Bezier volume representation of point cloud attributes
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.
1. A method comprising:
accessing, by one or more processors of an encoder machine, a point cloud that specifies a finite set of points in three-dimensional space; and
generating, by one or more processors of the encoder machine, a data structure that represents a volumetric function, the volumetric function representing a signal defined on the finite set of points of the accessed point cloud.
2. The method of claim 1 , further comprising:
determining the volumetric function based on values of the signal defined on the finite set of points of the accessed point cloud.
3. The method of claim 1 , further comprising:
providing the generated data structure to a decoder machine configured to recover values of the signal within a predetermined approximation threshold by evaluating the volumetric function on the finite set of points.
4. The method of claim 1 , wherein:
the generating the data structure that represents the volumetric function includes determining coefficients of basis functions that correspond to the signal defined on the finite set of points.
5. The method of claim 1 , wherein:
the volumetric function that represents the signal is a first volumetric function that represents geometry information of the point cloud;
the point cloud specifies a corresponding set of attributes for each point among the finite set of points; and
the method further comprises:
performing data compression on the sets of attributes that correspond to the finite set of 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 decoder machine by providing the generated data structure within a bit stream to the decoder machine.
8. A method comprising:
accessing, by one or more processors of a decoder machine, a data structure that represents a volumetric function, the volumetric function representing a signal on a finite set of points specified by a point cloud in three-dimensional space;
recovering, by one or more processors of the decoder machine, the point cloud within a predetermined approximation threshold by evaluating the volumetric function represented by the accessed data structure; and
causing, by one or more processors of the decoder machine, rendering and display of the recovered point cloud based on results of the evaluating of the volumetric function represented 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 determines values of the signal defined on the finite set of points specified by the point cloud.
10. The method of claim 8 , wherein:
the accessing of the data structure includes receiving the data structure within a bit stream generated by a encoder machine.
11. The method of claim 8 , wherein:
the accessed data structure includes coefficients of basis functions that correspond to the signal defined on the finite set of 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 information of the point cloud;
the point cloud specifies a corresponding set of attributes for each point among the finite set of points; and
the method further comprises:
evaluating a second volumetric function defined by the accessed data structure, the second volumetric function representing the sets of attributes that correspond to the finite set of 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 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. An encoder 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 finite set of points in three-dimensional space; and
generating a data structure that represents a volumetric function, the volumetric function representing a signal defined on the finite set of points of the accessed point cloud.
15. The encoder system of claim 14 , wherein the operations further comprise:
providing the generated data structure to a decoder machine configured to recover values of the signal within a predetermined approximation threshold by evaluating the volumetric function on the finite set of points.
16. A decoder 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 represents a volumetric function, the volumetric function representing a signal on a finite set of points specified by a point cloud in three-dimensional space;
recovering the point cloud within a predetermined approximation threshold by evaluating the volumetric function represented by the accessed data structure; and
causing rendering and display of the recovered point cloud based on results of the evaluating of the volumetric function represented by the accessed data structure.
17. A non-transitory machine-readable storage medium comprising instructions that, when executed by one or more processors of an encoder machine, cause the encoder machine to perform operations comprising:
accessing a point cloud that specifies a finite set of points in three-dimensional space; and
generating a data structure that represents a volumetric function, the volumetric function representing a signal defined on the finite set of points of 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 to a decoder machine configured to recover values of the signal within a predetermined approximation threshold by evaluating the volumetric function on the finite set of points.
19. A non-transitory machine-readable storage medium comprising instructions that, when executed by one or more processors of a decoder machine, cause the decoder machine to perform operations comprising:
accessing a data structure that represents a volumetric function, the volumetric function representing a signal on a finite set of points specified by a point cloud in three-dimensional space;
recovering the point cloud within a predetermined approximation threshold by evaluating the volumetric function represented by the accessed data structure; and
causing rendering and display of the recovered point cloud based on results of the evaluating of the volumetric function represented 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 determines values of the signal defined on the finite set of points specified by the point cloud.