A 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 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. To do this, we formulate a target cost function combining the dichromatic error and the smoothness priors for the surfaces under study. The dichromatic parameters are recovered through minimising this cost function in a coordinate descent manner. The algorithm is quite general in nature, admitting the enforcement of smoothness constraints and extending in a straightforward manner to trichromatic settings. Moreover, the objective function is convex with respect to the subset of variables to be optimised in each alternating step of the minimisation strategy. This gives rise to an optimal closed-form solution for each of the iterations in our algorithm. We illustrate the effectiveness of our method for purposes of illuminant spectrum recovery, skin recognition, material clustering and specularity removal. We also compare our results to a number of alternatives.