Piece-Wise Linear Inverse Mapping for Video Coding
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Solution Overview
Problem
Existing video encoding and decoding methods face inefficiencies in implementing inverse mapping processes due to the complexity and size of look-up tables required for inverse mapping functions, particularly in video codecs like HEVC and VVC, which hinder efficient coding performance.
Innovation Solution
The method involves approximating the inverse mapping function as a piece-wise linear function with equi-length intervals, allowing for simplified on-the-fly implementation using smaller look-up tables, reducing the computational burden and improving coding efficiency.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If the inverse mapping function is implemented using a precise look-up table, then mapping accuracy is improved, but device complexity and memory requirements increase
Solution Approach 1:
The inverse mapping function is divided into multiple piece-wise linear segments, where each segment approximates a portion of the inverse mapping curve. This segmentation allows the complex non-linear inverse mapping to be represented by simpler linear functions, reducing computational complexity while maintaining acceptable accuracy.
Solution Approach 2:
The patent changes the representation parameters of the inverse mapping function from a complete look-up table to a set of piece-wise linear parameters (breakpoints, slopes, intercepts). This parameter transformation reduces memory requirements and simplifies the implementation structure while preserving the essential mapping characteristics.
2Measurement precision
If the inverse mapping function is implemented using a look-up table, then mapping precision is improved, but processing speed decreases due to larger memory access requirements
Solution Approach 1:
The patent replaces the mechanical memory access operation (look-up table retrieval) with mathematical computation (evaluating piece-wise linear functions). This substitution eliminates the need for large memory structures and random access operations, reducing latency and improving processing speed while maintaining mapping precision through the mathematical model.
3Measurement precision
If a complete inverse mapping look-up table is used, then mapping accuracy is maintained, but memory usage increases
Solution Approach 1:
The patent extracts only the essential characteristics of the inverse mapping function by identifying key breakpoints and linear segments, discarding the redundant information present in a complete look-up table. This extraction process retains the critical mapping behavior while eliminating unnecessary memory storage requirements.
Solution Approach 2:
The piece-wise linear parameters serve as a lightweight, computationally efficient alternative to the heavy look-up table structure. These simplified parameters consume minimal memory resources while providing sufficient accuracy for the inverse mapping operation, effectively replacing the resource-intensive original approach.
Data Source
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Figure 2
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AI summary
Reshaping can be used to better exploit the sample value distribution of video data. When reshaping is used inside the coding loop, forward mapping is applied to prediction signals from intra or inter prediction, and inverse mapping is applied to reconstructed signals. To simplify the inverse mapping operations, in one embodiment, the inverse mapping function is modelled as a piece-wise linear function, and each line segment is defined on an equi-distant interval of a length equal to a power of 2. In this embodiment, the inverse mapping function is specified by the number of pieces, initial offset value and the slope for each piece. In one example, the slope parameters can be signaled directly in the bitstream. In another example, an initial estimate of the slope parameters can be obtained from the forward mapping function, and the difference between the initial estimate and the actual parameters are signaled.