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... methods are more efficient than simulated annealing and have produced good results. Dynamic programming. A different class of global optimization algorithms are those based on dynamic programming. While the 2D-optimization of Equation (3) can be shown to be NP-hard for common classes of smoothness functions [123], dynamic programming can find the global minimum for independent scanlines in polynomial time. Dynamic programming was first used for stereo vision in sparse, edge-based methods [3, 83]. More recent approaches have focused on the dense (intensity-based) scanline optimization problem [10, 9, 46, 31, 18, 13]. These approaches work by computing the minimum-cost path through the matrix of all pairwise matching costs between two corresponding scanlines. Partial occlusion is handled explicitly by assigning a group of pixels in one image to a single pixel in the other image. Figure 2 shows one such example. Problems with dynamic programming stereo include the selection of the right cost for occluded pixels and the difficulty of enforcing inter-scanline consistency, although several methods propose ways of addressing the latter [83, 9, 31, 18, 13]. Another problem is that the dynamic programming approa...

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...ependence on viewpoint. Since our notion of photo-consistency implicitly ensures that all these 3D shape cues are taken into account in the recovery process, our approach is related to work on stereo =-=[1, 14, 20]-=-, shape-from-contour [8, 9, 21], as well as shape-from-shading [22–24]. These approaches rely on studying a single 3D shape cue under the assumptions that (1) other sources of variability can be safel...

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...ies. Some improved windowbased methods, such as adaptive windows [16], shiftable windows [5] and compact windows [23] try to avoid the windows that span depth discontinuities. Bayesian methods (e.g., =-=[11,1,5,8,15]-=-) are global methods that model discontinuities and occlusion. Geiger et al. [11] derived an occlusion process and a disparity field from a matching process. Assuming an “order constraint” and “unique...

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...ound truth, so it is worth concentrating on errors larger than \Sigma1 disparity. Method Total errors Errors ? \Sigma1 GPM-MRF 8.6 2.8 LOG-filtered L 1 19.9 9.0 Normalized correlation 24.7 10.0 MLMHV =-=[2]-=- 24.5 11.0 We have also run our method on a number of standard benchmark images. The results are shown in figure 3. Various details in the images (such as the front parking meter in the meter image an...

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...rchers have found that occlusion regions are a major source of error[3]. Recent work on stereo occlusion, however, has shown that occlusion processing can be incorporated directly into stereo matching=-=[7, 18, 14, 21]-=-. Stereo imagery contains both occlusion edges and occlusion regions[18]. Occlusion regions are spatially coherent groups of pixels that appear in one image and not in the other. These occlusion regio...

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...er hand, the uniqueness constraint [15] enforces a one-to-one mapping between pixels in two images. 1 Microsoft Research Asia 2 Microsoft Research Beijing, P.R. China Redmond, WA, USA Most approaches =-=[1, 6, 11, 3]-=- that exploit the ordering constraint or uniqueness constraint use dynamic programming. Stereo matching is formulated as finding a minimumcost path in the matrix of all pairwise matching costs between...