The object-color solid.

Abstract

An algorithm is described that for the first time accurately computes the true object-color solid. Previous methods have computed only approximations to the true object-color solid since they have been based on Schrödinger's (partially incorrect) assumption that optimal reflectances contain only two transitions. There are, however, three- and four-transition optimal reflectances and these additional reflectances lead to a larger object-color solid than one based on two-transition reflectances alone. The differences between the approximate and true object-color solids have now been quantified. It is further shown that-despite there being optimal reflectances with up to four transitions-the object-color solid can, nonetheless, be parametrized in terms of only two variables. Finally, a method for solving a previously unsolved problem that Schrödinger posed a century ago is presented. Namely, for any given direction in color space, the algorithm determines the corresponding optimal reflectance.