Non-euclidean structure of the spectral color space
Reiner Lenz(1) Peter Meer(2)
Department of Science and Technology
(1)Linköping University, S-60174 Norrköping, Sweden
(2)Department of Electrical and Computer Engineering
Rutgers University, Piscataway, NJ 08855, USA
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
EUROPTO: Conference on Polarization and Color Techniques
in Industrial Inspection, Munich, Germany, June 1999.
SPIE Proceedings, vol. 3826, E.A. Marszalec and E. Trucco (Eds.),