Mathematical methods of color correction

In the reproduction of a color image, the illuminant under which the reproduction is viewed and compared to the original image will have a significant effect upon the color match between the images. The vector space approach to color systems has enabled a straight forward formalization of color reproduction problems. In this dissertation, methods of estimating CIE tristimulus values from recorded data of an image for a number of viewing illuminants are introduced. The methods include an approach which models the reflectance spectra with a small number of basis vectors; a linear minimum mean square error (LMMSE) estimator in tristimulus space and in a uniform color space; a linear transformation in tristimulus space which minimize a perceptual error and a set theoretic method in which physical constraints of the reflectance spectra are enforced to obtain a feasible solution. The sensitivity of the methods to noise and parameter perturbations is investigated through simulations.; If there are several viewing illuminants under which the original image and a reproduction are to match, then in recording a color image it is desirable to obtain, from a single device, CIE tristimulus values of the original image for each viewing illuminant. In this dissertation, methods of optimizing the spectral sensitivity of the recording device to enable accurate color correction for several viewing illuminants are introduced. The methods include minimizing the maximum error in tristimulus space, minimizing a weighted mean square error in a normalized tristimulus space, minimizing the maximum error in a perceptual color space, and minimizing a weighted mean square error in a perceptual color space. The relationship between signal-to-noise ratio and the number of filters is investigated, and a method of selecting filters in the presence of signal independent noise is introduced. The sensitivity of the color correction accuracy to filter perturbations is analyzed, and a criteria for minimizing the sensitivity of the filters to these perturbations is suggested.; The color correction methods are simulated at various signal-to-noise ratios using real reflectance spectra. The methods were implemented to perform a multi-illuminant calibration of a color printer.