Tetrahedral Interpolation for Color Gamut Conversion
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Solution Overview
Problem
Current color gamut conversion methods using tetrahedral interpolation are computationally intensive and power-consuming due to the need for calculating fourth-order matrix determinants for each pixel, failing to meet user requirements for efficiency and performance.
Innovation Solution
A method and device for color gamut conversion based on tetrahedral interpolation calculation, which calculates the volume of a tetrahedron and its sub-tetrahedrons using specific formulas, reducing the need for matrix determinants and optimizing the calculation process by using coordinates and side lengths of sampling points in a sampling space.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If tetrahedral interpolation is used for color gamut conversion, then color conversion accuracy is improved, but computational complexity and processing time increase
Solution Approach 1:
The patent divides the color space into multiple tetrahedrons formed by sampling points, and further segments each tetrahedron into four sub-tetrahedrons by introducing the interpolation point. This segmentation allows the complex interpolation calculation to be broken down into simpler volume calculations of sub-tetrahedrons, reducing computational complexity while maintaining accuracy.
Solution Approach 2:
The patent changes the calculation parameters from fourth-order matrix determinants to volume calculations based on coordinates and side lengths. By transforming the mathematical model from matrix-based to geometry-based parameter representation, the computational complexity is reduced while preserving the interpolation accuracy.
2Measurement precision
If tetrahedral interpolation with matrix determinants is applied, then interpolation accuracy is improved, but processing time increases
Solution Approach 1:
The patent replaces the mechanical calculation process of fourth-order matrix determinants with a geometric approach using volume calculations. This substitution of calculation methodology significantly reduces processing time while maintaining interpolation accuracy through the use of tetrahedron volume relationships.
Solution Approach 2:
The patent pre-calculates and stores the mapping values of the four vertices of each tetrahedron before performing the interpolation. This preliminary action of preparing vertex data allows the actual interpolation to proceed with simpler calculations, reducing processing time while maintaining accuracy.
3Measurement precision
If tetrahedral interpolation calculation is performed for each pixel, then color gamut conversion accuracy is improved, but power consumption increases
Solution Approach 1:
The patent changes the computational parameters from complex matrix determinants to simpler volume calculations based on coordinates and side lengths. This parameter transformation reduces the computational workload per pixel, thereby decreasing power consumption while maintaining color gamut conversion accuracy.
Solution Approach 2:
By segmenting the tetrahedron into four sub-tetrahedrons and using the volume relationship formula, the patent simplifies the calculation required for each pixel. This segmentation approach reduces the computational complexity per pixel, leading to lower power consumption while preserving conversion accuracy.
Data Source
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AI summary
A tetrahedral interpolation calculation method and apparatus, a gamut conversion method and apparatus, and a medium, the tetrahedral interpolation calculation method comprising: according to coordinates of a point to be interpolated in a sampling space, and the side length of a cube formed by eight nearby sampling points surrounding the point to be interpolated in the sampling space, calculating the volume of a tetrahedron and the volumes of four sub-tetrahedrons formed by the point to be interpolated and any three vertices in the tetrahedron; and according to a tetrahedral interpolation theorem formula, the volume of the tetrahedron, the volumes of the four sub-tetrahedrons, and mapping values of four vertices of the tetrahedron, obtaining an interpolation value of the point to be interpolated. By employing the described solution, tetrahedral interpolation calculation may be performed quickly and efficiently.