Non-euclidean structure of spectral color space
Reiner Lenz
Abstract:
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.
Keywords: Color spectra, eigenvector decomposition,
non-euclidean geometry, Mehler-Fok transform
