Color Conversion Matrix Formation Using Pseudo Inverse Matrices

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Solution Overview

Problem

Existing color reproduction technologies face challenges in efficiently forming color profiles for consumer devices due to individual differences and aging changes, requiring complex arithmetic operations and high processing loads to account for non-linear color mixtures.

Innovation Solution

A method involving constructing an nth-degree matrix using color patch data sets and obtaining a pseudo inverse matrix to form a color conversion matrix, simplifying the process through linear algebra operations and matrix operations on a computer.

Engineering Contradictions & Design Principles

VSEngineering Contradiction Analysis

1Measurement precision

If a higher-degree matrix is formed to consider nonlinear elements in color conversion, then color reproduction accuracy is improved, but processing complexity and computational load increase significantly

Engineering Contradiction:

Improvecolor reproduction accuracyVSAvoidprocessing complexity

Core Design Contradiction:

Measurement precisionVSDevice complexity

Solution Approach 1:

The patent segments the color conversion process into two distinct stages: (1) constructing an nth-degree matrix using color patch data sets, and (2) obtaining a pseudo inverse matrix to form the final color conversion matrix. This segmentation allows complex nonlinear color conversion to be broken down into manageable computational steps, reducing overall processing complexity while maintaining accuracy.

Inventive Principle:

Principle #1Segmentation

Solution Approach 2:

The patent performs preliminary construction of the nth-degree matrix using color patch data sets before actual color conversion operations. By pre-computing and storing the pseudo inverse matrix, the system eliminates the need for complex real-time calculations during color conversion, significantly reducing processing load while maintaining high color reproduction accuracy.

Inventive Principle:

Principle #10Preliminary action

2Reliability

If a profile is formed for each individual apparatus to eliminate color drift, then color reproduction consistency is improved, but processing time and computational resources increase

Engineering Contradiction:

Improvecolor reproduction consistencyVSAvoidprocessing time

Core Design Contradiction:

ReliabilityVSLoss of time

Solution Approach 1:

The patent enables each apparatus to self-form its own color profile using the standardized method. By providing a unified approach where each device independently constructs its nth-degree matrix and pseudo inverse matrix from its specific color patch data, the system eliminates color drift between devices without requiring centralized profile creation, thereby reducing processing time while maintaining consistency.

Inventive Principle:

Principle #25Self-service

Solution Approach 2:

The patent changes the approach from using fixed standard profiles to dynamically adjusting color conversion parameters based on each apparatus's specific characteristics. By forming device-specific nth-degree matrices from actual color patch data, the system adapts to individual apparatus variations, eliminating color drift while maintaining efficient processing through standardized algorithms.

Inventive Principle:

Principle #35Parameter changes

3Measurement precision

If the method of least squares is used to find optimal solutions for color conversion, then color reproduction accuracy is improved, but computational complexity increases due to partial differentiation operations

Engineering Contradiction:

Improvecolor reproduction accuracyVSAvoidcomputational complexity

Core Design Contradiction:

Measurement precisionVSDevice complexity

Solution Approach 1:

The patent replaces the mechanical differentiation operations of the method of least squares with matrix algebra operations. Instead of performing partial differentiation to find optimal solutions, the system uses pseudo inverse matrix calculations, which are computationally more efficient and easier to implement while achieving the same goal of finding optimal color conversion parameters.

Inventive Principle:

Principle #28Mechanics substitution (Replace mechanical system)

Solution Approach 2:

The patent inverts the traditional approach by constructing the nth-degree matrix first and then obtaining its pseudo inverse, rather than directly applying least squares optimization. This inversion of the computational sequence simplifies the mathematical operations required, reducing computational complexity while maintaining the ability to find optimal color conversion solutions.

Inventive Principle:

Principle #13The other way round (Inversion)

Data Source

PatentUS7414754B2Color conversion matrix forming method, color conversion table forming method, and program

Publication Date: 2008.08.19 CANON KK

AI summary

A method of easily obtaining a color conversion matrix serving as a foundation of color reproduction at a high speed irrespective of its degree is provided. The method has: a step of constructing nth-degree matrix coefficients regarding a first color space of a plurality of color patch data sets and obtaining a pseudo inverse matrix to the obtained matrix; and a step of forming a color conversion matrix from a product of a matrix constructed by color data regarding a second color space of the color patch data sets and the pseudo inverse matrix.