Abstract

Imposing smoothness priors is a key idea of the top-ranked global stereo models. Recent progresses demonstrated the power of sec- ond order priors which are usually defined by either explicitly consid- ering three-pixel neighborhoods, or implicitly using a so-called 3D-label for each pixel. In contrast to the traditional first-order priors which only prefer fronto-parallel surfaces, second-order priors encourage arbitrary collinear structures. However, we still can find defective regions in match- ing results even under such powerful priors, e.g., large textureless regions. One reason is that most of the stereo models are non-convex, where pixel- wise smoothness priors, i.e., local constraints, are too flexible to prevent the solution from trapping in bad local minimums. On the other hand, long-range spatial constraints, especially the segment-based priors, have advantages on this problem. However, segment-based priors are too rigid to handle curved surfaces. We present a mixture model to combine the benefits of these two kinds of priors, whose energy function consists of two terms 1) a Laplacian operator on the disparity map which imposes pixel-wise second-order smoothness; 2) a segment-wise matching cost as a function of quadratic surface, which encourages “as-rigid-as-possible” smoothness. To effectively solve the problem, we introduce an interme- diate term to decouple the two subenergies, which enables an alternated optimization algorithm that is about an order of magnitude faster than PatchMatch [1]. Our approach is one of the top ranked models on the Middlebury benchmark at sub-pixel accuracy.