Non-euclidean structure of spectral color space

Color processing methods can be divided into methods based on human color vision and spectral based methods. Human vision based methods usually describe color with three parameters which are easy to interpret since they model familiar color perception processes. They share however the limitations of human color vision such as metamerism. Spectral based methods describe colors by their underlying spectra and thus do not involve human color perception. They are often used in industrial inspection and remote sensing. Most of the spectral methods employ a low dimensional (three to ten) representation of the spectra obtained from an orthogonal (usually eigenvector) expansion. While the spectral methods have solid theoretical foundation, the results obtained are often difficult to interpret. In this paper we show that for a large family of spectra the space of eigenvector coefficients has a natural cone structure. Thus we can define a natural, hyperbolic coordinate system whose coordinates are closely related to intensity, saturation and hue. The relation between the hyperbolic coordinate system and the perceptually uniform Lab color space is also shown. Defining a Fourier transform in the hyperbolic space can have applications in pattern recognition problems.