Bezier volume representation of point cloud attributes

Abstract

The systems and methods discussed herein implement a volumetric approach to point cloud representation, compression, decompression, communication, or any suitable combination thereof. The volumetric approach can be used for both geometry and attribute compression and decompression, and both geometry and attributes can be represented by volumetric functions. To create a compressed representation of the geometry or attributes of a point cloud, a suitable set of volumetric functions are transformed, quantized, and entropy-coded. When decoded, the volumetric functions are sufficient to reconstruct the corresponding geometry or attributes of the point cloud.

What is claimed is: 
     
         1 . A method comprising:
 accessing, by one or more processors, a point cloud that specifies a set of three-dimensional (3D) points, and   generating, by the one or more processors, a data structure that indicates a volumetric function that corresponds to a signal defined on the set of 3D points specified by the accessed point cloud.   
     
     
         2 . The method of  claim 1 , further comprising:
 determining the volumetric function that corresponds to the signal based on values of the signal.   
     
     
         3 . The method of  claim 1 , further comprising:
 providing the generated data structure that indicates the volumetric function to a device configured to recover the point cloud by evaluating the volumetric function indicated by the data structure, the evaluating of the volumetric function including determining at least some values of the signal defined on the set of 3D points specified by the point cloud.   
     
     
         4 . The method of  claim 1 , wherein:
 the generating of the data structure that encodes the volumetric function includes determining coefficients of basis functions that correspond to the signal defined on the set of 3D points specified by the point cloud.   
     
     
         5 . The method of  claim 1 , wherein:
 the volumetric function that represents the signal is a first volumetric function that represents geometry of the point cloud that specifies the set of 3D points;   the point cloud specifies a corresponding set of attributes for each 3D point among the set of 3D points; and   the method further comprises:   performing data compression on the sets of attributes that correspond to the set of 3D points by determining a second volumetric function based on the sets of attributes.   
     
     
         6 . The method of  claim 5 , wherein:
 the generating of the data structure includes:
 determining coefficients of the second volumetric function; 
 quantizing the determined coefficients of the second volumetric function; and 
 performing entropy coding on the quantized coefficients of the second volumetric function. 
   
     
     
         7 . The method of  claim 6 , further comprising:
 providing the entropy coded and quantized coefficients of the second volumetric function within the generated data structure to a device.   
     
     
         8 . A method comprising:
 accessing, by one or more processors, a data structure that indicates a volumetric function that corresponds to a signal defined on a set of three-dimensional (3D) points specified by a point cloud;   recovering, by the one or more processors, the point cloud by evaluating the volumetric function indicated by the accessed data structure; and   causing, by the one or more processors, a rendering of the recovered point cloud based on the evaluating of the volumetric function indicated by the accessed data structure.   
     
     
         9 . The method of  claim 8 , wherein:
 in the recovering of the point cloud, the evaluating of the volumetric function includes determining at least some values of the signal defined on the set of 3D points specified by the point cloud.   
     
     
         10 . The method of  claim 8 , wherein:
 the accessing of the data structure includes receiving the data structure via a network from a device that generated the data structure.   
     
     
         11 . The method of  claim 8 , wherein:
 the accessed data structure includes coefficients of basis functions that correspond to the signal defined on the set of 3D points specified by the point cloud.   
     
     
         12 . The method of  claim 8 , wherein:
 the volumetric function that represents the signal is a first volumetric function that represents geometry of the point cloud that specifies the set of 3D points;   the point cloud specifies a corresponding set of attributes for each 3D point among the set of 3D points; and   the method further comprises:   evaluating a second volumetric function indicated by the accessed data structure, the second volumetric function determined based on the sets of attributes that correspond to the set of 3D points.   
     
     
         13 . The method of  claim 12 , further comprising:
 prior to the evaluating of the second volumetric function, determining the second volumetric function by performing operations comprising:
 performing entropy decoding on entropy coded and quantized coefficients of the second volumetric function; and 
 determining the coefficients of the second volumetric function by inverse quantizing the entropy decoded but still quantized coefficients of the second volumetric function. 
   
     
     
         14 . A system comprising:
 one or more processors; and   a memory storing instructions that, when executed by at least one processor among the one or more processors, cause the system to perform operations comprising:   accessing a point cloud that specifies a set of three-dimensional (3D) points; and   generating a data structure that indicates a volumetric function that corresponds to a signal defined on the set of 3D points specified by the accessed point cloud.   
     
     
         15 . The system of  claim 14 , wherein the operations further comprise:
 providing the generated data structure that indicates the volumetric function to a device configured to recover the point cloud by evaluating the volumetric function indicated by the data structure, the evaluating of the volumetric function including determining at least some values of the signal defined on the set of 3D points specified by the point cloud.   
     
     
         16 . A system comprising:
 one or more processors; and   a memory storing instructions that, when executed by at least one processor among the one or more processors, cause the system to perform operations comprising:   accessing a data structure that indicates a volumetric function that corresponds to a signal defined on a set of three-dimensional (3D) points specified by a point cloud;   recovering the point cloud by evaluating the volumetric function indicated by the accessed data structure; and   causing a rendering of the recovered point cloud based on the evaluating of the volumetric function indicated by the accessed data structure.   
     
     
         17 . A non-transitory machine-readable storage medium comprising instructions that, when executed by one or more processors of a machine, cause the machine to perform operations comprising:
 accessing a point cloud that specifies a set of three-dimensional (3D) points; and   generating a data structure that indicates a volumetric function that corresponds to a signal defined on the set of 3D points specified by the accessed point cloud.   
     
     
         18 . The non-transitory machine-readable storage medium of  claim 17 , wherein the operations further comprise:
 providing the generated data structure that indicates the volumetric function to a device configured to recover the point cloud by evaluating the volumetric function indicated by the data structure, the evaluating of the volumetric function including determining at least some values of the signal defined on the set of 3D points specified by the point cloud.   
     
     
         19 . A non-transitory machine-readable storage medium comprising instructions that, when executed by one or more processors of a machine, cause the machine to perform operations comprising:
 accessing a data structure that indicates a volumetric function that corresponds to a signal defined on a set of three-dimensional (3D) points specified by a point cloud;   recovering the point cloud by evaluating the volumetric function indicated by the accessed data structure; and   causing a rendering of the recovered point cloud based on the evaluating of the volumetric function indicated by the accessed data structure.   
     
     
         20 . The non-transitory machine-readable storage medium of  claim 19 , wherein:
 in the recovering of the point cloud, the evaluating of the volumetric function includes determining at least some values of the signal defined on the set of 3D points specified by the point cloud.