Color constancy. I. Basic theory of two-stage linear recovery of spectral descriptions for lights and surfaces.

Changing a scene's illuminant causes the chromatic properties of reflected lights to change. This change in the lights from surfaces provides spectral information about surface reflectances and illuminants. We examine conditions under which these properties may be recovered by using bilinear models. Necessary conditions that follow from comparing the number of equations and the number of unknowns in the recovery procedure are not sufficient for unique recovery. Necessary and sufficient conditions follow from demanding a one-to-one relationship between quantum catch data and sets of lit surfaces. We present an algorithm for determining whether spectral descriptions of lights and surfaces can be recovered uniquely from reflected lights.