@TechReport{Shekhovtsov-CAK-2010-35, IS = { zkontrolovano 31 Jan 2011 }, UPDATE = { 2010-02-01 }, author = {Shekhovtsov, Alexander and Hlav{\'a}{\v c}, V{\'a}clav}, title = {Joint Image {GMM} and Shading {MAP} Estimation}, institution = {Department of Cybernetics, Faculty of Electrical Engineering, Czech Technical University}, address = {Prague, Czech Republic}, year = {2010}, month = {January}, type = {Research Report}, number = {K333--35/10, CTU--CMP--2010--03}, issn = {1213-2365}, pages = {15}, figures = {4}, psurl = {[Shekhovtsov-TR-2010-03.pdf]}, project = {ICT-215078 DIPLECS, 1M0567}, annote = {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 is a (piecewise-)smoothly varying grayscale 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 solve for shading and mean parameters of the mixture model jointly for both kinds of the regularization.}, keywords = {Total variation, decomposition, shading, retinex}, }