Abstract: In stereo matching cost filtering methods and energy minimization algorithms are considered as two different techniques. Due to their global extend energy minimization methods obtain good stereo matching results. However, they tend to fail in occluded regions, in which cost filtering approaches obtain better results. In this paper we intend to combine both approaches with the aim to improve overall stereo matching results. We show that a global optimization with a fully connected model can be solved by cost fil tering methods. Based on this observation we propose to perform stereo matching as a two-step energy minimization algorithm. We consider two MRF models: a fully connected model defined on the complete set of pixels in an image and a conventional locally connected model. We solve the energy minimization problem for the fully connected model, after which the marginal function of the solution is used as the unary potential in the locally connected MRF model. Experiments on the Middlebury stereo datasets show that the proposed method achieves state-of-the-arts results.