Reconstructing Spectra from Tristimulus Values Using PCA
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Solution Overview
Problem
The challenge lies in converting color information represented by Lab values back into the spectral domain, particularly for different observers and illuminants, as existing methods reduce the information from 36 spectral samples to 3 tristimulus values, losing detail and limiting applications in printing and color reproduction.
Innovation Solution
A method using Principal Component Analysis (PCA) to generate reflectance spectrum values from tristimulus values, incorporating additional knowledge of print process parameters, and employing reference spectra to improve accuracy and avoid physical limitations like negative or excessive reflectance values.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Quantity of substance
If tristimulus values are used to represent color, then the information amount is reduced from 36 to 3 values, but the ability to calculate perceived color under arbitrary illuminants and observers is lost
Solution Approach 1:
The patent pre-calculates and stores transformation matrices for converting between spectral data and tristimulus values under multiple standard illuminants and observer conditions. This preliminary preparation enables the system to quickly adapt to different viewing conditions without requiring full spectral measurements, thus maintaining versatility while using reduced color data.
Solution Approach 2:
The patent introduces an intermediary transformation matrix that bridges the gap between tristimulus values and spectral domain representations. This matrix acts as a mediator that allows conversion to different illuminant and observer conditions without needing the original full spectrum, preserving adaptability while working with compressed color data.
2Measurement precision
If spectral data is converted to Lab values for color encoding, then the color perception accuracy is improved, but the spectral information required for physical print models is lost
Solution Approach 1:
The patent creates a mathematical copy of spectral information through transformation matrices that can be regenerated from Lab values. Instead of storing actual spectral data, the system creates computable representations that replicate spectral behavior for print modeling purposes while maintaining the benefits of Lab color space for perception accuracy.
Solution Approach 2:
The patent transforms the representation parameters from full spectral data to compressed Lab values with associated transformation matrices. This parameter change enables the system to work with fewer values while still recovering spectral characteristics when needed for physical print model calculations.
3Device complexity
If a simple conversion method from Lab to spectrum is used, then the computational complexity is reduced, but the accuracy of reconstructed spectra deteriorates
Solution Approach 1:
The patent pre-computes and stores lookup tables and transformation matrices during an offline training phase. This preliminary action moves the complex computational work to a setup stage, allowing the actual conversion from Lab to spectrum to use simpler, faster matrix operations while maintaining high reconstruction accuracy through the pre-optimized transformation data.
Data Source
AI summary
To bring color, described by Lab values only, back into the spectral domain the invention discloses a method for automatically generating reflectance spectrum values from tristimulus values using a computer system administrating a database with data matrices of reflectance spectra of different colors differentiated by at least the process parameters print technology, substrate and print order of inks, wherein a) given tristimulus values of a color are classified with regard to the process parameters, b) in the database the data matrices of reflectance spectra of the respective color with the most matching process parameters are identified and c) the identified data matrix is used to define the reflectance spectrum values for the respective color.