The hyperbolic geometry of illumination induced chromaticity changes.

Reiner Lenz(1)    Pedro Latorre Carmona(2)   Peter Meer(3)

(1)Department of Science and Technology
Linköping University, S-60174 Norrköping, Sweden

(2)Comp. Languages and Systems, Jaume I University Castellon, Spain

(3)Department of Electrical and Computer Engineering
Rutgers University, Piscataway, NJ 08855, USA

The non-negativity of color signals implies that they span a conical space with a hyperbolic geometry. We use perspective projections to separate intensity from chromaticity, and for 3-D color descriptors the chromatic properties are represented by points on the unit disk. Descriptors derived from the same object point but under different imaging conditions can be joined by a hyperbolic geodesic. The properties of this model are investigated using multichannel images of natural scenes and black body illuminants of different temperatures. We show, over a series of static scenes with different illuminants, how illumination changes influence the hyperbolic distances and the geodesics. Descriptors derived from conventional RGB images are also addressed.

2007 Computer Vision and Pattern Recognition Conference, Minneapolis, Minnesota, June 2007.
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