A linear model of the reconstruction of surface appearance under changes of illumination

Spectral properties of reflected light depend on the compound product of the spectral radiant power distribution of the light source and the surface reflectance function. A linear model for recalculating the tristimulus values of a reflected light under a new illumination with respect to reference illuminant was developed. Decomposition of the compound product is achieved by using the first three eigenvectors of Munsell colours for reconstructing the surface reflectance function and imitating an illuminant with a broad-band spectral radiant power. A square matrix of the linear transformation operator depends on the illumination changes. The eigenvectors of the transformation matrix are assumed as hypothetical channels and it is shown that, in general, simple von-Kries-type scaling of their sensitivity functions is an inadequate method for perfect colour constancy. Performance of the computational algorithm was tested on a set of Munsell chips. Tristimulus values of Munsell chips under illuminant C (x=0.3101, y=0.3162) were taken from the Munsell Renotation System (Newall et al, 1943 Journal of the Optical Society of America 33 385 - 418) as input data. Output data were calculated for changes to illuminant A (x=0.4476, y=0.4075) and illuminant S (x=0.2319, y=0.2318), and compared with experimentally obtained data (Kelly et al, 1943 Journal of the Optical Society of America 33 355 - 375). No significant difference between theoretical and experimental data was found.