On counting metamers

Objects reflecting lights, which invoke the identical responses of the photoreceptors, are called metameric. Metameric objects match each other in color. Assuming all the reflecting objects equiprobable, the probability density distribution on the set of all the classes of mutually metameric objects is evaluated. Metamerism depends on illumination. Objects metameric under one illumination might produce different photoreceptor responses (i.e., mismatch each other) under the other illumination. In particular, objects mapping to a single point in the photoreceptor response space under one illumination map to a volume (referred to as the metamer mismatch volume) in the photoreceptor response space under the second illumination. The probability density distribution in the metamer mismatch volume is also evaluated. Its center is expressed as a function of the photoreceptor spectral sensitivities and the spectral power distributions of the illuminants. Potential application of the obtained results to color management is discussed.