Universal Color Index Cube Root Transformation
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Solution Overview
Problem
Current color measurement systems, such as the CIE L*a*b* standard, confound reflectance spectra with illumination and observer effects, leading to nonlinear transformations and errors in color specification, particularly in the Munsell color space, which affects precision in color reproduction and mixing.
Innovation Solution
Applying a cube root transformation to reflectance spectra at the beginning of calculations instead of the end, allowing for a simplified analytic relationship between physical and perceptual color systems, enabling precise linear transformations between reflectance spectra and Munsell color space, eliminating the need for look-up tables and improving precision in color specification.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If conventional color measurement systems (CIE L*a*b*) are used to transform reflectance spectra into color spaces, then color specification can be obtained, but nonlinear effects and perceptual similarities differ in different parts of the space, reducing measurement precision
Solution Approach 1:
The patent applies a cube root transformation to the reflectance spectra at the beginning of the calculation process, before transforming to color space. This preliminary transformation linearizes the relationship between spectral differences and perceptual color differences, eliminating the need for complex nonlinear transformations and look-up tables later in the process.
Solution Approach 2:
Instead of applying the cube root transformation at the end of the color space calculation (as in conventional CIE L*a*b* systems), the patent inverts the approach by applying it at the beginning to the reflectance spectra. This reversal simplifies the entire transformation chain and maintains linearity throughout the color specification process.
2Manufacturing precision
If color matching functions are used to transform reflectance spectra into CIE color spaces, then color location can be calculated, but the definition confounds reflectance spectra with illuminate and observer, leading to errors in color reproduction
Solution Approach 1:
The patent extracts and separates the cube root transformation from the conventional color matching function process. By applying the transformation directly to the reflectance spectra before color space transformation, it eliminates the confounding of reflectance spectra with illuminate and observer characteristics that occurs in standard CIE systems, thereby improving color reproduction accuracy.
3Measurement precision
If complex calculations with look-up tables are used to place samples in CIE L*a*b* chromaticity space, then color location can be determined, but the process is computationally intensive and less precise
Solution Approach 1:
By applying the cube root transformation preliminarily to the reflectance spectra, the patent creates a linearized input that can be directly transformed into color space using simple matrix operations. This eliminates the need for computationally intensive look-up tables and iterative calculations, significantly improving calculation efficiency while maintaining or enhancing precision.
Data Source
AI summary
A method for establishing a relationship between a physical structure of reflectance spectra as defined in a Euclidean color space and a perceptual space of color appearance defined in terms of human perception of colors is performed by obtaining a cube root spectrum of the physical reflectance spectrum in a selected spectral range, reconstructing the cube root of the physical reflectance spectrum by a weighted linear combination of three basis functions, the weights of the linear combination of the basis functions constituting the coordinates in a three-dimensional Euclidean color space with respect to which similarities and differences among reflectance spectra in metric terms and a color characterized in a perceptual space of color appearance can be analyzed, and making an analytic comparison between a physical system in the three-dimensional Euclidean color space and the perceptual system by means of a linear transformation therebetween.