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... [53] (9 × 9 SAD with shiftable windows, followed by consistency checking and interpolation of uncertain areas); (15) Stochastic diffusion, Lee et al. [68] (a variant of Bayesian diffusion [97]); (16) Fast correlation algorithm, Muhlmann et al. [79] (an efficient implementation of correlation-based matching with consistency and uniqueness validation); (17) Discontinuity-preserving regularization, Shao [104] (a multi-view technique for virtual view generation); (18) Maximum-surface technique, Sun [108] (a fast stereo algorithm using rectangular subregions); (19) Belief propagation, Sun et al. [109] (a MRF formulation using Bayesian belief propagation); (20) Layered stereo, Lin and Tomasi [69] (a preliminary version of an extension of the multiway-cut method [14]). Some of these algorithms do not compute disparity estimates everywhere, in particular those that explicitly model occlusions (3 and 11), but also (16) which leaves lowconfidence regions unmatched. In these cases we fill unmatched areas as described for the DP method in Section 4.3. Table 5 summarizes the results for all algorithms. As in the previous section, we report BO (bad pixels nonocc) as a measure of overall performance...

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...se send e-mail to: tpami@computer.org, and reference IEEECS Log Number TPAMI-0097-0205. outside this class, then one has to use other techniques such as max-product belief propagation (BP) [6], [22], =-=[27]-=-, [35]. BP can be applied to any function of the form as in (1), but it has some drawbacks. First, it usually finds a solution with higher energy than graph cuts (in cases when graph cuts can be appli...

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.... 2.4 Discrete Optimization Algorithms A number of recent approaches use discrete optimization algorithms, similar to those employed in stereo matching, such as graph cuts [14] and belief propagation =-=[71]-=-. Discrete optimization methods approximate the continuous space of solutions with a greatly simplified problem. The hope is that this will enable a more thorough and complete search of the state spac...

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...andom Field (MRF) energy functions providing a clean and computationally-tractable formulation, for which good approximate solutions exist using Graph-cuts [5], [14], [21] or Loopy Belief Propagation =-=[27]-=-. They can also be formulated as continuous PDE evolutions on the depth maps [26]. However, a key limitation of these solutions is that they can only represent depth maps with a unique disparity per p...

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...ues can enforce these constraints efficiently, but only within individual scanlines [1, 11]. This typically leads to streaking effects. Global approaches like Graph Cuts [7, 2] and Belief Propagation =-=[10]-=- enforce the matching constraints in two dimensions. Both approaches are quite memory intensive and Graph Cuts is rather slow. However, it has been shown [4] that Belief Propagation can be implemented...

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... converges. For a graph with multiple loops, loopy belief propagation usually gives a local minimum if it converges. Recent empirical results on several computer vision problems [Freeman et al. 2000; =-=Sun et al. 2002-=-] show that belief propagation is often a very good approximation even for graphs with thousands of loops. Furthermore, in our image completion, we typically do not have a graph with multiple loops. I...