The success of variational methods for optical flow computation lies in their ability to regularize the problem at a differential (pixel) level and combine piecewise smoothness of the flow field with the brightness constancy assumptions. However, the piecewise smoothness assumption is often motivated by heuristic or algorithmic considerations. Lately, new priors were proposed to exploit the structural properties of the flow. Yet, most of them still utilize a generic regularization term.In this paper we consider optical flow estimation in static scenes. We show that introducing a suitable motion model for the optical flow allows us to pose the regularization term as a geometrically meaningful one. The proposed method assumes that the visible surface can be approximated by a piecewise smooth planar manifold. Accordingly, the optical flow between two consecutive frames can be locally regarded as a homography consistent with the epipolar geometry and defined by only three parameters at each pixel. These parameters are directly related to the equation of the scene local tangent plane, so that their spatial variations should be relatively small, except for creases and depth discontinuities. This leads to a regularization term that measures the total variation of the model parameters and can be extended to a Mumford-Shah segmentation of the visible surface. This new technique yields significant improvements over state of the art optical flow computation methods for static scenes.
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