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This paper proposes a new stereo model which encodes the simple assumption that the scene is composed of a few, smooth surfaces. A key feature of our model is the surface-based representation, where each pixel is assigned to a 3D surface (planes or B-splines). This representation enables several important contributions: Firstly, we formulate a higher-order prior which states that pixels of similar appearance are likely to belong to the same 3D surface. This enables to incorporate the very popular color segmentation constraint in a soft and principled way. Secondly, we use a global MDL prior to penalize the number of surfaces. Thirdly, we are able to incorporate, in a simple way, a prior which favors low curvature surfaces. Fourthly, we improve the asymmetric occlusion model by disallowing pixels of the same surface to occlude each other. Finally, we use the known fusion move approach which enables a powerful optimization of our model, despite the infinite number of possible labelings (surfaces).