Spectral color information is used nowadays in many different applications. Accurate spectral images are usually very large files, but a proper compression method can reduce needed storage space remarkably with a minimum loss of information. In this paper we introduce a principal component analysis (PCA) -based compression method of spectral color information. In this approach spectral data is weighted with a proper weight function before forming the correlation matrix and calculating the eigenvector basis. First we give a general framework for how to use weight functions in compression of relevant color information. Then we compare the weighted compression method with the traditional PCA compression method by compressing and reconstructing the Munsell data set consisting of 1,269 reflectance spectra and the Pantone data set consisting of 922 reflectance spectra. Two different weight functions are proposed and tested. We show that weighting clearly improves retention of color information in the PCA-based compression process.

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A novel general transformation between reflectance spectra and the corresponding coordinates of the

In this study, we have analyzed statistical properties of the values of the first- and second-order derivatives of spectral reflectance curves. We show that values of all four tested spectral data sets have very similar statistical properties. We set outer limits that bound the clear majority of the values of the first- and second-order derivatives. These limits define smoothness of all nonfluorescent reflectance curves, and they can be used to form a new object color solid inside classical MacAdam limits, including all possible colors generated by smooth nonfluorescent reflectance spectra. We have used the CIELAB color space and filled the new object color solid with a hexagonal closest packing-point lattice to estimate that there exist about 2.5 million different colors, when viewed under the D65 standard illumination.

Principal component analysis (PCA) and weighted PCA were applied to spectra of optimal colors belonging to the outer surface of the object-color solid or to so-called MacAdam limits. The correlation matrix formed from this data is a circulant matrix whose biggest eigenvalue is simple and the corresponding eigenvector is constant. All other eigenvalues are double, and the eigenvectors can be expressed with trigonometric functions. Found trigonometric functions can be used as a general basis to reconstruct all possible smooth reflectance spectra. When the spectral data are weighted with an appropriate weight function, the essential part of the color information is compressed to the first three components and the shapes of the first three eigenvectors correspond to one achromatic response function and to two chromatic response functions, the latter corresponding approximately to Munsell opponent-hue directions 9YR-9B and 2BG-2R.