Optimal Solution of the Dichromatic Model for Multispectral Photometric Invariance

In this paper, we address the problem of photometric invariance in multispectral imaging making use of an optimisation approach based upon the dichromatic model. In this manner, we can cast the problem of recovering the spectra of the illuminant, the surface reflectance and the shading and specular factors in a structural optimisation setting. Making use of the additional information provided by multispectral imaging and the structure of image patches, we recover the dichromatic parameters of the scene. Thus, we formulate a target cost function combining the dichromatic error and the smoothness priors for surfaces with uniform reflectance. The dichromatic parameters are recovered through minimising this cost function in a coordinate descent manner. To this end, we make use of regular albedo patches in the scene selected automatically. The algorithm is shown to be robust, and since the cost function is convex in nature, the resulting solution is globally optimal. We illustrate the effectiveness of our method for purposes of illuminant spectrum recovery and skin recognition. We also compare our results to a number of alternatives.