Patent Publication Number: US-2020296427-A1

Title: A method and apparatus for encoding/decoding the colors of a point cloud representing a 3d object

Description:
FIELD 
     The present principles generally relate to coding and decoding the colors of a point cloud representing a 3D object. Particularly, but not exclusively, the technical field of the present principles are related to octree-based encoding/decoding of point cloud. 
     BACKGROUND 
     The present section is intended to introduce the reader to various aspects of art, which may be related to various aspects of the present principles that are described and/or claimed below. This discussion is believed to be helpful in providing the reader with background information to facilitate a better understanding of the various aspects of the present principles. Accordingly, it should be understood that these statements are to be read in this light, and not as admissions of prior art. 
     A point cloud is a set of points usually intended to represent the external surface of a 3D object but also more complex geometries like hair, fur that may not be represented efficiently by other data format like meshes. Each point of a point cloud is often defined by a 3D spatial location (X, Y, and Z coordinates in the 3D space) and possibly by other associated attributes such as color, represented in the RGB or YUV color space for example, a transparency, a reflectance, a two-component normal vector, etc. 
     A colored point cloud may be a set of 6-components points (X, Y, Z, G, B) or equivalently (X, Y, Z, Y, U, V) where (X,Y,Z) defines the spatial location of a point in a 3D space and (R,G,B) or (Y,U,V) defines a color of this point. 
     In the following the term “point cloud” refers to any point cloud including a colored point cloud. 
     Colored point clouds may be static or dynamic depending on whether or not the cloud evolves with respect to time. It should be noticed that in case of a dynamic point cloud; the number of points is not constant but, on the contrary, generally evolves with time. A dynamic point cloud is thus a time-ordered list of sets of points. 
     Practically, colored point clouds may be used for various purposes such as culture heritage/buildings in which objects like statues or buildings are scanned in 3D in order to share the spatial configuration of the object without sending or visiting it. Also, it is a way to ensure preserving the knowledge of the object in case it may be destroyed; for instance; a temple by an earthquake. Such colored point clouds are typically static and huge. 
     Another use case is in topography and cartography in which, by using 3D representations, maps are not limited to the plane and may include the relief. 
     Automotive industry and autonomous cars are also domains in which point clouds may be used. Autonomous cars should be able to “probe” their environment to take safe driving decision based on the reality of their immediate neighboring. Typical sensors produce dynamic point clouds that are used by the decision engine. These point clouds are not intended to be viewed by a human being. They are typically small, not necessarily colored, and dynamic with a high frequency of capture. They may have other attributes like the reflectance that is a valuable information correlated to the material of the physical surface of sensed object and may help the decision. 
     Virtual Reality (VR) and immersive worlds have become a hot topic recently and foreseen by many as the future of 2D flat video. The basic idea is to immerse the viewer in an environment all round him by opposition to standard TV where he can only look at the virtual world in front of him. There are several gradations in the immersivity depending on the freedom of the viewer in the environment. Colored point clouds are a good format candidate to distribute VR worlds. They may be static or dynamic and are typically of averaged size, say no more than a few millions of points at a time. 
     Point cloud compression will succeed in storing/transmitting 3D objects for immersive worlds only if the size of the bitstream is low enough to allow a practical storage/transmission to the end-user. 
     It is also crucial to be able to distribute dynamic point clouds to the end-user with a reasonable consumption of bandwidth while maintaining an acceptable (or preferably very good) quality of experience. Similarly to video compression, a good use of temporal correlation is thought to be the crucial element that will lead to efficient compression of dynamic point clouds. 
     Well-known approaches project a colored point cloud representing the geometry and colors of a 3D object, onto the faces of a cube encompassing the 3D object to obtain videos on texture and depth, and code the texture and depth videos using a legacy encoder such as 3D-HEVC (an extension of HEVC whose specification is found at the ITU website, T recommendation, H series, h265, http://www.itu.int/rec/T-REC-H.265-201612-I/en annex G and I). 
     Performance of compression is close to video compression for each projected point, but some contents may be more complex because of occlusions, redundancy and temporal stability when dynamic point clouds are considered. Consequently, point cloud compression is more demanding than video compression in term of bit-rates. 
     Regarding occlusions, it is virtually impossible to get the full geometry of a complex topology without using many projections. The required resources (computing power, storage memory) for encoding/decoding all these projections are thus usually too high. 
     Octree-based encoding is also a well-known approach for encoding the geometry of a point cloud. An octree-based structure is obtained for representing the geometry of the point cloud by splitting recursively a cube encompassing the point cloud until the leaf cubes, associated with the leaf nodes of said octree-based structure, contain no more than one point of the point cloud. The spatial locations of the leaf cubes of the octree-based structure thus represent the spatial locations of the points of the point cloud, i.e. its geometry. 
     Encoding colors of the points in the leaf cubes requires very high bitrate especially when the geometry of the point cloud is complex because it requires a lot of leaf cubes. 
     Therefore, there is a trade-off to be found between obtaining a good representation of the geometry of a point cloud without requiring a high bitrate for encoding the colors of said point cloud. 
     SUMMARY 
     The following presents a simplified summary of the present principles to provide a basic understanding of some aspects of the present principles. This summary is not an extensive overview of the present principles. It is not intended to identify key or critical elements of the present principles. The following summary merely presents some aspects of the present principles in a simplified form as a prelude to the more detailed description provided below. 
     Generally speaking, the present principles relates to a method for encoding the colors of a point cloud representing a 3D object. The method comprises obtaining a set of points approximating the geometry of said point cloud, and encoding a color information data indicating that the color of at least one of the point of said set of points is encoded in a bitstream and that the colors of the other points of said set of points are not encoded in the bitstream. 
     In that way, at the decoding side, the colors of the points that define the geometry of the decoded point cloud are obtained either by decoding the bitstream or from the colors of already colorized decoded points, and thus according to said decoded color information data. 
     This leads to significant reduction of the bitrate required for encoding the colors of the points approximating the colors of the point cloud. 
     According to an embodiment, at least one point of the set of points is a point in a leaf cube associated with a leaf node of an octree-based structure approximating the geometry of the point cloud. 
     According to an embodiment, said octree-based structure is determined by optimizing a trade-off between a bit-rate for encoding a candidate octree-based structure approximating the points of the point cloud, and a distortion taking into account spatial distances between, on one hand, said points of the point cloud, and on the other hand, points which are included in leaf cubes associated with leaf nodes of the candidate octree-based structure and which approximate the points of the point cloud. 
     According to an embodiment, at least one point of the set of points is an up-sampled point obtained by up-sampling recursively the points associated with said octree-based structure. 
     According to an embodiment, at least one point of the set of points is a point of an inverse-projected point cloud. 
     According to an embodiment, the inverse-projected point cloud IPPC by inverse-projecting at least one texture and depth images representative of a part of the point cloud. 
     According to another of their aspects, the present principles relate to a method for decoding, from a bitstream, the colors of a point cloud representing a 3D object. The method comprises:
         obtaining, from the bitstream, a set of points approximating the geometry of said point cloud;   decoding a color information data from the bitstream;   for each point of the set of points,
           when the color information data (indicates that the color of a point is encoded in the bitstream, decoding the color of the point from the bitstream; and   otherwise, obtaining the color of the point from the colors of neighboring points.   
               

     According to an embodiment, at least one point of the set of points is a point in a leaf cube associated with a leaf node of an octree-based structure approximating the geometry of the point cloud. 
     According to an embodiment, at least one point of the set of points is an up-sampled point obtained by up-sampling recursively the points associated with said octree-based structure. 
     According to an embodiment, at least one point of the set of points is a point of an inverse-projected point cloud. 
     According to an embodiment, when the color of an up-sampled point is not encoded in the bitstream, the color of said up-sampled point is obtained from the color of at least one point in a leaf cube of the octree-based structure located around the up-sampled point. 
     According to an embodiment, when the color of an up-sampled point is not encoded in the bitstream, the color of said up-sampled point is obtained from the color of at least one points in leaf cubes around the up-sampled point, and the color of at least one points of said inverse-projected point cloud. 
     According to another of their aspects, the present principles relate to a signal carrying on data representative of a set of points approximating the geometry of a point cloud. The signal also carries a color information data indicating that the color of at least one of the point of said set of points is also carried by the signal and that the colors of the other points of said set of points are not carried by the signal. 
     The specific nature of the present principles as well as other objects, advantages, features and uses of the present principles will become evident from the following description of examples taken in conjunction with the accompanying drawings. 
    
    
     
       BRIEF DESCRIPTION OF DRAWINGS 
       In the drawings, examples of the present principles are illustrated. It shows: 
         FIG. 1  illustrates an example of an octree-based structure; 
         FIG. 2  shows schematically a diagram of the steps of the method for encoding the colors of a point cloud representing a 3D object in accordance with an example of the present principles; 
         FIG. 3  shows the diagram of the sub-steps of the step  210  in accordance with an embodiment of the present principles; 
         FIG. 4  shows an illustration of an example of a candidate octree-based structure; 
         FIG. 5  shows schematically a diagram of the steps of the method for up-sampling recursively the points P i  associated with the octree-based structure O with a maximum depth level δ in accordance with an embodiment of step  210 ; 
         FIGS. 6 a - b    illustrate the up-sampling in accordance with an example of the present principles; 
         FIG. 7  illustrates a variant of the method of  FIG. 5  in accordance with an example of the present principles; 
         FIG. 8  shows schematically a diagram of the steps of the method for decoding, from a bitstream, the colors of a point cloud representing a 3D object in accordance with an example of the present principles. 
         FIG. 9  shows an example of an architecture of a device in accordance with an example of present principles; and 
         FIG. 10  shows two remote devices communicating over a communication network in accordance with an example of present principles; 
         FIG. 11  shows the syntax of a signal in accordance with an example of present principles. 
     
    
    
     Similar or same elements are referenced with the same reference numbers. 
     DESCRIPTION OF EXAMPLE OF THE PRESENT PRINCIPLES 
     The present principles will be described more fully hereinafter with reference to the accompanying figures, in which examples of the present principles are shown. The present principles may; however; be embodied in many alternate forms and should not be construed as limited to the examples set forth herein. Accordingly, while the present principles are susceptible to various modifications and alternative forms, specific examples thereof are shown by way of examples in the drawings and will herein be described in detail. It should be understood, however, that there is no intent to limit the present principles to the particular forms disclosed, but on the contrary, the disclosure is to cover all modifications, equivalents, and alternatives falling within the spirit and scope of the present principles as defined by the claims. 
     The terminology used herein is for the purpose of describing particular examples only and is not intended to be limiting of the present principles. As used herein, the singular forms “a”, “an” and “the” are intended to include the plural forms as well, unless the context clearly indicates otherwise. It will be further understood that the terms “comprises”, “comprising,” “includes” and/or “including” when used in this specification, specify the presence of stated features, integers, steps, operations, elements, and/or components but do not preclude the presence or addition of one or more other features, integers, steps, operations, elements, components, and/or groups thereof. Moreover, when an element is referred to as being “responsive” or “connected” to another element, it can be directly responsive or connected to the other element, or intervening elements may be present. In contrast, when an element is referred to as being “directly responsive” or “directly connected” to other element, there are no intervening elements present. As used herein the term “and/or” includes any and all combinations of one or more of the associated listed items and may be abbreviated as “/”. 
     It will be understood that, although the terms first, second, etc. may be used herein to describe various elements, these elements should not be limited by these terms. These terms are only used to distinguish one element from another. For example, a first element could be termed a second element, and, similarly, a second element could be termed a first element without departing from the teachings of the present principles. 
     Although some of the diagrams include arrows on communication paths to show a primary direction of communication, it is to be understood that communication may occur in the opposite direction to the depicted arrows. 
     Some examples are described with regard to block diagrams and operational flowcharts in which each block represents a circuit element, module, or portion of code which comprises one or more executable instructions for implementing the specified logical function(s). It should also be noted that in other implementations, the function(s) noted in the blocks may occur out of the order noted. For example, two blocks shown in succession may, in fact, be executed substantially concurrently or the blocks may sometimes be executed in the reverse order, depending on the functionality involved. 
     Reference herein to “in accordance with an example” or “in an example” means that a particular feature, structure, or characteristic described in connection with the example can be included in at least one implementation of the present principles. The appearances of the phrase in accordance with an example” or “in an example” in various places in the specification are not necessarily all referring to the same example, nor are separate or alternative examples necessarily mutually exclusive of other examples. 
     Reference numerals appearing in the claims are by way of illustration only and shall have no limiting effect on the scope of the claims. 
     While not explicitly described, the present examples and variants may be employed in any combination or sub-combination. 
     The present principles are described for encoding/decoding the colors of a point cloud but extends to the encoding/decoding of the colors of a sequence of point clouds because each point cloud of the sequence is sequentially encoded/decoded as described below. 
     In the following, an image contains one or several arrays of samples (pixel values) in a specific image/video format which specifies all information relative to the pixel values of an image (or a video) and all information which may be used by a display and/or any other device to visualize and/or decode an image (or video) for example. An image comprises at least one component, in the shape of a first array of samples, usually a luma (or luminance) component, and, possibly, at least one other component, in the shape of at least one other array of samples, usually a color component. Or, equivalently, the same information may also be represented by a set of arrays of color samples, such as the traditional tri-chromatic RGB representation. 
     A pixel value is represented by a vector of nv values, where nv is the number of components. Each value of a vector is represented with a number of bits which defines a maximal dynamic range of the pixel values. 
     A depth image is an image whose pixel values depths of 3D points. Usually, a depth image is a grey levels image. 
     An octree-based structure comprises a root node, at least one leaf node and possibly intermediate nodes. A leaf node is a node of the octree-based structure which has no child. All other nodes have children. Each node of an octree-based structure is associated with a cube. Thus, an octree-based structure comprises a set of at least one cube associated with node(s). 
     A leaf cube is a cube associated with a leaf node of an octree-based structure. 
     In the example illustrated on  FIG. 1 , the cube associated with the root node (depth 0) is split into 8 sub-cubes (depth 1) and two sub-cubes of depth 1 are then split into 8 sub-cubes (last depth=maximum depth=2). 
       FIG. 2  shows schematically a diagram of the steps of the method for encoding the colors of a point cloud IPC representing a 3D object in accordance with an example of the present principles. 
     In step  210 , a module M 1  obtains a set of points SP approximating the geometry of said point cloud IPC. 
     In step  220 , a module M 2  encodes a color information data CID indicating that the color of at least one of the point of said set of points SP is encoded in a bitstream and that the colors of the other points of said set of points are not encoded in the bitstream. 
     According to an embodiment of steps  210 , at least one point of the set of points SP is a point P i  in a leaf cube associated with a leaf node of an octree-based structure O approximating the geometry of the point cloud IPC. 
       FIG. 3  shows the diagram of the sub-steps of the step  210  in accordance with an embodiment of the present principles. 
     According to this embodiment, a Rate Distortion optimization (RDO) process is used to determine a best octree-based structure O for approximating the geometry of the point cloud IPC. The points P in leaf cubes associated with leaf nodes of said octree-based structure O approximate the points of the point cloud IPC, i.e. the geometry of the point cloud IPC. 
     A RDO process finds a best octree-based structure O from N candidate octree-based structures O n  (n∈[1; N]). The basic principle is to test successively each candidate octree-based structure O n  and for each candidate octree-based structure O n  to calculate a Lagrangian cost C n  given by: 
         C   n   =D   n   +λR   n   (1)
 
     where R n  and D n  are respectively the bit-rate and distortion detailed below, and λ is a fixed Lagrange parameter that may be fixed for all the candidate octree-based structures O n . 
     The best octree-based structure O is then obtained by optimizing a trade-off between the bit-rate R n  for encoding a candidate octree-based structure O n  approximating the points P or  of the point cloud, i.e. by minimizing the Lagrangian cost C n : 
     
       
         
           
             
               
                 
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     High values for the Lagrangian parameter strongly penalize the bit-rate R n  and lead to a low quality of approximation, while low values for the Lagrangian parameter allow easily high values for R n  and lead to high quality of approximation. The range of values for lambda depends on the distortion metric and most importantly the distance between two adjacent points. Assuming that this distance is unity, typical values for lambda are in the range from a few hundreds, for very poor coding, to a tenth of unity for good coding. These values are indicative and may also depend on the content. 
     Determining a best octree-based structure O is now detailed in accordance with an embodiment of the present principles. 
     In step  300 , the module M 1  obtains a set of N candidate octree-based structures O n  and obtains a set of points P n  for each candidate octree-based structure O n . The points P n  are points which are included in leaf cubes associated with leaf nodes of a candidate octree-based structure O n . The points P n  approximate the points of the point cloud IPC. 
     In step  310 , the module M 1  obtains the bit-rate R n  for encoding each candidate octree-based structure O n . 
     In step  320 , the module M 1  obtains the points P or  of the point cloud IPC. 
     In step  330 , the module M 1  obtains a distortion D n  for each candidate octree-based structure O n , each distortion D n  takes into account the spatial distances between, on one hand, the points P or , and on the other hand, the points P n . 
     In step  340 , the module M 1  calculates the Lagrangian cost C n  according to equation (1) for each candidate octree-based structure O n . 
     In step  350 , the module M 1  obtains the best octree-based structure O according to equation (2) once all the candidate octree-based structures O n  have been considered. 
     According to an embodiment of step  300 , a candidate octree-based structure O n  comprises at least one leaf node and the leaf cube associated to a leaf node may (or not) include a single point P n . 
     Each single point is a point P i  of the best octree-based structure O is a point of the set of points SP. 
       FIG. 4  shows an illustration of an example of a candidate octree-based structure O n  according to this embodiment. This figure represents an example of a quadtree-based structure that splits a square, but the reader will easily extend it to the 3D case by replacing the square by a cube. 
     According to this example, the cube is split into 4 sub-cubes C 1 , C 2  C 3  and C 4  (depth 1). The sub-cube C 1  is associated with a leaf node and does not contain any point. The sub-cube C 2  is recursively split into 4 sub-cubes (depth 2). The sub-cube C 3  is also recursively split and the sub-cube C 4  is not split but a point, located in the center of the cube for example, is associated with it, . . . , etc. 
     On the right part of  FIG. 4  is shown an illustration of the candidate octree-based structure. A black circle indicates that a node is split. A binary flag is associated with each white circle (leaf node) to indicate if the square (a cube in the 3D case) includes (1) or not (0) a point. 
     According to this example, a point is located in the center of a cube because it avoids any additional information about the spatial location of that point once the cube is identified in the octree-based structure. But the present principles are not limited to this example and may extend to any other spatial location of a point in a cube. 
     The present principles are not limited to the candidate octree-based structure illustrated on  FIG. 4  but extend to any other octree-based structure comprising at least one leaf node whose associated leaf cube includes at least one point. These points are thus the points of the set of points SP. 
     According to an embodiment of step  330 , the distortion D n  is a metric given by: 
         D   n   =d ( P   n   ,P   OR )+ d ( P   OR   ,P   n ) 
     where d(A,B) is a metric that measures the spatial distance from a set of points A to a set of points B. This metric is not symmetric, this means that distance from A to B differs from the distance from B to A. 
     The distance d(P n ,P OR ) ensures that the points included P n  in leaf cubes associated with leaf nodes of a candidate octree-based structure O n  are not too far from the point cloud IPC, avoiding coding irrelevant points. 
     The distance d(P OR ,P n ) ensures that each point of the point cloud IPC is approximated by points not too far from them, i.e. ensures that all parts of the point cloud IPC are well approximated. 
     According to an embodiment of step  330 , the distance d(A,B) is given by: 
     
       
         
           
             
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     where the norm is the Euclidan distance and q closest (p,B) is the closest point of B from a point p of A defined as 
     
       
         
           
             
               
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     According to an embodiment of the step  340 , a candidate octree-based structure O n  is encoded by a set of binary flags. Some of these binary flags are associated with the nodes of said candidate octree-based structure O n  to indicate if the cubes associated with said nodes are split or not, and some other of these binary flags are associated with leaf nodes of said candidate octree-based structure O n  to indicate if the leaf cubes associated with leaf nodes of said candidate octree-based structure O n  includes or not points representative of at least a part of the point cloud IPC. The bit-rate R n  for encoding said candidate octree-based structure O n  is then the sum of the numbers of these binary flags. 
     According to a variant, at least one first sequence of bits is formed from said binary flags and said at least one sequence of bits is entropy-coded. The bit-rate R n  is then obtained from the entropy-encoded version of said at least one sequence of bits. 
     According to an alternative to this embodiment of the step  340 , the syntax used to encode a candidate octree-based structure O n  may comprise an index of a table (Look-Up-Table) that identifies a candidate octree-based structure among a set of candidate octree-based structures determined beforehand, for example by an end-user. This table of candidate octree-based structures is known at the decoder. A set of bits (one or more bytes) are used for encoding said index of a table. The bit-rate R n  is thus the bit-rate required for encoding said index. 
     The geometry of the octree-based structure O may be encoded by a set of binary flags. Some of these binary flags are associated with the nodes of said octree-based structure O to indicate if the cubes associated with said nodes are split or not, and some other of these binary flags are associated with leaf nodes of said octree-based structure O to indicate if the leaf cubes associated with leaf nodes of said octree-based structure O includes or not points representative of at least a part of the point cloud IPC. 
     According to a variant, at least one first sequence of bits is formed from said binary flags and said at least one sequence of bits is entropy-coded. 
     According to an alternative, the syntax used to encode said octree-based structure O may comprise an index of a table (Look-Up-Table) that identifies a candidate octree-based structure among a set of candidate octree-based structures determined beforehand, for example by an end-user. This table of candidate octree-based structures is known at the decoder. A set of bits (one or more bytes) are used for encoding said index of a table. The bit-rate R n  is thus the bit-rate required for encoding said index. 
     When the color of a point P i  in a leaf cube of said octree-based structure O is encoded in the bitstream F 1 , said color may be encoded by at least one byte, typically three bytes, one per color component. 
     According to a variant of an embodiment of step  210 , at least one point of the set of points SP is an up-sampled point P up  obtained by up-sampling recursively the points P i  associated with the octree-based structure O. 
       FIG. 5  shows schematically a diagram of the steps of the method for up-sampling recursively the points P i  associated with the octree-based structure O with a maximum depth level δ in accordance with an embodiment of step  210 . 
     In step  510 , a module M 3  obtains a set of I point P i  (I is greater than or equals 1) from the octree-based structure O. Each of said points P i  is located at the center of a leaf cube C i  itself associated with a leaf node N i  at the maximum depth level δ. Assuming that all cubes of a same depth have a same size, the points P i  are positioned on a regular 3D grid of step the size of the cube of maximum depth level δ. The points P i  of this grid are said to be of precision level π=δ. 
     Some of the leaf nodes may be located at a depth level lower than the maximum depth level. 
     According to a variant of step  510 , the octree-based structure O is said completed by splitting recursively the leaf cubes associated with said leaf nodes at depth levels lower than the maximum depth level until their depth levels reach the maximum depth level. At each iteration, four child nodes are added to the octree-based structure with a point P i  preferably located in its center. 
     The purpose of the up-sampling process is to up-sample said points P i  up to a precision level πexp that is the precision level associated with a regular 3D grid of step the size of cubes of maximum depth level δexp=πexp. Typically, the maximum depth level δexp would be associated with leaf cubes of unitary size, i.e. the minimum size of a “3D pixel” (=a small cube) in the rendering process of the point cloud. 
     At each iteration, the set of I points P i  is considered. 
     In step  520 , a point P i  is considered. A module M 4  determines if a neighbor (on the regular 3D grid) point NEI i,j  is located in a neighborhood of the point P i , and, for each of the J neighbor points NEI i,j , in step  530 , a module M 5  determines a new point NP i,j . The new point NP i,j  is located at the middle of a segment joining the point P i  and the neighbor point NEI i,j . 
     The new points NP i,j  are added to the set of points P i  and the new set of points P i  is considered for the next iteration. The points of the new set of points P i  are located on a new regular 3D grid of step half the step of the regular grid on which the points of the old set of points P i  are located. In other words, the precision level of the grid has been increased by 1 during the steps  520  and  530 . 
     The iterations stop when the precision level π of the points P i  reaches the expected precision level πexp, at each iteration the precision level π being increased by 1. 
     The output of  FIG. 5  is the set of points P i  obtained after the last iteration, this last set being referred as up-sampled points P up . 
       FIGS. 6 a - b    illustrate the determination of neighbor points NEI i,j  and new point NP i,j  in steps  520  and  530 . 
     In  FIG. 6 a   , is represented all possible neighboring points (white circles) of a point P i  (black point). The regular 3D grid represented on the figure is of precision level π as the precision level of the grid of the point P i  is π. 
     The neighborhood of this point P i  is defined, according to an embodiment, by adding the values +S, 0 or −S to at least one of the coordinates of the point P i , where S is the step of the regular 3D grid of precision level π. S=1 for the example illustrated on  FIG. 6 a   . Then, the point P i  may have at most 26 neighbor points represented by circles. 
     In  FIG. 6 b   , is represented an example wherein the point P i  has two neighbor points NEI i,1  and NEI i,2 . A new point NP i,1  is added at the middle of a segment defined by the points P i  and NEI i,1 , and a new point NP i,2  is added at the middle of a segment defined by the points P i  and NEI i,2 . The new grid illustrated on  FIG. 6 b    (right) is of precision level π+1, i.e. has a step half the step of the grid of precision level π illustrated on  FIG. 6 b    (left). 
     The present principles are not limited to this example but may extend to any other method for defining a neighborhood of the point P i  and to any other method for defining a new point from two existing points located in a neighborhood of the point P i . 
     Determining if a neighbor point NEI i,j  is located in a neighborhood of the point P i  as described above leads to many couples of points to be tested as illustrated in  FIG. 6   a.    
     This number of 26 couples of points to be tested may be reduced to 13 according to a variant illustrated in  FIG. 7  where 3 of said 13 couples of points consider neighbor points along segment starting from the point P i , 6 of said 13 couples of points consider neighbor points along small diagonal starting from the point P i , and 4 of said 13 couples of points consider the neighbor points along all long diagonal starting from the point P i . 
     Said variant avoids thus to check twice the same couple of points, thus the number of 26/2=13 couples to be checked in step  520 . 
     According to an embodiment of step  210 , at least one point of the set of points SP is a point P IP  of an inverse-projected point cloud IIPC. 
     According to an embodiment of step  210 , the module M 1  obtains points P IP  of the inverse-projected point cloud IPPC by inverse-projecting at least one texture and depth images representative of the point cloud IPC, as proposed, for example, in “Image-Based Surface Compression”, Tilo Ochutta &amp; Dietmar Saupe, September 2008, in Computer Graphics Forum. 
     Basically, the point cloud IPC is projected on texture images which represent the color of the points of the point cloud IPC and on depth images which represent the distances between the planes of the texture images and the points of the point cloud IPC. Thus, a point P IP  in the 3D space may be obtained from pixel of the texture images and its associated depth obtained from a depth image, and the set of points P IP  form the inverse-projected point cloud IIPC. Said inverse-projected point cloud IIPC is thus an approximation of both the geometry and colors of the points of the point cloud IPC and the colors of the point cloud IPC are encoded by encoding the texture images. 
     According to an embodiment of step  220 , the color information data CID is defined in order to signal that:
         the colors of the points P i  are encoded in the bitstream F 1 ;   the colors of the points P IP  are also encoded in the bitstream F 1 ; and   the color of at least one up-sampled point P up  is not encoded in the bitstream.       

     This embodiment is advantageous because it allows a precise approximation of the geometry of the point cloud IPC by up-sampling the points P i  associated with the octree-based structure O without requiring a high bitrate for encoding the up-sampled points, which are retrieved at the decoding side from the octree-based structure O, and for encoding the colors of said up-sampled points which are obtained from the colors of previously decoded points. 
     According to a variant of step  220 , the color information data CID indicate if the colors of a sub-set of points of the set of points SP are encoded in the bitstream F 1 . 
     According to an embodiment, the points of the sub-set points may be points spatially close to each other and having a similar color. Euclidean distance may be used for estimating the spatial distance between two points and a difference between the colors of points may be compared to a threshold to decide the similarity between two colors. 
     This embodiment is advantageous for large region with similar colors because only a single color for multiple points and the color information data CID has to be encoded, reducing thus the global bitrate for encoding the colors of the point cloud. 
     According to an embodiment of step  220 , the color information data CID comprises at least a binary flag equals to 1 to indicate that the color of a point of the set of points SP is encoded in the bitstream and 0 otherwise. 
     According to an embodiment of step  220 , the color information data CID comprises at least one binary flag equals to 1 to indicate that the colors of a sub-set of points of the set of points SP are encoded in the bitstream and 0 otherwise. 
       FIG. 8  shows schematically a diagram of the steps of the method for decoding, from a bitstream, the colors of a point cloud IPC representing a 3D object in accordance with an example of the present principles. 
     In step  800 , a module M 6  obtains a set of points SP from the bitstream F 1 . This set of points SP approximates the geometry of the point cloud IPC. According to an embodiment of step  800 , at least one point of the set of points SP is a point P i  in a leaf cube associated with a leaf node of an octree-based structure O approximating the geometry of the point cloud IPC. 
     In this case, the module M 6  decodes the octree-based structure O from the bitstream F 1 . 
     According to an embodiment of the step  800 , the octree-based structure O is decoded from a set of binary flags. Some of these binary flags indicate if cubes associated with nodes of said octree-based structure O are split or not, and some other of these binary flags indicate if the leaf cubes associated with leaf nodes of said octree-based structure O includes or not points representative of at least a part of the point cloud IPC. 
     The octree-based structure O is then built and a point P i  is or not included in each leaf cube according to some of those binary flags. 
     According to a variant, at least one first sequence of bits is entropy-decoded and said binary flags are obtained from said at least one decoded sequence. 
     According to an alternative, the syntax used to decode the octree-based structure O may comprise an index of a table (Look-Up-Table) that identifies a candidate octree-based structure among a set of candidate octree-based structures determined beforehand, for example by an end-user. This table of candidate octree-based structures is known at the decoder. The module M 6  decodes a set of bit(s) and determined said index of a table from said decoded set of bit(s). 
     When the color of a point P i  is decoded in the bitstream F 1 , said color may be decoded from at least one byte, typically three bytes, one per color component. 
     According to an embodiment of step  800 , at least one point of the set of points SP is an up-sampled point P up  obtained by up-sampling recursively the points P i  associated with the octree-based structure O as detailed in  FIGS. 5-7 . 
     According to an embodiment of step  800 , at least one point of the set of points SP is a point P IP  of an inverse-projected point cloud IIPC. The module M 6  decodes at least one texture and depth image representative of the point cloud IPC from the bitstream F 1  and obtained said inverse-projected point cloud IIPC by inverse-projecting said at least one decoded texture and depth images as explained above in relation with an embodiment of step  210 . 
     In step  810 , a module M 7  decodes a color information data CID from the bitstream F 1 . 
     In step  820 , for each point P of the set of points SP, a module M 8  determines if the color information data CID indicates if the color of a point P is encoded in the bitstream F 1 . 
     If the color of a point P is encoded in the bitstream F 1 , in step  830 , a module M 9  decodes the color Col of the point P from the bitstream F 1 . 
     Otherwise, in step  840 , a module M 10  obtains the color of the point P from the colors of neighboring points P j . 
     According to an embodiment, the color of the point P is obtained by the average or the median value of the colors of the neighboring points P j . 
     According to an embodiment of step  840 , a neighboring point P j  of a point P is a point spatially close to the point P according to an Euclidean distance. 
     According to an embodiment of step  840 , when the color of an up-sampled point P up  is not encoded in the bitstream F 1 , the color of said up-sampled point P up  is obtained from the color of at least one point P i  in a leaf cubes of the octree-based structure O located around the up-sampled point P up . 
     For example, a point P i  is considered as being located around an up-sampled point if an Euclidean distance between the points P i  and P up  is lower than a threshold. 
     In a variant, the color of said up-sampled point P up  is obtained from the color of at least one points P i  in leaf cubes around the up-sampled point P up , and the color of at least one inverse-projected point P IP . 
     On  FIG. 1-8 , the modules are functional units, which may or not be in relation with distinguishable physical units. For example, these modules or some of them may be brought together in a unique component or circuit, or contribute to functionalities of a software. A contrario, some modules may potentially be composed of separate physical entities. The apparatus which are compatible with the present principles are implemented using either pure hardware, for example using dedicated hardware such ASIC or FPGA or VLSI, respectively «Application Specific Integrated Circuit», «Field-Programmable Gate Array», «Very Large Scale Integration», or from several integrated electronic components embedded in a device or from a blend of hardware and software components. 
       FIG. 9  represents an exemplary architecture of a device  900  which may be configured to implement a method described in relation with  FIG. 1-8 . 
     Device  900  comprises following elements that are linked together by a data and address bus  901 :
         a microprocessor  902  (or CPU), which is, for example, a DSP (or Digital Signal Processor);   a ROM (or Read Only Memory)  903 ;   a RAM (or Random Access Memory)  904 ;   an I/O interface  905  for reception of data to transmit, from an application; and   a battery  906 .       

     In accordance with an example, the battery  906  is external to the device. In each of mentioned memory, the word «register» used in the specification can correspond to area of small capacity (some bits) or to very large area (e.g. a whole program or large amount of received or decoded data). The ROM  903  comprises at least a program and parameters. The ROM  903  may store algorithms and instructions to perform techniques in accordance with present principles. When switched on, the CPU  902  uploads the program in the RAM and executes the corresponding instructions. 
     RAM  904  comprises, in a register, the program executed by the CPU  902  and uploaded after switch on of the device  900 , input data in a register, intermediate data in different states of the method in a register, and other variables used for the execution of the method in a register. 
     The implementations described herein may be implemented in, for example, a method or a process, an apparatus, a software program, a data stream, or a signal. Even if only discussed in the context of a single form of implementation (for example, discussed only as a method or a device), the implementation of features discussed may also be implemented in other forms (for example a program). An apparatus may be implemented in, for example, appropriate hardware, software, and firmware. The methods may be implemented in, for example, an apparatus such as, for example, a processor, which refers to processing devices in general, including, for example, a computer, a microprocessor, an integrated circuit, or a programmable logic device. Processors also include communication devices, such as, for example, computers, cell phones, portable/personal digital assistants (“PDAs”), and other devices that facilitate communication of information between end-users. 
     In accordance with an example of encoding or an encoder, the point cloud IPC is obtained from a source. For example, the source belongs to a set comprising:
         a local memory ( 903  or  904 ), e.g. a video memory or a RAM (or Random Access Memory), a flash memory, a ROM (or Read Only Memory), a hard disk;   a storage interface ( 905 ), e.g. an interface with a mass storage, a RAM, a flash memory, a ROM, an optical disc or a magnetic support;   a communication interface ( 905 ), e.g. a wireline interface (for example a bus interface, a wide area network interface, a local area network interface) or a wireless interface (such as a IEEE 802.11 interface or a Bluetooth® interface); and   an image capturing circuit (e.g. a sensor such as, for example, a CCD (or Charge-Coupled Device) or CMOS (or Complementary Metal-Oxide-Semiconductor)).       

     In accordance with an example of the decoding or a decoder, the decoded point cloud is sent to a destination; specifically, the destination belongs to a set comprising:
         a local memory ( 903  or  904 ), e.g. a video memory or a RAM, a flash memory, a hard disk;   a storage interface ( 905 ), e.g. an interface with a mass storage, a RAM, a flash memory, a ROM, an optical disc or a magnetic support;   a communication interface ( 905 ), e.g. a wireline interface (for example a bus interface (e.g. USB (or Universal Serial Bus)), a wide area network interface, a local area network interface, a HDMI (High Definition Multimedia Interface) interface) or a wireless interface (such as a IEEE 802.11 interface, WiFi® or a Bluetooth® interface);   a rendering device; and   a display.       

     In accordance with examples of encoding or encoder, the bitstream F 1  is sent to a destination. As an example, the bitstream F 1  is stored in a local or remote memory, e.g. a video memory ( 904 ) or a RAM ( 904 ), a hard disk ( 903 ). In a variant, the bitstream F 1  is sent to a storage interface ( 905 ), e.g. an interface with a mass storage, a flash memory, ROM, an optical disc or a magnetic support and/or transmitted over a communication interface ( 905 ), e.g. an interface to a point to point link; a communication bus, a point to multipoint link or a broadcast network. 
     In accordance with examples of decoding or decoder, the bitstream F 1  is obtained from a source. Exemplarily, a bitstream is read from a local memory, e.g. a video memory ( 904 ), a RAM ( 904 ), a ROM ( 903 ), a flash memory ( 903 ) or a hard disk ( 903 ). In a variant, the bitstream is received from a storage interface ( 905 ), e.g. an interface with a mass storage, a RAM, a ROM, a flash memory, an optical disc or a magnetic support and/or received from a communication interface ( 905 ), e.g. an interface to a point to point link, a bus, a point to multipoint link or a broadcast network. 
     In accordance with examples, device  900  being configured to implement an encoding method described in relation with  FIG. 1-7 , belongs to a set comprising:
         a mobile device;   a smartphone or a TV set with 3D capture capability   a communication device;   a game device;   a tablet (or tablet computer);   a laptop;   a still image camera;   a video camera;   an encoding chip;   a still image server; and   a video server (e.g. a broadcast server, a video-on-demand server or a web server).       

     In accordance with examples, device  900  being configured to implement a decoding method described in relation with  FIG. 5-8 , belongs to a set comprising:
         a mobile device;   a Head Mounted Display (HMD)   (mixed reality) smartglasses   an holographic device   a communication device;   a game device;   a set top box;   a TV set;   a tablet (or tablet computer);   a laptop;   a display   a sterescopic display and   a decoding chip.       

     According to an example of the present principles, illustrated in  FIG. 10 , in a transmission context between two remote devices A and B over a communication network NET, the device A comprises a processor in relation with memory RAM and ROM which are configured to implement a method for encoding a colored point cloud as described in relation with the  FIGS. 1-7  and the device B comprises a processor in relation with memory RAM and ROM which are configured to implement a method for decoding as described in relation with  FIGS. 5-8 . 
     In accordance with an example, the network is a broadcast network, adapted to broadcast encoded colored point clouds from device A to decoding devices including the device B. 
     A signal, intended to be transmitted by the device A, carries the bitstream F 1 . 
     This signal may thus carry on data representative of a set of points approximating the geometry of a point cloud, characterized in that it also carries a color information data (CID) indicating that the color of at least one of the point of said set of points is also carried by the signal and that the colors of the other points of said set of points are not carried by the signal. 
       FIG. 11  shows an example of the syntax of such a signal when the data are transmitted over a packet-based transmission protocol. Each transmitted packet P comprises a header H and a payload PAYLOAD. 
     According to embodiments, the payload PAYLOAD may comprise at least one of the following elements:
         a color information data (CID) indicating that the color of at least one of the point of said set of points is also carried by the signal and that the colors of the other points of said set of points are not carried by the signal.       

     Implementations of the various processes and features described herein may be embodied in a variety of different equipment or applications. 
     Examples of such equipment include an encoder, a decoder, a post-processor processing output from a decoder, a pre-processor providing input to an encoder, a video coder; a video decoder, a video codec, a web server, a set-top box, a laptop, a personal computer, a cell phone, a PDA, a HMD, smart glasses, and any other device for processing an image or a video or other communication devices. As should be clear, the equipment may be mobile and even installed in a mobile vehicle. 
     Additionally, the methods may be implemented by instructions being performed by a processor, and such instructions (and/or data values produced by an implementation) may be stored on a computer readable storage medium. A computer readable storage medium can take the form of a computer readable program product embodied in one or more computer readable medium(s) and having computer readable program code embodied thereon that is executable by a computer. A computer readable storage medium as used herein is considered a non-transitory storage medium given the inherent capability to store the information therein as well as the inherent capability to provide retrieval of the information therefrom. A computer readable storage medium can be, for example, but is not limited to, an electronic, magnetic, optical, electromagnetic, infrared, or semiconductor system, apparatus, or device, or any suitable combination of the foregoing. It is to be appreciated that the following, while providing more specific examples of computer readable storage mediums to which the present principles can be applied, is merely an illustrative and not exhaustive listing as is readily appreciated by one of ordinary skill in the art: a portable computer diskette; a hard disk; a read-only memory (ROM); an erasable programmable read-only memory (EPROM or Flash memory); a portable compact disc read-only memory (CD-ROM); an optical storage device; a magnetic storage device; or any suitable combination of the foregoing. 
     The instructions may form an application program tangibly embodied on a processor-readable medium. 
     Instructions may be, for example, in hardware, firmware, software, or a combination. Instructions may be found in, for example, an operating system, a separate application, or a combination of the two. A processor may be characterized, therefore, as, for example, both a device configured to carry out a process and a device that includes a processor-readable medium (such as a storage device) having instructions for carrying out a process. Further, a processor-readable medium may store, in addition to or in lieu of instructions, data values produced by an implementation. 
     As will be evident to one of skill in the art, implementations may produce a variety of signals formatted to carry information that may be, for example, stored or transmitted. The information may include, for example, instructions for performing a method, or data produced by one of the described implementations. For example, a signal may be formatted to carry as data the rules for writing or reading the syntax of a described example of the present principles, or to carry as data the actual syntax-values written by a described example of the present principles. Such a signal may be formatted, for example, as an electromagnetic wave (for example, using a radio frequency portion of spectrum) or as a baseband signal. The formatting may include, for example, encoding a data stream and modulating a carrier with the encoded data stream. The information that the signal carries may be, for example, analog or digital information. The signal may be transmitted over a variety of different wired or wireless links, as is known. The signal may be stored on a processor-readable medium. 
     A number of implementations have been described. Nevertheless, it will be understood that various modifications may be made. For example, elements of different implementations may be combined, supplemented, modified, or removed to produce other implementations. Additionally, one of ordinary skill will understand that other structures and processes may be substituted for those disclosed and the resulting implementations will perform at least substantially the same function(s), in at least substantially the same way(s), to achieve at least substantially the same result(s) as the implementations disclosed. Accordingly, these and other implementations are contemplated by this application.