A method for computing spectral reflectance

Psychophysical experiments show that the perceived colour of an object is relatively independent of the spectrum of the incident illumination and mainly depends on the surface spectral reflectance. We first demonstrate a possible solution to this undetermined problem for a Mondrian world of flat rectangular patches. We expand the illumination and surface reflectances in terms of a finite number of basis functions. We assume that the number of colour receptors is greater than the number of basis functions. This yields a set of nonlinear equations for each colour patch. Number counting arguments show that, given a sufficient number of surface patches with the same illumination, there are enough equations to determine the surface reflectances up to an overall scaling factor. This theory is similar to previous and independent work by Maloney and Wandell (Maloney 1985). We demonstrate a simple method of solving these non-linear equations. We generalize to situations where the illumination varies in space and the objects are three dimensional shapes. To do this we define a method for detecting material changes, a colour edge detector, and illustrate a way of detecting the colour of a material at its boundaries and propagating it inwards.