3D Mesh Octree Entropy Coding for Varying Symbol Statistics
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Solution Overview
Problem
Existing entropy encoding methods are inefficient when dealing with sequences of symbols that have varying statistics, as they either incur high overhead by dividing portions into sub-sequences or fail to utilize the statistical properties of different symbol sets effectively.
Innovation Solution
A hierarchical entropy encoding/decoding method that partitions a sequence of symbols into three parts, using different symbol sets for each part based on their statistical properties, with a pre-determined symbol set and a universal symbol set to efficiently encode and decode geometry data in 3D meshes, reducing overhead and improving compression efficiency.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Productivity
If a sequence of symbols with varying statistics is encoded using a single statistical model, then the encoding process is simple, but the compression efficiency is poor
Solution Approach 1:
The sequence of symbols is divided into multiple portions, each portion being encoded using a statistical model adapted to its local characteristics. This segmentation allows the encoder to capture varying statistics in different regions of the data, improving compression efficiency while maintaining manageable complexity through localized processing.
Solution Approach 2:
The statistical model is made adaptive by dynamically switching between different symbol sets (first symbol set for frequent symbols, second symbol set for less frequent symbols) based on the actual data distribution encountered during encoding. This dynamic adaptation allows the system to optimize compression efficiency for each portion of the sequence without requiring complex pre-analysis.
2Productivity
If the sequence is divided into multiple portions with different statistical models, then compression efficiency improves, but overhead increases
Solution Approach 1:
Two symbol sets are merged into a unified hierarchical structure where the first symbol set (for frequent symbols) and the second symbol set (for less frequent symbols) work together in a coordinated manner. This merging allows the encoder to handle multiple symbol distributions without requiring separate complete encodings, thereby reducing overhead while maintaining compression efficiency.
Solution Approach 2:
The first symbol set is nested within the second symbol set to form a hierarchical encoding structure. When a symbol from the first symbol set is encountered, it is encoded directly; when a symbol from the second symbol set is encountered, it is encoded through the hierarchical structure. This nesting allows efficient encoding of both frequent and less frequent symbols within a unified framework, minimizing overhead.
3Productivity
If multiple symbol sets are used for different portions, then coding efficiency for varying statistics improves, but the number of symbol sets required increases
Solution Approach 1:
The hierarchical symbol set structure serves multiple functions: the first symbol set handles frequent symbols efficiently, the second symbol set handles less frequent symbols, and together they provide a universal encoding solution for sequences with varying statistics. This multi-functionality allows a single hierarchical structure to replace what would otherwise require multiple separate symbol sets, reducing overall complexity.
Solution Approach 2:
The system changes the parameter of symbol set selection dynamically based on the statistical characteristics of the data being encoded. By adapting which symbol set is used based on the local data distribution, the system achieves high coding efficiency for varying statistics without requiring a large number of fixed symbol sets, as the same hierarchical structure can adapt to different symbol distributions.
Data Source
AI summary
A particular implementation receives geometry data of a 3D mesh, and represents the geometry data with an octree. The particular implementation partitions the octree into three parts, wherein the symbols corresponding to the middle part of the octree are hierarchical entropy encoded. To partition the octree into three parts, different thresholds are used. Depending on whether a symbol associated with a node is an S1 symbol, the child node of the node is included in the middle part or the upper part of the octree. In hierarchical entropy encoding, a non-S1 symbol is first encoded as a pre-determined symbol ‘X’ using symbol set S2={S1, ‘X’} and the non-S1 symbol itself is then encoded using symbol set S0 (S2⊂S0), and an S1 symbol is encoded using symbol set S2. Another implementation defines corresponding hierarchical entropy decoding. A further implementation reconstructs the octree and restores the geometry data of a 3D mesh from the octree representation.