Chroma Mapping Functions Hue Sector Partitioning
Find Innovative SolutionsGenerate Solutions
Solution Overview
Problem
Current gamut mapping methods, particularly linear and high-degree polynomial chroma mapping, suffer from significant interpolation errors, especially for primary colors, leading to clipping, desaturation, and undesirable oscillations in smooth areas, which compromise color preservation and artistic control.
Innovation Solution
The method employs chroma mapping functions specific to each angular hue sector, defined by key hue leaf functions, ensuring continuity and reduced complexity, using polynomial functions with varying parameters to approximate different behaviors and manage second-order discontinuities, thereby reducing interpolation errors and maintaining artistic control.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If high-degree polynomial chroma mapping functions are used, then mapping precision for primary colors is improved, but interpolation errors and oscillations increase
Solution Approach 1:
The color space is segmented into multiple angular hue sectors, each processed by a dedicated low-degree polynomial mapping function. This segmentation prevents the oscillations and interpolation errors that occur when using a single high-degree polynomial across the entire hue range, while still achieving precise mapping for primary colors through sector-specific optimization.
Solution Approach 2:
Different polynomial mapping functions with varying degrees and parameters are applied to different hue sectors based on local color characteristics. Primary color sectors receive higher-degree polynomials for precise mapping, while other sectors use lower-degree functions to avoid oscillations, achieving local optimization without global instability.
2Device complexity
If piecewise linear mapping functions are used, then computational complexity is reduced, but color continuity and smoothness deteriorate
Solution Approach 1:
The patent replaces linear mapping segments with curved polynomial mapping functions that provide continuous derivatives across sector boundaries. This curvature ensures smooth color gradients and eliminates the visible banding that would result from piecewise linear transitions, while keeping individual polynomial degrees low for computational efficiency.
3Ease of manufacture
If homogeneous non-linear chroma mapping is applied, then implementation simplicity is improved, but adaptability to different hue behaviors is reduced
Solution Approach 1:
The mapping system dynamically selects and parameters-adjusts polynomial functions based on the specific hue sector being processed. Each sector can have optimized polynomial parameters that adapt to its unique color characteristics, providing hue-specific adaptability while maintaining a unified polynomial-based framework for implementation simplicity.
Data Source
Figure 1~2
Figure 3
Figure 4
AI summary
This determination comprises: defining key constant-hue leaves such as to partition the gamut mapping color space into angular hue sectors; for each key constant hue leaf, defining a key hue leaf chroma mapping function; for each angular hue sector, defining a continuous angular hue sector chroma mapping function such that, for any source color belonging to one of the two key constant-hue leaves delimiting this angular hue sector, this continuous chroma mapping function allows to map the chroma of said source color according to the key hue leaf chroma mapping function of the key constant-hue leaf to which said source color belongs. Preferably, this mapping functions are non linear polynomials.