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Proceedings Paper

Structures in color space
Author(s): Alexander P. Petrov
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Paper Abstract

Classic colorimetry and the traditionally used color space do not represent all perceived colors (for example, browns look dark yellow in colorimetric conditions of observation) so, the specific goal of this work is to suggest another concept of color and to prove that the corresponding set of colors is complete. The idea of our approach attributing color to surface patches (not to the light) immediately ties all the problems of color perception and vision geometry. The equivalence relation in the linear space of light fluxes F established by a procedure of colorimetry gives us a 3D color space H. By definition we introduce a sample (sigma) (surface patch) as a linear mapping (sigma) : L yields H, where L is a subspace of F called the illumination space. A Dedekind structure of partial order can be defined in the set of the samples: two samples (alpha) and (Beta) belong to one chromatic class if ker(alpha) equals ker(Beta) and (alpha) > (Beta) if ker(alpha) ker(Beta) . The maximal elements of this chain create the chromatic class BLACK. There can be given geometrical arguments for L to be 3D and it can be proved that in this case the minimal element of the above Dedekind structure is unique and the corresponding chromatic class is called WHITE containing the samples (omega) such that ker(omega) equals {0} L. Color is defined as mapping C: H yields H and assuming color constancy the complete set of perceived colors is proved to be isomorphic to a subset C of 3 X 3 matrices. This subset is convex, limited and symmetrical with E/2 as the center of symmetry. The problem of metrization of the color space C is discussed and a color metric related to shape, i.e., to vision geometry, is suggested.

Paper Details

Date Published: 30 September 1996
PDF: 6 pages
Proc. SPIE 2826, Vision Geometry V, (30 September 1996); doi: 10.1117/12.251805
Show Author Affiliations
Alexander P. Petrov, Kurchatov Institute (Russia)

Published in SPIE Proceedings Vol. 2826:
Vision Geometry V
Robert A. Melter; Angela Y. Wu; Longin Jan Latecki, Editor(s)

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