satisfied (NO in S 2353 ), the three-dimensional data decoding device sets b−1 to variable b (S 2355 ). 
     Finally, the three-dimensional data decoding device determines whether b&lt;0 is satisfied (S 2356 ). When b&lt;0 is not satisfied (NO in S 2356 ), the three-dimensional data decoding device performs step S 2352  and the subsequent steps again. When b&lt;0 is satisfied (YES in S 2356 ), the three-dimensional data decoding device completes the process. 
     Next, a configuration example of the three-dimensional data encoding device will be described.  FIG.  170    is a block diagram of three-dimensional data encoding device  2300  according to the present embodiment. Three-dimensional data encoding device  2300  includes octree generator  2301  and entropy encoder  2302 . 
     Octree generator  2301  generates, for example, an octree from inputted three-dimensional points (a point cloud), and generates a corresponding one of an occupancy code and leaf information for each node of the octree. 
     Entropy encoder  2302  encodes the occupancy code of each node. Entropy encoder  2302  switches between occupancy code encoding methods according to whether an occupancy code of a parent node is a 1-bit occupied code. For example, when the occupancy code of the parent node is the 1-bit occupied code, entropy encoder  2302  performs occupied position encoding on the occupancy code; and when the parent node is not the 1-bit occupied code, entropy encoder  2302  performs arithmetic encoding on a value of the occupancy code using a coding table. 
     Next, a configuration example of the three-dimensional data decoding device will be described.  FIG.  171    is a block diagram of three-dimensional data decoding device  2310  according to the present embodiment. Three-dimensional data decoding device  2310  includes octree generator  2311  and entropy decoder  2312 . 
     Octree generator  2311  generates an octree of a space (a node) using, for example, header information of a bitstream. For example, octree generator  2311  generates a large space (a root node) using the size of a space along the x-axis, y-axis, and z-axis directions appended to the header information, and generates an octree by generating eight small spaces A (nodes A 0  to A 7 ) by dividing the space into two along each of the x-axis, y-axis, and z-axis directions. In a similar way, octree generator  2311  further divides each of nodes A 0  to A 7  into eight small spaces. As stated above, octree generator  2311  repeats the generation of an octree. 
     Entropy decoder  2312  decodes an occupancy code of each node. Entropy decoder  2312  switches between occupancy code decoding methods according to whether a decoded occupancy code of a parent node is a 1-bit occupied code. For example, when the decoded occupancy code of the parent node is the 1-bit occupied code, entropy decoder  2312  decodes the occupancy code using occupied position decoding; and when the parent node is not the 1-bit occupied code, entropy decoder  2312  performs arithmetic decoding on a value of the occupancy code using a coding table. 
     As stated above, the three-dimensional data encoding device according to the present embodiment performs the process illustrated in  FIG.  172   . First, the three-dimensional data encoding device generates a bit sequence (e.g., an occupancy code) including N-bit information that is information of a current node included in an N-ary tree structure of three-dimensional points included in three-dimensional data and that indicates whether a three-dimensional point is present in each of child nodes belonging to the current node, where N is an integer greater than or equal to 2 (S 2361 ). 
     Next, the three-dimensional data encoding device generates (i) position information indicating a head position (e.g., a 1-bit occupied position) that is a position at which a predetermined code appears first in the bit sequence when the bit sequence is scanned in a predetermined scan order, and (ii) a remaining bit that is part of the bit sequence after the head position in the predetermined scan order (S 2362 ). Here, for example, the predetermined code is 1. 
     Then, the three-dimensional data encoding device encodes the position information and the remaining bit as information of the current node (S 2363 ). In other words, the three-dimensional data encoding device generates, as the information of the current node, a bitstream including the position information and the remaining bit. 
     Accordingly, the three-dimensional data encoding device can improve the coding efficiency. 
     For example, the three-dimensional data encoding device has a first mode (e.g., occupied position encoding) for encoding the position information and the remaining bit and a second mode (e.g., direct encoding) for encoding the bit sequence, and selects one of the first mode and the second mode based on whether a peripheral node of the current node includes a three-dimensional point. 
     Accordingly, the three-dimensional data encoding device can improve the coding efficiency by selecting a mode according to a state of the peripheral three-dimensional point. 
     For example, the three-dimensional data encoding device selects the first mode when a total number of peripheral nodes each including a three-dimensional point among peripheral nodes of the current node or a proportion of the peripheral nodes each including a three-dimensional point to the peripheral nodes of the current node is less than a predetermined threshold value; and the three-dimensional data encoding device selects the second mode when the total number of the peripheral nodes or the proportion of the peripheral nodes is greater than the predetermined threshold value. 
     For example, the three-dimensional data encoding device selects one of the first mode and the second mode based on a bit sequence of a parent node of the current node. 
     For example, the three-dimensional data encoding device selects the first mode when a total number of child nodes each including a three-dimensional point among child nodes belonging to the parent node is less than a predetermined threshold value, the total number of the child nodes being indicated by the bit sequence of the parent node; and the three-dimensional data encoding device selects the second mode when the total number of the child nodes is greater than the predetermined threshold value. 
     For example, the three-dimensional data encoding device includes a processor and memory, and the processor performs the above process using the memory. 
     Moreover, the three-dimensional data decoding device according to the present embodiment performs the process illustrated in  FIG.  173   . First, the three-dimensional data decoding device decodes, from a bitstream, (i) position information indicating a head position (e.g., a 1-bit occupied position) that is a position at which a predetermined code appears first in a bit sequence (e.g., an occupancy code) when the bit sequence is scanned in a predetermined scan order, and (ii) a remaining bit that is part of the bit sequence after the head position in the predetermined scan order, the bit sequence including N-bit information that is information of a current node included in an N-ary tree structure of three-dimensional points included in three-dimensional data and that indicates whether a three-dimensional point is present in each of child nodes belonging to the current node, where N is an integer greater than or equal to 2 (S 2371 ). In other words, the three-dimensional data decoding device obtains, from the bitstream, the position information and the remaining bit. Additionally, for example, the predetermined code is 1. 
     Next, the three-dimensional data decoding device restores the bit sequence of the current node from the position information and the remaining bit (S 2372 ), and restores the N-ary tree structure using the bit sequence (S 2373 ). In other words, the three-dimensional data decoding device restores position information of three-dimensional points. 
     Accordingly, the three-dimensional data decoding device can improve the coding efficiency. 
     For example, the three-dimensional data decoding device has a first mode (occupied position decoding) for decoding the position information and the remaining bit and a second mode (direct decoding) for decoding the bit sequence, and selects one of the first mode and the second mode based on whether a peripheral node of the current node includes a three-dimensional point. 
     Accordingly, the three-dimensional data decoding device can improve the coding efficiency by selecting a mode according to a state of the peripheral three-dimensional point. 
     For example, the three-dimensional data decoding device selects the first mode when a total number of peripheral nodes each including a three-dimensional point among peripheral nodes of the current node or a proportion of the peripheral nodes each including a three-dimensional point to the peripheral nodes of the current node is less than a predetermined threshold value; and the three-dimensional data decoding device selects the second mode when the total number of the peripheral nodes or the proportion of the peripheral nodes is greater than the predetermined threshold value. 
     For example, the three-dimensional data decoding device selects one of the first mode and the second mode based on a bit sequence of a parent node of the current node. 
     For example, the three-dimensional data decoding device selects the first mode when a total number of child nodes each including a three-dimensional point among child nodes belonging to the parent node is less than a predetermined threshold value, the total number of the child nodes being indicated by the bit sequence of the parent node; and the three-dimensional data decoding device selects the second mode when the total number of the child nodes is greater than the predetermined threshold value. 
     For example, the three-dimensional data decoding device includes a processor and memory, and the processor performs the above process using the memory. 
     Embodiment 15 
     In the present embodiment, a three-dimensional data encoding device performs quantization on three-dimensional position information of an inputted three-dimensional point cloud, and encodes the three-dimensional position information using an octree structure. At this time, three-dimensional points (hereinafter referred to as duplicated points) occur that have the same three-dimensional position but have different attribute information such as a color or a degree of reflection due to quantization. The three-dimensional data encoding device appends, to a header, information for controlling how to encode these duplicated points as leaf information of an octree. As a result, a three-dimensional data decoding device can decode the leaf information correctly. Here, the expression “have the same three-dimensional position . . . due to quantization” includes a state in which, as with point A and point B illustrated in  FIG.  174   , original three-dimensional positions are close to each other and values of the three-dimensional positions become identical due to quantization of information of the three-dimensional positions. 
     For example, the three-dimensional data encoding device appends, to header information, a merge duplicated point flag (MergeDuplicatedPointFlag) that is a flag for controlling whether to merge duplicated points.  FIG.  175    is a diagram schematically illustrating a process according to a merge duplicated point flag. 
     When the merge duplicated point flag is 1, the three-dimensional data encoding device merges duplicated points into a point and encodes the point. Here, the term “merge” means, when, for example, point A and point B are duplicated points, keeping point A and removing point B or vice versa. It should be noted that, in such case, the three-dimensional data encoding device may calculate new attribute information from pieces of attribute information, such as a color or a degree of reflection, of point A and point B; and may assign the calculated attribute information to the merged point. For example, the three-dimensional data encoding device may assign an average value of the pieces of attribute information of point A and point B to the merged point. 
     Moreover, since each leaf when encoding is performed using the octree includes a single point when the merge duplicated point flag is 1, the three-dimensional data encoding device need not encode, as leaf information, information indicating how many three-dimensional points the leaf includes. The three-dimensional data encoding device may also encode three-dimensional position information of the single point in the leaf, and information regarding attribute information such as a color or a degree of reflection. 
     As stated above, when duplicated points are unnecessary after decoding, the three-dimensional data encoding device sets a merge duplicated point flag to 1, appends the merge duplicated point flag to a stream, merges the duplicated points, and encodes the merged point. Consequently, it is possible to reduce a data mount of the unnecessary duplicated points, thereby increasing the coding efficiency. 
     When the merge duplicated point flag is 0, the three-dimensional data encoding device encodes information of the duplicated points as leaf information. For example, since each leaf may include one or more duplicated points, the three-dimensional data encoding device encodes information indicating how many three-dimensional points the leaf includes. The three-dimensional data encoding device may also encode attribute information of each of the duplicated points. For example, when point A and point B are present as duplicated points in a leaf, the three-dimensional data encoding device may encode information indicating that two points are present in the leaf. In addition, the three-dimensional data encoding device may encode attribute information of each of point A and point B. 
     As stated above, when duplicated points are necessary after decoding, the three-dimensional data encoding device sets a merge duplicated point flag to 0, appends the merge duplicated point flag to a stream, and encodes the duplicated points. As a result, the three-dimensional data decoding device can decode information regarding the duplicated points correctly. 
     For example, as an example of quantization of a three-dimensional position, the three-dimensional data encoding device calculates a quantization position (x/qx, y/qy, z/qz) by dividing a three-dimensional position (x, y, z) by a quantization parameter (qx, qy, qz). 
     The merge duplicated point flag may be included in header information of a bitstream. For example, the merge duplicated point flag may be included in the header of a bitstream such as WLD, SPC, or VLM. 
     It should be noted that although examples of the attribute information include a color or a degree of reflection in the above description, the attribute information is not limited to this. For example, the attribute information may include a normal vector of a point, information indicating a degree of importance of a point, a three-dimensional feature of a point, or position information such as a latitude, a longitude, and an altitude of a point. 
     The term “merge” represents combining two or more points into a point. In addition, the term “merge” may represent combining M or more points into N points, where M&gt;N. 
     As stated above, duplicated points occur that have the same coordinates as a three-dimensional point cloud but has different attribute information such as a color or a degree of reflection due to quantization. For example, although point A and point B have different three-dimensional positions before quantization, there occurs a case in which point A and point B come to have the same three-dimensional position but have different attribute information due to quantization. In short, point A and point B are duplicated points. 
     It should be noted that the above case is not limited to quantization, and there is also a case in which duplicated points are caused to occur by a sensor such as LiDAR obtaining three-dimensional positions and attribute information of a point cloud of the same object at different times or in different directions. 
     The expression “have the same three-dimensional position” is not limited to a case in which three-dimensional positions are completely the same. For example, when a difference between three-dimensional positions of point A and point B is less than or equal to threshold value a, the three-dimensional data encoding device may regard point A and point B as having the same three-dimensional position and determine that point A and point B are duplicated points. In addition, the three-dimensional data encoding device may add threshold value a to a stream and notify the three-dimensional data decoding device that any point less than or equal to threshold value a has been handled as a duplicated point. 
     Moreover, the three-dimensional data encoding device may use the three-dimensional position of point A as a three-dimensional position of a duplicated point. Alternatively, the three-dimensional data encoding device may use the three-dimensional position of point B as a three-dimensional position of a duplicated point. Alternatively, the three-dimensional data encoding device may use, as a three-dimensional position of a duplicated point, a three-dimensional position calculated from the three-dimensional position of point A and the three-dimensional position of point B. For example, the three-dimensional data encoding device may use an average value between the three-dimensional position of point A and the three-dimensional position of point B. 
     The three-dimensional data encoding device may merge, among duplicated points, points having the same three-dimensional position and the same attribute information or may delete one of the points regardless of a value of a merge duplicated point flag. 
     When a merge duplicated point flag is 1, the three-dimensional data encoding device may merge M points in a leaf into N points, where M&gt;N. In this case, the three-dimensional data encoding device may encode, as leaf information, each of pieces of three-dimensional position information and pieces of attribute information of N points. In addition, the three-dimensional data encoding device may calculate N pieces of attribute information using M pieces of attribute information. 
     The three-dimensional data encoding device may add the number of points (N) in a leaf after merging to a header and notify the number of the points (N) to the three-dimensional data decoding device. A value of N may be set in advance as a fixed value by standards etc. This eliminates the need for adding information indicating N for each leaf, and it is thus possible to reduce a generated coding amount. Accordingly, the three-dimensional data decoding device can decode N points correctly. 
     When a merge duplicated point flag is 1, duplicated points are merged into a point. For example, the three-dimensional data encoding device may merge point A and point B into point C having the same three-dimensional position information as point A and point B. It should be noted that the three-dimensional data encoding device may assign, to point C, an average value of pieces of attribute information, such as a color or a degree of reflection, of point A and point B. Additionally, the three-dimensional data encoding device may merge point B with point A or merge point A with point B. 
     Next, an example of a syntax of a merge duplicated point flag will be described.  FIG.  176    is a diagram illustrating an example of a syntax of header information.  FIG.  177    is a diagram illustrating an example of a syntax of information of a node. 
     As illustrated in  FIG.  176   , the header information includes a merge duplicated point flag (MergeDuplicatedPointFlag). The merge duplicated point flag is information indicating whether to merge duplicated points. For example, a value of 1 of the merge duplicated point flag indicates that duplicated points are to be merged, and a value of 0 of the merge duplicated point flag indicates that duplicated points are not to be merged. 
     It should be noted that the three-dimensional data encoding device may specify whether to merge duplicated points, based on standards or a profile or level, etc. of standards, without appending a merge duplicated point flag to a header. This enables the three-dimensional data decoding device to determine whether a stream includes a duplicated point by reference to standards information, and to restore a bitstream correctly. 
     As illustrated in  FIG.  177   , the information of the node includes isleaf and num_point_per_leaf. isleaf is a flag indicating whether a current node is a leaf. A value of 1 indicates that a current node is a leaf, and a value of 0 indicates that a current node is not a leaf but a node. It should be noted that information indicating whether a node is a leaf need not be appended to a header. In this case, the three-dimensional data decoding device determines whether a node is a leaf using another method. For example, the three-dimensional data decoding device may determine whether each node of an octree is divided into the smallest possible size, and may determine that a node is a leaf when determining that each node is divided into the smallest possible size. This eliminates the need for encoding the flag indicating whether the node is the leaf, which makes it possible to reduce the code amount of the header. 
     num_point_per_leaf is leaf information and indicates the number of three-dimensional points included in a leaf. When a merge duplicated point flag is 0, num_point_per_leaf is encoded. Additionally, since the number of points in a leaf is 1 when a merge duplicated point flag is 1, num_point_per_leaf is not encoded. Accordingly, it is possible to reduce the code amount. 
     It should be noted that although whether to encode leaf information is selected directly according to a merge duplicated point flag in the example described here, whether to encode leaf information may be selected indirectly. For example, the three-dimensional data encoding device may change single_point_per_leaf illustrated in  FIG.  156    according to a merge duplicated point flag, and select whether to encode leaf information, based on the syntax illustrated in  FIG.  156   . In other words, when the merge duplicated point flag is 1, the three-dimensional data encoding device may set single_point_per_leaf to 1; and when the merge duplicated point flag is 0, the three-dimensional data encoding device may set single_point_per_leaf to 0. In this case, the three-dimensional data encoding device also need not append the merge duplicated point flag to a bitstream. 
     The three-dimensional data encoding device may entropy encode num_point_per_leaf. At this time, the three-dimensional data encoding device may also perform encoding while switching coding tables. For example, the three-dimensional data encoding device may perform arithmetic encoding on the first bit using coding table A, and may perform arithmetic encoding on a remaining bit using coding table B. 
     As stated above, the three-dimensional data encoding device appends, to the header of a bitstream, information indicating whether to merge duplicated points, and selects whether to merge the duplicated points according to the value. When merging the duplicated points, the three-dimensional data encoding device need not encode, as leaf information, the number of points included in a leaf. When not merging the duplicated points, the three-dimensional data encoding device may encode, as leaf information, the number of points included in a leaf. 
     The three-dimensional data encoding device may also entropy encode isleaf, MergeDuplicatedPointFlag, and num_point_per_leaf generated by the above method. For example, the three-dimensional data encoding device may binarize each value and perform arithmetic encoding on the value. 
     Although the octree structure has been described as an example in the present embodiment, the present disclosure is not necessarily limited to this. The aforementioned procedure may be applied to an N-ary tree such as the quadtree and the hexadecatree, or other tree structures, where N is an integer greater than or equal to 2. 
     When encoding is performed with a merge duplicated point flag=1, and an original inputted three-dimensional point cloud or quantized three-dimensional point cloud includes duplicated points, lossy coding is used, and it is thus possible to reduce the code amount. Besides, when the original inputted three-dimensional point cloud includes no duplicated point and encoding is performed using lossless coding (encoding is performed while skipping quantization), the three-dimensional data encoding device may perform encoding with the merge duplicated point flag=1. Accordingly, it is possible to reduce a code amount by as much as a code amount resulting from not encoding num_point_per_leaf while maintaining lossless coding. 
     Moreover, when the three-dimensional data encoding device encodes, as leaf information, each of two or more duplicated points in the same leaf, the three-dimensional data encoding device may also encode each of pieces of attribute information (e.g., a color or a degree of reflection) of the respective points. In this case, the pieces of attribute information of the respective points may be associated in a coding order of the points. For example, when the three-dimensional data encoding device encodes each of points A and B in the same leaf as leaf information, the three-dimensional data encoding device may encode pieces of attribute information of both points A and B and append the pieces of attribute information to a bitstream. Additionally, the pieces of attribute information may be associated in a coding order of points A and B. For example, when each three-dimensional position is encoded in order from point A to point B, it is conceivable that the pieces of attribute information are encoded in order from point A to point B and are associated. 
     Moreover, when the three-dimensional data encoding device merges M or more point clouds in the same leaf and encodes the merged point clouds as N points, where M&gt;N, the three-dimensional data encoding device may round off M or more pieces of attribute information of M or more point clouds by, for example, averaging to generate pieces of attribute information of N points, and may encode the pieces of attribute information. For example, when the three-dimensional data encoding device merges points A and B in the same leaf into a point and encodes the point, the three-dimensional data encoding device may round off pieces of attribute information of points A and B by, for example, averaging to calculate attribute information of the point, and may encode the calculated attribute information. 
     Moreover, the three-dimensional data encoding device may change a method of calculating attribute information according to a degree of importance or feature of a point. For example, the three-dimensional data encoding device may give a high weight to attribute information of a point having a high degree of importance or a point having a great feature, calculate a weighted average value, and use the calculated value as attribute information after merging. In addition, the three-dimensional data encoding device may change a weight according to a difference between three-dimensional positions before and after quantization. For example, a higher weight may be given as the difference is smaller, a weighted average value may be calculated, and the calculated value may be used as attribute information after merging. 
     Next, a procedure for a three-dimensional data encoding process performed by the three-dimensional data encoding device will be described.  FIG.  178    and  FIG.  179    each are a flowchart of a three-dimensional data encoding process performed by the three-dimensional data encoding device. 
     First, the three-dimensional data encoding device determines whether to merge duplicated points and perform encoding (S 2401 ). For example, when the three-dimensional data encoding device prioritizes the coding efficiency, the three-dimensional data encoding device may determine to merge duplicated points. When duplicated points are necessary in the three-dimensional data decoding device, the three-dimensional data encoding device may also determine not to merge the duplicated points. Moreover, when an inputted three-dimensional point cloud includes no duplicated point, and no lossless coding, that is, no quantization is performed, the three-dimensional data encoding device may set a merge duplicated point flag to 1. Since this prevents the number of points in a leaf from being encoded as leaf information, it is possible to reduce the code amount. 
     When the three-dimensional data encoding device merges the duplicated points and performs encoding (YES in S 2401 ), the three-dimensional data encoding device sets a merge duplicated point flag to 1 and appends the merge duplicated point flag to a header (S 2402 ). 
     When the three-dimensional data encoding device neither merges the duplicated points nor performs encoding (NO in S 2401 ), the three-dimensional data encoding device sets a merge duplicated point flag to 0 and appends the merge duplicated point flag to a header (S 2403 ). 
     Next, the three-dimensional data encoding device quantizes three-dimensional positions of an inputted three-dimensional point cloud (S 2404 ). 
     As an example of quantization of a three-dimensional position, the three-dimensional data encoding device calculates a quantization position (x/qx, y/qy, z/qz) by dividing a three-dimensional position (x, y, z) by a quantization parameter (qx, qy, qz). Additionally, the three-dimensional data encoding device may append the quantization parameter to the header, and the three-dimensional data decoding device may perform inverse quantization using the quantization parameter. It should be noted that the three-dimensional data encoding device may skip quantization at the time of lossless coding. 
     Then, the three-dimensional data encoding device determines whether the merge duplicated point flag is 1 (S 2405 ). When the merge duplicated point flag is 1 (YES in S 2405 ), the three-dimensional data encoding device merges duplicated points of the quantized three-dimensional point cloud (S 2406 ). It should be noted that when lossless coding is performed and the inputted three-dimensional point cloud includes no duplicated point, the three-dimensional data encoding device may skip this step. 
     When the merge duplicated point flag is 0 (NO in S 2405 ), the three-dimensional data encoding device merges no duplicated points. 
     After that, the three-dimensional data encoding device divides a node into an octree (S 2411 ). For example, the three-dimensional data encoding device may calculate an occupancy code of each node of an octree sequentially while performing octree division initially on a large space (a root node) including a quantized three-dimensional point cloud, and may encode the calculated occupancy code. In addition, the three-dimensional data encoding device may perform octree division repeatedly and encode leaf information when octree division cannot be performed. It should be noted that the three-dimensional data encoding device may calculate occupancy codes and pieces of leaf information of all nodes in advance, and then encode these pieces of information. 
     Next, the three-dimensional data encoding device determines whether the next node (a current node) is a leaf (S 2412 ). For example, the three-dimensional data encoding device may determine whether an octree is divided into the smallest possible size, and may determine that a node is a leaf when determining that the octree is divided into the smallest possible size. 
     When the current node is the leaf (YES in S 2412 ), the three-dimensional data encoding device determines whether a merge duplicated point flag is 0 (S 2413 ). When the merge duplicated point flag is 0 (YES in S 2413 ), the three-dimensional data encoding device encodes the number of three-dimensional points included in the leaf (num_point_per_leaf) (S 2414 ). When the merge duplicated point flag is 1 (NO in S 2413 ), the three-dimensional data encoding device does not encode the number of three-dimensional points included in the leaf (num_point_per_leaf). 
     Moreover, when the current node is not the leaf (NO in S 2412 ), the three-dimensional data encoding device encodes an occupancy code of the current node (S 2415 ). 
     Then, the three-dimensional data encoding device determines whether processing of all the nodes is completed (S 2416 ). When the processing of all the nodes is not completed (NO in S 2416 ), the three-dimensional data encoding device performs step S 2412  and the subsequent steps on the next node. 
     When the processing of all the nodes is completed (YES in S 2416 ), the three-dimensional data encoding device encodes attribute information regarding the encoded three-dimensional points (S 2417 ). 
     It should be noted that the three-dimensional data encoding device may adjust the size of the large space (the root node) along the x-axis, y-axis, or z-axis to a power-of-two size so that the large space can be always divided equally into two with respect to each axis. Besides, the three-dimensional data encoding device may adjust the size of the large space so that a divided node always becomes a cube. For example, when three-dimensional positions of three-dimensional point clouds take a value from 0 to 256 along the x-axis, a value from 0 to 120 along the y-axis, and a value from 0 to 62 along the z-axis, first, the three-dimensional data encoding device compares the minimum value and the maximum value of each axis and calculates the minimum value and the maximum value of coordinates of all the point clouds. In this case, the minimum value is 0, and the maximum value is 256. Next, the three-dimensional data encoding device calculates values that include the calculated minimum value and maximum value and enable the large space to have the power-of-two size. In this case, the size is 512, and the minimum value and maximum value of the coordinates in the space are 0 and 511, respectively. As a result, it is possible to include point clouds in a range of 0 to 256. In this case, the three-dimensional data encoding device also starts octree division initially on a large space having a size of 512×512×512. 
     Next, a procedure for a three-dimensional data decoding process performed by the three-dimensional data decoding device will be described.  FIG.  180    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 a merge duplicated point flag in the header of a bitstream (S 2421 ). 
     Next, the three-dimensional data decoding device divides a node into an octree (S 2422 ). For example, the three-dimensional data decoding device generates an octree of a space (a node) using header information etc. of a bitstream. For example, the three-dimensional data decoding device generates a large space (a root node) using the size of a space along the x-axis, y-axis, and z-axis directions appended to the header information, and generates an octree by generating eight small spaces A (nodes A 0  to A 7 ) by dividing the space into two along each of the x-axis, y-axis, and z-axis directions. In a similar way, the three-dimensional data decoding device further divides each of nodes A 0  to A 7  into eight small spaces. As stated above, the three-dimensional data decoding device performs decoding of an occupancy code of each node and decoding of leaf information in sequence through the above-mentioned process. 
     Then, the three-dimensional data decoding device determines whether the next node (a current node) is a leaf (S 2423 ). When the current node is the leaf (YES in S 2423 ), the three-dimensional data decoding device determines whether a merge duplicated point flag is 0 (S 2424 ). When the merge duplicated point flag is 0 (YES in S 2424 ), the three-dimensional data decoding device decodes the number of three-dimensional points included in the leaf (num_point_per_leaf) from the bitstream (S 2425 ). On the other hand, when the merge duplicated point flag is 1 (NO in S 2424 ), the three-dimensional data decoding device does not decode the number of three-dimensional points included in the leaf (num_point_per_leaf) from the bitstream. 
     Moreover, when the next node is not the leaf (NO in S 2423 ), the three-dimensional data decoding device decodes an occupancy code of the current node from the bitstream (S 2426 ). 
     After that, the three-dimensional data decoding device calculates three-dimensional positions of leaves using the decoded occupancy code and information about the number of times octree division is performed etc (S 2427 ). For example, when the large space has a size of 8×8×8, performing octree division three times causes a node to have a size of 1×1×1. This size (1×1×1) is the smallest divisible unit (leaf). Additionally, the three-dimensional data decoding device determines whether each leaf includes a point, based on a decoded occupancy code of a parent node of the leaf. Accordingly, the three-dimensional data decoding device can calculate a three-dimensional position of each leaf. 
     Next, the three-dimensional data decoding device inverse quantizes the calculated three-dimensional positions (S 2428 ). Specifically, the three-dimensional data decoding device calculates three-dimensional positions of a point cloud by performing inverse quantization using a quantization parameter decoded from the header. For example, as an example of inverse quantization of a three-dimensional position, the three-dimensional data decoding device calculates an inverse quantization position (x×qx, y×qy, z×qz) by multiplying a three-dimensional position (x, y, z) prior to inverse quantization by a quantization parameter (qx, qy, qz). It should be noted that the three-dimensional data decoding device may skip inverse quantization at the time of lossless coding. In addition, when a scale need not be returned to an original scale, the three-dimensional data decoding device may skip inverse quantization even at the time of no lossless coding (lossy coding). For example, when not an absolute positional relationship between three-dimensional points but a relative positional relationship between three-dimensional points is necessary, the three-dimensional data decoding device may skip inverse quantization. 
     Then, the three-dimensional data decoding device determines whether processing of all the nodes is completed (S 2429 ). When the processing of all the nodes is not completed (NO in S 2429 ), the three-dimensional data decoding device performs step S 2423  and the subsequent steps on the next node. 
     When the processing of all the nodes is completed (YES in S 2429 ), the three-dimensional data decoding device finally decodes attribute information regarding the decoded three-dimensional points from the bitstream (S 2430 ). It should be noted that when the merge duplicated point flag is 1, attribute information is associated with each point having a different decoded three-dimensional position after the decoding. Also, when the merge duplicated point flag is 0, different pieces of attribute information are decoded and associated with points having the same decoded three-dimensional position. 
     Next, a configuration example of the three-dimensional data encoding device will be described.  FIG.  181    is a block diagram of three-dimensional data encoding device  2400  according to the present embodiment. Three-dimensional data encoding device  2400  includes quantizer  2401 , octree generator  2402 , merge determiner  2403 , and entropy encoder  2404 . 
     Quantizer  2401  quantizes inputted three-dimensional points (a point cloud). It should be noted that in the event of lossless coding, quantization may be skipped. 
     Octree generator  2402  generates, for example, an octree from the inputted three-dimensional points (the point cloud), and generates a corresponding one of an occupancy code and leaf information for each node of the octree. 
     Merge determiner  2403  determines whether to merge duplicated points and perform encoding, and sets a value of a merge duplicated point flag, based on a result of the determination. For example, merge determiner  2403  determines the value of the merge duplicated point flag using information of a quantized three-dimensional point cloud. For example, merge determiner  2403  determines the value of the merge duplicated point flag, based on whether the quantized three-dimensional point cloud includes duplicated points. 
     Entropy encoder  2404  generates a bitstream by encoding the leaf information according to the merge duplicated point flag. Entropy encoder  2404  may append the merge duplicated point flag to the bitstream. Moreover, entropy encoder  2404  may encode the occupancy code. Furthermore, entropy encoder  2404  may encode attribute information regarding encoded three-dimensional points. 
     Next, a configuration example of the three-dimensional data decoding device will be described.  FIG.  182    is a block diagram of three-dimensional data decoding device  2410  according to the present embodiment. Three-dimensional data decoding device  2410  includes octree generator  2411 , merge information decoder  2412 , entropy decoder  2413 , and inverse quantizer  2414 . 
     Octree generator  2411  generates an octree of a space (a node) using, for example, header information of a bitstream. For example, octree generator  2411  generates a large space (a root node) using the size of a space along the x-axis, y-axis, and z-axis directions appended to the header information, and generates an octree by generating eight small spaces A (nodes A 0  to A 7 ) by dividing the space into two along each of the x-axis, y-axis, and z-axis directions. In a similar way, octree generator  2411  further divides each of nodes A 0  to A 7  into eight small spaces. As stated above, octree generator  2411  repeats the generation of an octree. 
     Merge information decoder  2412  decodes a merge duplicated point flag from the header information of the bitstream. It should be noted that merge information decoder  2412  may be included in entropy decoder  2413 . 
     Entropy decoder  2413  decodes leaf information according to information of the decoded merge duplicated point flag, and generates a three-dimensional point cloud (three-dimensional positions). It should be noted that entropy decoder  2413  may decode attribute information regarding decoded three-dimensional points. 
     Inverse quantizer  2414  performs inverse quantization on the three-dimensional positions of the decoded point cloud, and generates an output three-dimensional point cloud. It should be noted that in the event of lossless coding, inverse quantization may be skipped. In addition, when a scale need not be returned to an original scale, the three-dimensional data decoding device may skip inverse quantization even in the event of lossy coding. For example, when not an absolute positional relationship between three-dimensional points but a relative positional relationship between three-dimensional points is necessary, the three-dimensional data decoding device may skip inverse quantization. 
     Next, a variation of the three-dimensional data encoding process performed by the three-dimensional data encoding device will be described.  FIG.  183    is a flowchart of a variation of the three-dimensional data encoding process. 
     First, the three-dimensional data encoding device quantizes three-dimensional positions of an inputted three-dimensional point cloud (S 2441 ). For example, as an example of quantization of a three-dimensional position, the three-dimensional data encoding device calculates a quantization position (x/qx, y/qy, z/qz) by dividing a three-dimensional position (x, y, z) by a quantization parameter (qx, qy, qz). Additionally, the three-dimensional data encoding device may append the quantization parameter to a header, and the three-dimensional data decoding device may perform inverse quantization using the quantization parameter. It should be noted that the three-dimensional data encoding device may skip quantization at the time of lossless coding. 
     Next, the three-dimensional data encoding device determines whether the quantized three-dimensional point cloud includes duplicated points (S 2442 ). For example, the three-dimensional data encoding device compares pieces of three-dimensional position information of all three-dimensional point clouds, and makes the determination, based on whether there is the same value. Alternatively, the three-dimensional data encoding device may calculate a difference between all the pieces of three-dimensional position information, and determine that the quantized three-dimensional point cloud includes no duplicated point when an absolute value of the difference is greater than a predetermined threshold value. 
     When the three-dimensional point cloud includes the duplicated points (YES in S 2442 ), the three-dimensional data encoding device determines whether to merge the duplicated points and perform encoding (S 2443 ). For example, when the three-dimensional data encoding device prioritizes the coding efficiency, the three-dimensional data encoding device may determine to merge duplicated points. When duplicated points are necessary in the three-dimensional data decoding device, the three-dimensional data encoding device may also determine not to merge duplicated points. 
     When the three-dimensional point cloud includes no duplicated point (NO in S 2442 ) or the duplicated points are to be merged (YES in S 2443 ), the three-dimensional data encoding device sets a merge duplicated point flag to 1 and appends the merge duplicated point flag to a header (S 2444 ). In contrast, when the duplicated points are not to be merged (NO in S 2443 ), the three-dimensional data encoding device sets a merge duplicated point flag to 0 and appends the merge duplicated point flag to a header (S 2445 ). 
     After that, the three-dimensional data encoding device determines whether the merge duplicated point flag is 1 (S 2446 ). When the merge duplicated point flag is 1 (YES in S 2446 ), the three-dimensional data encoding device merges duplicated points of the quantized three-dimensional point cloud (S 2447 ). It should be noted that when lossless coding is performed and the inputted three-dimensional point cloud includes no duplicated point, the three-dimensional data encoding device may skip this step. When the merge duplicated point flag is 0 (NO in S 2446 ), the three-dimensional data encoding device does not merge duplicated points of the quantized three-dimensional point cloud. Subsequent steps are the same as those illustrated in  FIG.  179   . 
     As stated above, when a leaf included in an N-ary tree structure of three-dimensional points included in three-dimensional data includes two three-dimensional points, and a difference between three-dimensional positions of the two three-dimensional points is less than a predetermined threshold value, where N is an integer greater than or equal to 2, the three-dimensional data encoding device according to the present embodiment appends, to a bitstream, first information (e.g., a merge duplicated point flag) indicating whether to merge the two three-dimensional points; when the first information indicates that the two three-dimensional points are to be merged, the three-dimensional data encoding device merges the two three-dimensional points and encodes a merged three-dimensional point; and when the first information indicates that the two three-dimensional points are not to be merged, the three-dimensional data encoding device encodes each of the two three-dimensional points. 
     According to this configuration, the three-dimensional data encoding device can not only select whether to merge three-dimensional points but also notify the three-dimensional data decoding device whether three-dimensional points are merged. 
     For example, when the first information indicates that the two three-dimensional points are not to be merged, the three-dimensional data encoding device appends second information regarding the leaf (e.g., leaf information) to the bitstream; and when the first information indicates that the two three-dimensional points are to be merged, the three-dimensional data encoding device appends no leaf information to the bitstream. 
     For example, the second information indicates the number of three-dimensional points included in the leaf. 
     For example, the three-dimensional data encoding device quantizes three-dimensional positions of inputted three-dimensional points to generate three-dimensional positions of the three-dimensional points. 
     For example, the three-dimensional data encoding device includes a processor and memory, and the processor performs the above process using the memory. 
     When a leaf included in an N-ary tree structure of three-dimensional points included in three-dimensional data includes two three-dimensional points, and a difference between three-dimensional positions of the two three-dimensional points is less than a predetermined threshold value, where N is an integer greater than or equal to 2, the three-dimensional data decoding device according to the present embodiment decodes, from a bitstream, first information (e.g., a merge duplicated point flag) indicating whether the two three-dimensional points are merged; when the first information indicates that the two three-dimensional points are not merged, the three-dimensional data decoding device decodes second information regarding the leaf (e.g., leaf information) from the bitstream; and when the first information indicates that the two three-dimensional points are merged, the three-dimensional data decoding device decodes no leaf information from the bitstream. 
     For example, the second information indicates the number of three-dimensional points included in the leaf. 
     For example, the three-dimensional data decoding device restores three-dimensional positions of the three-dimensional points using the leaf information, and inverse quantizes the restored three-dimensional positions. 
     For example, the three-dimensional data decoding device includes a processor and memory, and the processor performs the above process using the memory. 
     It should be noted that the methods of the present embodiment may be applied even when duplicated points and non-duplicated points are present in a quantized leaf.  FIG.  184    is a diagram for illustrating this process. For example, as illustrated in  FIG.  184   , point A, point B, and point D are present in a leaf in a state prior to quantization. Quantization causes point A and point B to have the same three-dimensional position, and point A and point B become duplicated points. In contrast, since point D has a different three-dimensional position from the other points, point D does not become a duplicated point. Such a case occurs when octree division is not performed up to the smallest unit of division and a node in processing is encoded as a leaf. 
     In such a case, when a merge duplicated point flag (MergeDuplicatedPointFlag) is 0, the three-dimensional data encoding device encodes information indicating how many point clouds each leaf includes, position information of each point cloud, and attribute information of each point cloud. Here, position information may be absolute coordinates relative to a reference position of each point cloud or may include relative coordinates of points included in a leaf as described above. For example, the three-dimensional data encoding device may encode information indicating that a leaf includes point A, point B, and point D, position information of each of the points, and attribute information of each of the points. 
     Moreover, when a merge duplicated point flag is 1, the three-dimensional data encoding device merges duplicated points in a leaf. For example, the three-dimensional data encoding device merges point A and point B and encodes position information and attribute information after the merging. At this time, since point D is not merged, the three-dimensional data encoding device encodes position information and attribute information of point D separately. 
     Furthermore, the three-dimensional data encoding device may encode information indicating the number of points included in a leaf after merging. In an example illustrated in  FIG.  184   , since the three-dimensional data encoding device merges point A and point B into a point but does not merge point D, the three-dimensional data encoding device encodes the number of points included in the leaf as 2. 
     When a merge duplicated point flag is 1, the three-dimensional data encoding device may merge M duplicated points in a leaf into N points, where M&gt;N. In this case, the three-dimensional data encoding device may encode, as leaf information, each of pieces of three-dimensional position information and attribute information of N points and each of pieces of position information and attribute information of non-merged points. In addition, the three-dimensional data encoding device may calculate N pieces of attribute information using M pieces of attribute information. 
     Furthermore, the three-dimensional data encoding device may encode information indicating the number of points included in a leaf. In the example illustrated in  FIG.  184   , the three-dimensional data encoding device may encode information indicating the number of points included in a leaf as 3. Additionally, the three-dimensional data encoding device may encode pieces of position information and attribute information of all points. 
     Embodiment 16 
     In the present embodiment, a three-dimensional data encoding device obtains information of neighboring nodes each having a different parent node, by searching encoded nodes.  FIG.  185    is a diagram illustrating an example of neighboring nodes. In the example illustrated in  FIG.  185   , three neighboring nodes belong to the same parent node as a current node. The three-dimensional data encoding device obtains neighboring information of these three neighboring nodes by checking an occupancy code of the parent node. 
     Three remaining neighboring nodes each belong to a parent node different from the parent node of the current node. The three-dimensional data encoding device obtains neighboring information of these three neighboring nodes by checking information of encoded nodes. Here, neighboring information includes information indicating whether a node includes a point cloud (is occupied). In addition, an encoded node is, for example, a node belonging to the same layer as a current node in an octree; 
       FIG.  186    is a diagram illustrating an example of nodes to be searched. The three-dimensional data encoding device searches a search range including the encoded nodes illustrated in  FIG.  186    for information of a neighboring node.  FIG.  187    is a diagram for illustrating a search process for a neighboring node. As illustrated in  FIG.  187   , information of encoded nodes is stored in a queue. The three-dimensional data encoding device obtains information of a neighboring node by searching the queue from its head. For example, a search order for a queue is a coding order. 
     The three-dimensional data encoding device calculates an occupancy code of a current node by calculating information indicating whether child nodes are occupied. At this time, the three-dimensional data encoding device updates neighboring information of each child node. For example, the three-dimensional data encoding device determines whether a neighboring node having the same parent node as the current node is occupied, based on an occupancy code. Moreover, the three-dimensional data encoding device searches a queue that stores encoded node information for information indicating whether a neighboring node having a parent node different from the parent node of the current node is occupied, and determines whether the neighboring node having the parent node different from the parent node of the current node is occupied, based on the searched information. Furthermore, the three-dimensional data encoding device updates neighboring information of each child node, and stores the updated neighboring information into the queue to calculate a neighboring node of a child node for the next node. 
     In each searching, the three-dimensional data encoding device updates neighboring information of both a current node and a searched node.  FIG.  188    and  FIG.  189    each are a diagram for illustrating this update process. As illustrated in  FIG.  188   , in each searching, the three-dimensional data encoding device updates neighboring information of both a current node and a searched node. In other words, the neighboring information is transmitted in both directions. That the searched node is a neighboring node is added to information of the current node, and that the current node is a neighboring node is added to information of a neighboring node. 
     As illustrated in  FIG.  189   , in a search process, an immediately preceding current node can become a searched node. In this case, neighboring information of the immediately preceding current node is updated. 
     In order to ensure the longest processing time for hardware implementation, the three-dimensional data encoding device may complete a search process before a neighboring node is found.  FIG.  190    is a diagram for illustrating this operation. 
     As illustrated in  FIG.  190   , a search threshold value is predetermined that is a threshold value for stopping a search. This search threshold value indicates, for example, the number of searches performed on a queue from its head. 
     In an example illustrated in (1) of  FIG.  190   , a greater number of search steps than a search threshold value is required to search a queue for information of a neighboring node. In this example, the three-dimensional data encoding device performs a search up to the search threshold value and completes the search process. 
     In an example illustrated in (2) of  FIG.  190   , it is possible to search a queue for a neighboring node with a fewer number of search steps than the search threshold value. In this example, the three-dimensional data encoding device searches for the neighboring node and completes the search process. 
     As stated above, the three-dimensional data encoding device may provide a parameter (a search threshold value) for limiting the number of searches. By limiting the number of searches, it is possible to find a neighboring node while keeping a processing time for searching within a certain time. Additionally, the three-dimensional data encoding device may append, to the header etc. of a bitstream, information indicating a limiting value (a search threshold value) for the number of searches. Alternatively, the number of searches may be specified by standards etc. Accordingly, since a three-dimensional data decoding device can determine a limiting value for the number of searches from a header or requirements of standards, the three-dimensional data decoding device can decode a stream correctly. 
     Next, a specific example of a structure of a queue of encoded nodes will be described. In order to identify a neighborhood of a current node, each element of a queue of encoded nodes has an index in a three-dimensional space. Examples of this index include a Morton code; 
       FIG.  191    is a diagram illustrating an example of indexes for which Morton codes are used.  FIG.  192    is a diagram illustrating an example of a queue for which Morton codes are used. In the example illustrated in  FIG.  191   , the current node has an index of 3, the left node has an index of 2, and the lower node has an index of 1. It is possible to determine a neighboring node using the Morton codes as the indexes in the above manner. 
     The use of Morton codes produces the following effects. The first effect makes it possible to speed up a search process. Here, a search process in which x, y, z coordinates are used is more complex than a process of finding a Morton code that is a single integer. 
     The second effect makes it possible to reduce an amount of data to be held, by using Morton codes. Specifically, when x, y, z coordinates are used, three 32-bit data are required. In contrast, a node can be identified by one 64-bit data, by using Morton codes. 
     It should be noted that any method other than Morton codes may be used as a method of converting a three-dimensional position into an integer. For example, space-filling curve capable of converting a three-dimensional position into an integer, such as Hilbert curve, may be used. 
     Next, a configuration example of the three-dimensional data encoding device according to the present embodiment will be described.  FIG.  193    is a block diagram of three-dimensional data encoding device  2500  according to the present embodiment. Three-dimensional data encoding device  2500  includes octree generator  2501 , parent node information obtainer  2502 , encoding mode selector  2503 , searcher  2504 , geometry information calculator  2505 , coding table selector  2506 , and entropy encoder  2507 . 
     Octree generator  2501  generates, for example, an octree from inputted three-dimensional points (a point cloud), and generates an occupancy code for each node of the octree. 
     Parent node information obtainer  2502  obtains neighboring information of a neighboring node from an occupancy code of a parent node of a current node. In other words, parent node information obtainer  2502  obtains, for example, neighboring information of neighboring nodes that are, among neighboring nodes, neighboring nodes belonging to the same parent node as the current node and account for half of the neighboring nodes. 
     Encoding mode selector  2503  selects an encoding mode (a coding mode). For example, this encoding mode includes a mode for performing one of a search process and a process of obtaining neighboring information from an occupancy code of a parent node, and a mode for performing the both. 
     Searcher  2504  obtains neighboring information of a neighboring node through a search process, using information of encoded nodes. Although this search process requires some processing time, the search process makes it possible to obtain neighboring information of all neighboring nodes. 
     Geometry information calculator  2505  generates neighboring information (occupancy information of a neighboring node) to be used for selecting a coding table, by using one of the neighboring information obtained by parent node information obtainer  2502  and the neighboring information obtained by searcher  2504 , or by integrating the both. 
     Coding table selector  2506  selects a coding table to be used for entropy encoding, using the occupancy information of the neighboring node generated by geometry information calculator  2505 . 
     Entropy encoder  2507  generates a bitstream by entropy encoding an occupancy code of the current node using the selected coding table. It should be noted that entropy encoder  2507  may append, to the bitstream, information indicating the selected coding table. 
     Next, a configuration example of the three-dimensional data decoding device according to the present embodiment will be described.  FIG.  194    is a block diagram of three-dimensional data decoding device  2510  according to the present embodiment. Three-dimensional data decoding device  2510  includes octree generator  2511 , parent node information obtainer  2512 , decoding mode selector  2513 , searcher  2514 , geometry information calculator  2515 , coding table selector  2516 , and entropy decoder  2517 . 
     Octree generator  2511  generates an octree of a space (nodes) using header information etc. of a bitstream. For example, octree generator  2511  generates a large space (a root node) using the size of a space along the x-axis, y-axis, and z-axis directions appended to the header information, and generates an octree by generating eight small spaces A (nodes A 0  to A 7 ) by dividing the space into two along each of the x-axis, y-axis, and z-axis directions. In addition, nodes A 0  to A 7  are set as a current node in sequence. 
     Parent node information obtainer  2512  obtains neighboring information of a neighboring node from an occupancy code of a parent node of a current node. In other words, parent node information obtainer  2512  obtains, for example, neighboring information of neighboring nodes that are, among neighboring nodes, neighboring nodes belonging to the same parent node as the current node and account for half of the neighboring nodes. 
     Decoding mode selector  2513  selects a decoding mode. For example, this decoding mode corresponds to the above encoding mode, and includes a mode for performing one of a search process and a process of obtaining neighboring information from an occupancy code of a parent node, and a mode for performing the both. 
     Searcher  2514  obtains neighboring information of a neighboring node through a search process, using information of decoded nodes. Although this search process requires some processing time, the search process makes it possible to obtain neighboring information of all neighboring nodes. 
     Geometry information calculator  2515  generates neighboring information (occupancy information of a neighboring node) to be used for selecting a coding table, by using one of the neighboring information obtained by parent node information obtainer  2512  and the neighboring information obtained by searcher  2514 , or by integrating the both. 
     Coding table selector  2516  selects a coding table to be used for entropy decoding, using the occupancy information of the neighboring node generated by geometry information calculator  2515 . 
     Entropy decoder  2517  generates three-dimensional points (a point cloud) by entropy decoding an occupancy code using the selected coding table. It should be noted that entropy decoder  2517  may obtain information of the selected coding table from the bitstream, and entropy decode an occupancy code of the current node using the coding table indicated by the information. 
     Each bit of an occupancy code (8 bits) included in a bitstream indicates whether a corresponding one of eight small spaces A (node A 0  to node A 7 ) includes a point cloud. Moreover, the three-dimensional data decoding device generates an octree by dividing small space node A 0  into eight small spaces B (node B 0  to node B 7 ), and calculates information indicating whether each node of small spaces B includes a point cloud, by decoding an occupancy code. As stated above, the three-dimensional data decoding device decodes an occupancy code of each node while generating an octree by dividing a large space into small spaces. 
     Hereinafter, procedures for a three-dimensional data encoding process and a three-dimensional data decoding process according to the present embodiment will be described.  FIG.  195    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 defines a space (a current node) including part or all of an inputted three-dimensional point cloud (S 2501 ). Next, the three-dimensional data encoding device generates eight small spaces (nodes) by dividing the current node into eight (S 2502 ). Then, the three-dimensional data encoding device generates an occupancy code of the current node according to whether each node includes a point cloud (S 2503 ). After that, the three-dimensional data encoding device calculates neighboring information of a neighboring node of the current node from an occupancy code of a parent node of the current node (S 2504 ). 
     Next, the three-dimensional data encoding device selects an encoding mode (S 2505 ). For example, the three-dimensional data encoding device selects an encoding mode for performing a search process. Then, the three-dimensional data encoding device obtains remaining neighboring information by searching for information of encoded nodes. In addition, the three-dimensional data encoding device generates neighboring information to be used for selecting a coding table, by integrating the neighboring information calculated in step S 2504  and the neighboring information obtained by the search process (S 2506 ). 
     After that, the three-dimensional data encoding device selects a coding table to be used for entropy encoding, based on the neighboring information generated in step S 2506  (S 2507 ). Next, the three-dimensional data encoding device entropy encodes the occupancy code of the current node using the selected coding table (S 2508 ). Finally, the three-dimensional data encoding device repeats a process of dividing each node into eight and encoding an occupancy code of each node until each node cannot be divided (S 2509 ). In other words, steps S 2502  to S 2508  are recursively repeated; 
       FIG.  196    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 defines a space (a current node) to be decoded, using header information of a bitstream (S 2511 ). Next, the three-dimensional data decoding device generates eight small spaces (nodes) by dividing the current node into eight (S 2512 ). Then, the three-dimensional data decoding device calculates neighboring information of a neighboring node of the current node from an occupancy code of a parent node of the current node (S 2513 ). 
     After that, the three-dimensional data decoding device selects a decoding mode corresponding to the above encoding mode (S 2514 ). For example, the three-dimensional data decoding device selects a decoding mode for performing a search process. Next, the three-dimensional data decoding device obtains remaining neighboring information by searching for information of decoded nodes. In addition, the three-dimensional data decoding device generates neighboring information to be used for selecting a coding table, by integrating the neighboring information calculated in step S 2513  and the neighboring information obtained by the search process (S 2515 ). 
     Then, the three-dimensional data decoding device selects a coding table to be used for entropy decoding, based on the neighboring information generated in step S 2515  (S 2516 ). After that, the three-dimensional data decoding device entropy decodes an occupancy code of the current node using the selected coding table (S 2517 ). Finally, the three-dimensional data decoding device repeats a process of dividing each node into eight and decoding an occupancy code of each node until each node cannot be divided (S 2518 ). In other words, steps S 2512  to S 2517  are recursively repeated. 
     The following describes an encoding mode (a decoding mode). An encoding mode includes at least one of (1) the first mode for skipping a search process, (2) the second mode for performing a search process and stopping the process at the above-mentioned search threshold value, or (3) the third mode for performing a search process and searching for all encoded (decoded) nodes. 
     In other words, the three-dimensional data decoding device may select, as an encoding mode, whether to skip a neighboring node search or to search for a neighboring node. Moreover, when the three-dimensional data encoding device searches for a neighboring node, the three-dimensional data encoding device may limit the number of searches to at most a predetermined threshold value. Furthermore, the three-dimensional data encoding device may append information indicating this threshold value to the header of a bitstream. Alternatively, the threshold value may be specified by standards etc. Additionally, the three-dimensional data encoding device may change the threshold value for each node. For example, the number of neighboring node candidates increases as a value of a layer of an octree increases (deepens). For this reason, the three-dimensional data encoding device may increase the threshold value as the value of the layer of the octree increases (deepens). A referable range may change for each layer to which nodes belong. In other words, a range for one or more referable neighboring nodes among neighboring nodes spatially neighboring a current node may vary according to a layer to which the current node belongs in a tree structure. Here, even when parameter values indicating a referable range set to a header etc. are identical, a space represented by a node decreases with a deeper layer. In other words, a range of a space in which nodes are referable may be absolutely narrower with a deeper layer. 
     Moreover, the three-dimensional data encoding device may append information indicating an encoding mode to the header of a bitstream. An encoding mode may be specified by standards etc. In consequence, since the three-dimensional data decoding device can determine a decoding mode (an encoding mode) from a decoded header or requirements of standards, the three-dimensional data decoding device can decode a stream correctly. 
     Furthermore, the three-dimensional data encoding device may encode an encoding mode for each node, and change an encoding mode for each node. For example, the three-dimensional data encoding device performs encoding using all encoding modes once, and determines an encoding mode most suitable for the three-dimensional data decoding device from a standpoint of coding efficiency and processing time. Then, the three-dimensional data encoding device may encode, for each node, information indicating the determined encoding mode. As a result, the three-dimensional data decoding device can decode a bitstream correctly by decoding the encoding mode encoded for each node. 
     Moreover, the three-dimensional data encoding device may encode an encoding mode for each set of predetermined nodes, and change an encoding mode on a set basis. It should be noted that a set of nodes is, for example, a set of nodes included in the same layer of an octree. 
     It should be noted that the three-dimensional data decoding device may also determine a decoding mode (an encoding mode) in the same manner. In other words, the three-dimensional data encoding device and the three-dimensional data decoding device may estimate an encoding mode for each node in the same manner, and select whether to search for a neighboring node for each node. As a result, the three-dimensional data encoding device and the three-dimensional data decoding device determine whether a current node requires a neighboring node search, search for the neighboring node when determining that the current node requires the neighboring node search, and skip the neighboring node search when determining that the current node requires no neighboring node search. In addition, it is not necessary to transmit information indicating an encoding mode. Accordingly, it is possible to reduce the amount of processing while improving the coding efficiency. 
     For example, the three-dimensional data encoding device and the three-dimensional data decoding device determine whether a current node requires a neighboring node search, from, for example, an occupancy code of a parent node. Here, when all of occupancy information of three neighboring nodes calculated from the occupancy code of the parent node are 1, there is a high possibility that other neighboring nodes are occupied. For this reason, in this case, the three-dimensional data encoding device and the three-dimensional data decoding device determine that a current node requires a neighboring node search. 
     Furthermore, the three-dimensional data encoding device and the three-dimensional data decoding device may determine whether a current node requires a neighboring node search, from a value of a layer of an octree. For example, when a layer has a small value (is close to a root node), there is a high possibility that octree division has not been performed sufficiently. For this reason, the three-dimensional data encoding device and the three-dimensional data decoding device may determine that neighboring nodes are likely to be occupied, and determine that a current node requires a neighboring node search. As stated above, the three-dimensional data encoding device and the three-dimensional data decoding device can perform encoding and decoding correctly while reducing the code amount, by estimating an encoding mode in the same manner. 
     Moreover, the three-dimensional data encoding device and the three-dimensional data decoding device may estimate an encoding mode (a decoding mode) for each set of predetermined nodes in the same manner, and change an encoding mode on a set basis. As a result, the three-dimensional data encoding device and the three-dimensional data decoding device determine whether the set of the nodes requires a neighboring node search, search for a neighboring node when determining that the set of the nodes requires the neighboring node search, and skip the neighboring node search when determining that the set of the nodes requires no neighboring node search. Accordingly, it is possible to reduce the amount of processing while improving the coding efficiency. 
     It should be noted that a set of nodes is, for example, a set of nodes included in the same layer of an octree. Since this enables the three-dimensional data encoding device and the three-dimensional data decoding device to select whether to search for a neighboring node for each layer, the three-dimensional data encoding device and the three-dimensional data decoding device can improve the coding efficiency while reducing the processing time. For example, when a layer has a small value (is close to a root node), there is a high possibility that octree division has not been performed sufficiently. For this reason, the three-dimensional data encoding device and the three-dimensional data decoding device may determine that neighboring nodes are likely to be occupied, and determine that a current node requires a neighboring node search. 
     Next, an example of a syntax of information etc. indicating an encoding mode will be described.  FIG.  197    is a diagram illustrating an example of a syntax of header information.  FIG.  198    is a diagram illustrating an example of a syntax of information of a node. 
     As illustrated in  FIG.  197   , header information includes coding_mode 1  and limit_num_of_search. coding_mode 1  is information indicating whether to search for a neighboring node. For example, a value of 0 indicates that a neighboring node is not to be searched for, a value of 1 indicates that a neighboring node is to be searched for for all nodes, and a value of 2 indicates that a neighboring node search is to be changed for each node. 
     It should be noted that the three-dimensional data encoding device may specify whether to search for a neighboring node, based on standards or a profile or level etc. of standards, without appending coding_mode 1  to a header. This enables the three-dimensional data decoding device to determine whether the neighboring node has been searched for by reference to standards information, and to restore a bitstream correctly. 
     limit_num_of_search is information indicating a neighboring threshold value, and indicates, for example, a limit on the number of searches (a search threshold value) when a neighboring node is searched for. For example, a value of 0 indicates no limit on the number of searches, and a value of at least 1 indicates a limit on the number of searches. 
     limit_num_of search is included in header information when a value of coding_mode 1  is at least 1. It should be noted that the three-dimensional data encoding device need not include limit_num_of_search in a header when there is always no need to limit a search. In addition, the three-dimensional data encoding device may provide limit_num_of_search for each layer of an octree and include limit_num_of search in a header. 
     Additionally, a value of limit_num_of_search may be determined before coding. For example, the value is set to no limit when a high-performance device performs encoding or decoding, and the value is set to a limit when a low-performance device performs encoding or decoding. 
     As illustrated in  FIG.  198   , information of a node includes coding_mode 2  and occupancy_code. coding_mode 2  is included in the information of the node when a value of coding_mode 1  is 2. coding_mode 2  is information indicating whether to search for a neighboring node for each node. For example, a value of 0 indicates that a neighboring node is not to be searched for, and a value of 1 indicates that a neighboring node is to be searched for. 
     It should be noted that when coding_mode 2  is 1, the three-dimensional data encoding device and the three-dimensional data decoding device may set a limit on the number of searches to limit_num_of_search appended to a header. Moreover, the three-dimensional data encoding device may encode, for each node, information indicating a limit on the number of searches. 
     Furthermore, the three-dimensional data encoding device need not encode a value of coding_mode 2 , and the three-dimensional data decoding device may estimate a value of coding_mode 2 . For example, the three-dimensional data decoding device estimates a value of coding_mode 2  from an occupancy code of a parent node or layer information of an octree. 
     occupancy_code is an occupancy code of a current node, and is information indicating whether child nodes of the current node are occupied. The three-dimensional data encoding device and the three-dimensional data decoding device calculate occupancy information of a neighboring node according to a value of coding_mode 2 , and encode or decode occupancy_code while changing a coding table, based on the value. 
     Moreover, the three-dimensional data encoding device may entropy encode coding_mode 1 , limit_num_of_search, or coding_mode 2  generated by the above-mentioned method. For example, the three-dimensional data encoding device binarizes each value and performs arithmetic encoding on the value. 
     Although the octree structure has been described as an example in the present embodiment, the present disclosure is not necessarily limited to this. The above-mentioned procedure may be applied to an N-ary tree such as a binary tree, a quadtree, and a hexadecatree, or other tree structures, where N is an integer greater than or equal to 2. 
     The following describes the details of a three-dimensional data encoding process.  FIG.  199    is a flowchart of a three-dimensional data encoding process according to the present embodiment. First, the three-dimensional data encoding device defines a space (a current node) including part or all of an inputted three-dimensional point cloud (S 2521 ). Next, the three-dimensional data encoding device generates eight small spaces (nodes) by dividing the current node into eight (S 2522 ). Then, the three-dimensional data encoding device generates an occupancy code of the current node according to whether pneach node includes a point cloud (S 2523 ). After that, the three-dimensional data encoding device calculates neighboring information of a neighboring node of the current node from an occupancy code of a parent node of the current node (S 2524 ). 
     Next, the three-dimensional data encoding device determines whether to perform a search process, by checking an encoding mode (S 2525 ). For example, when (1) coding_model is 1 or (2) coding_model is 2 and coding_mode 2  is 1, the three-dimensional data encoding device determines to perform a search process (YES in S 2525 ); and in other cases, the three-dimensional data encoding device performs no search process (NO in S 2525 ). It should be noted that the three-dimensional data encoding device determines whether to search for a neighboring node for all nodes (a value of coding_model) and whether to search for a neighboring node for each node (a value of coding_mode 2 ), by the above-mentioned method etc. 
     For example, the three-dimensional data encoding device estimates whether a current node requires a neighboring node search (a value of coding_mode 2 ), from an occupancy code of a parent node. Here, when all of occupancy information of three neighboring nodes calculated from the occupancy code of the parent node are 1, there is a high possibility that the other neighboring nodes are occupied. For this reason, the three-dimensional data encoding device determines that the current node requires the neighboring node search (the value of coding_mode 2  is 1). In addition, when the three-dimensional data decoding device estimates coding_mode 2 , the three-dimensional data encoding device need not encode coding_mode 2 . 
     When the three-dimensional data encoding device performs a search process (YES in S 2525 ), the three-dimensional data encoding device obtains remaining neighboring information by searching for information of encoded nodes. For example, when a value of limit_num_of_search is not 0 (no limit on the number of searches), the three-dimensional data encoding device searches for a neighboring node while limiting the number of searches according to the value. In addition, the three-dimensional data encoding device sets a value of limit_num_of_search using the above-mentioned method etc. Additionally, the three-dimensional data encoding device integrates the neighboring information calculated from the occupancy code of the parent node and the neighboring information obtained by the search process (S 2526 ). Then, the three-dimensional data encoding device selects a coding table to be used for entropy encoding, based on the neighboring information generated in step S 2526  (S 2527 ). 
     In contrast, when the three-dimensional data encoding device performs no search process (NO in S 2525 ), the three-dimensional data encoding device selects a coding table to be used for entropy encoding, based on the neighboring information calculated from the occupancy code of the parent node in step S 2524  (S 2527 ). 
     After that, the three-dimensional data encoding device entropy encodes the occupancy code of the current node using the selected coding table (S 2528 ). Moreover, the three-dimensional data encoding device encodes coding_mode 1  and limit_num_of_search as header information. Furthermore, the three-dimensional data encoding device encodes coding_mode 2  for each node. 
     Finally, the three-dimensional data encoding device repeats a process of dividing each node into eight and encoding an occupancy code of each node until each node cannot be divided (S 2529 ). In other words, steps S 2522  to S 2528  are recursively repeated. 
     The following describes the details of a three-dimensional data decoding process.  FIG.  200    is a flowchart of a three-dimensional data decoding process according to the present embodiment. First, the three-dimensional data decoding device defines a space (a current node) to be decoded, using header information of a bitstream (S 2531 ). At this time, the three-dimensional data decoding device decodes coding_mode 1  and limit_num_of_search of the header information. 
     Next, the three-dimensional data decoding device generates eight small spaces (nodes) by dividing the current node into eight (S 2532 ). Then, the three-dimensional data decoding device calculates neighboring information of a neighboring node of the current node from an occupancy code of a parent node of the current node (S 2533 ). 
     After that, the three-dimensional data decoding device determines whether to perform a search process, by checking a decoding mode corresponding to an encoding mode (S 2534 ). For example, when (1) coding_mode 1  is 1 or (2) coding_mode 1  is 2 and coding_mode 2  is 1, the three-dimensional data decoding device determines to perform a search process (YES in S 2534 ); and in other cases, the three-dimensional data decoding device performs no search process (NO in S 2534 ). In addition, the three-dimensional data decoding device decodes coding_mode 2  for, for example, each node. 
     It should be noted that the three-dimensional data decoding device may determine whether a current node requires a neighboring node search (a value of coding_mode 2 ), using the same process as the process in the three-dimensional data encoding device. For example, the three-dimensional data decoding device estimates whether a current node requires a neighboring node search, from an occupancy code of a parent node. Here, when all of occupancy information of three neighboring nodes calculated from the occupancy code of the parent node are 1, there is a high possibility that other neighboring nodes are occupied. For this reason, the three-dimensional data decoding device determines that the current node requires the neighboring node search (the value of coding_mode 2  is 1). In addition, when the three-dimensional data decoding device estimates coding_mode 2 , the three-dimensional data decoding device need not decode coding_mode 2 . 
     Next, when the three-dimensional data decoding device performs a search process (YES in S 2534 ), the three-dimensional data decoding device obtains remaining neighboring information by searching for information of decoded nodes. For example, when a value of limit_num_of_search is not 0 (no limit on the number of searches), the three-dimensional data decoding device searches for a neighboring node while limiting the number of searches according to the value. Additionally, the three-dimensional data decoding device integrates the neighboring information calculated from the occupancy code of the parent node and the neighboring information obtained by the search process (S 2535 ). Then, the three-dimensional data decoding device selects a coding table to be used for entropy decoding, based on the neighboring information generated in step S 2535  (S 2536 ). 
     In contrast, when the three-dimensional data decoding device performs no search process (NO in S 2534 ), the three-dimensional data decoding device selects a coding table to be used for entropy decoding, based on the neighboring information calculated from the occupancy code of the parent node in step S 2533  and the neighboring information obtained by the search process (S 2536 ). 
     After that, the three-dimensional data decoding device entropy decodes an occupancy code of the current node using the selected coding table (S 2537 ). Finally, the three-dimensional data decoding device repeats a process of dividing each node into eight and decoding an occupancy code of each node until each node cannot be divided (S 2538 ). In other words, steps S 2532  to S 2537  are recursively repeated. 
     It should be noted that the above description shows an example in which nodes to be searched are encoded nodes, nodes to be searched are not necessarily limited to this. For example, the three-dimensional data encoding device may obtain information of neighboring nodes of all the nodes belonging to the same layer, by performing a search using the method described in the present embodiment, and then may encode an occupancy code of each node using the obtained information of the neighboring nodes. 
     As stated above, the three-dimensional data encoding device according to the present embodiment performs the process illustrated in  FIG.  201   . The three-dimensional data encoding device encodes information of a current node included in an N-ary tree structure of three-dimensional points included in three-dimensional data, where N is an integer greater than or equal to 2. In the encoding, the three-dimensional data encoding device encodes first information (e.g., limit_num_of_search) indicating a range for one or more referable neighboring nodes among neighboring nodes spatially neighboring the current node (S 2541 ), and encodes the current node with reference to a neighboring node within the range (S 2542 ). 
     With this, since the three-dimensional data encoding device limits referable neighboring nodes, the three-dimensional data encoding device reduces the amount of processing. 
     For example, in the encoding, the three-dimensional data encoding device selects a coding table based on whether the neighboring node within the range includes a three-dimensional point, and entropy encodes the information (e.g., an occupancy code) of the current node using the coding table selected. 
     For example, in the encoding, the three-dimensional data encoding device performs a search for information of the one or more referable neighboring nodes among the neighboring nodes spatially neighboring the current node, and the first information indicates a range for the search. 
     For example, in the search, the three-dimensional data encoding device searches for information of nodes in a predetermined order, and the first information indicates a total number of nodes (e.g., a search threshold value) on which the search is to be performed. 
     For example, in the search, indexes of Morton codes are used. 
     For example, in the encoding, the three-dimensional data encoding device encodes second information (coding_mode 1 ) indicating whether the range for the one or more referable neighboring nodes is to be limited, and encodes the first information when the second information indicates that the range for the one or more referable neighboring nodes is to be limited. 
     For example, the range for the one or more referable neighboring nodes changes according to a layer to which the current node belongs in the N-ary tree structure. 
     For example, the three-dimensional data encoding device includes a processor and memory, and the processor performs the above process using the memory. 
     Moreover, the three-dimensional data decoding device according to the present embodiment performs the process illustrated in  FIG.  202   . The three-dimensional data decoding device decodes information of a current node included in an N-ary tree structure of three-dimensional points included in three-dimensional data, where N is an integer greater than or equal to 2. In the decoding, the three-dimensional data decoding device decodes, from a bitstream, first information (e.g., limit_num_of_search) indicating a range for one or more referable neighboring nodes among neighboring nodes spatially neighboring the current node (S 2551 ), and decodes the current node with reference to a neighboring node within the range (S 2552 ). 
     With this, since the three-dimensional data decoding device limits referable neighboring nodes, the three-dimensional data decoding device reduces the amount of processing. 
     For example, in the decoding, the three-dimensional data decoding device selects a coding table based on whether the neighboring node within the range includes a three-dimensional point, and entropy decodes the information (e.g., an occupancy code) of the current node using the coding table selected. 
     For example, in the decoding, the three-dimensional data decoding device performs a search for information of the one or more referable neighboring nodes among the neighboring nodes spatially neighboring the current node, and the first information indicates a range for the search. 
     For example, in the search, the three-dimensional data decoding device searches for information of nodes in a predetermined order, and the first information indicates a total number of nodes (e.g., a search threshold value) on which the search is to be performed. 
     For example, in the search, indexes of Morton codes are used. 
     For example, in the decoding, the three-dimensional data decoding device decodes second information (coding_model) indicating whether the range for the one or more referable neighboring nodes is to be limited, and decodes the first information when the second information indicates that the range for the one or more referable neighboring nodes is to be limited. 
     For example, the range for the one or more referable neighboring nodes changes according to a layer to which the current node belongs in the N-ary tree structure. 
     For example, the three-dimensional data decoding device includes a processor and memory, and the processor performs the above process using the memory. 
     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. 
     Although only some exemplary embodiments of the present disclosure have been described in detail above, those skilled in the art will readily appreciate that many modifications are possible in the exemplary embodiments without materially departing from the novel teachings and advantages of the present disclosure. Accordingly, all such modifications are intended to be included within the scope 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.