The hyperbolic geometry of illumination induced chromaticity changes

Reiner Lenz and Pedro Latorre-Carmona and Peter Meer

The non-negativity of color signals implies that they spana 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 alsoaddressed.

(BibTeX entry) (IEEE)