Joint Image GMM and Shading MAP Estimation

We consider a simple statistical model of the image, in which the image is represented as a sum of two parts: one part is explained by an i.i.d. color Gaussian mixture and the other part by a (piecewise-) smooth gray scale shading function. The smoothness is ensured by a quadratic (Tikhonov) or total variation regularization. We derive an EM algorithm to estimate simultaneously the parameters of the mixture model and the shading. Our algorithms for both kinds of the regularization solve for shading and mean parameters of the mixture model jointly.