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...lation [51, 19] and the rank transform [129]. (This can also be viewed as a preprocessing step; see Section 3.1.) On the other hand, global algorithms make explicit smoothness assumptions and then solve an optimization problem. Such algorithms typically do not perform an aggregation step, but rather seek a disparity assignment (step 3) that minimizes a global cost function that combines data (step 1) and smoothness terms. The main distinction between these algorithms is the minimization procedure used, e.g., simulated annealing [75, 6], probabilistic (mean-field) diffusion [97], or graph cuts [23]. In between these two broad classes are certain iterative algorithms that do not explicitly state a global function that is to be minimized, but whose behavior mimics closely that of iterative optimization algorithms [73, 97, 132]. Hierarchical (coarse-to-fine) algorithms resemble such iterative algorithms, but typically operate on an image pyramid, where results from coarser levels are used to constrain a more local search at finer levels [126, 90, 11]. 3.1. Matching cost computation The most common pixel-based matching costs include squared intensity differences (SD) [51, 1, 77, 107] and ab...

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...s Corporate Research, Imaging & Visualization, Princeton NJ 08540, USA yuri@scr.siemens.com 2 Cornell University, Computer Science, Upson Hall, Ithaca NY 14853, USA vnk@cs.cornell.edu Abstract. After =-=[10, 15, 12, 2, 4]-=- minimum cut/maximumsow algorithms on graphs emerged as an increasingly useful tool for exact or approximate energy minimization in low-level vision. The combinatorial optimization literature provides...

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... locally). The minimum cut in turn can be computed very efficiently by max flow algorithms. These methods have been successfully used for a wide variety of vision problems including image restoration =-=[7, 8, 12, 14]-=-, stereo and motion [4, 7, 8, 13, 16, 20, 21], voxel occupancy [23], multicamera scene reconstruction [18] and medical imaging [5, 6, 15]. The output ofsthese algorithms is generally a solution with s...

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...sible solutions di#er substantially. This changes the computational nature of the problem. Solving this minimization for arbitrary graphs and arbitrary functions m i , d ij is an NP-hard problem (see =-=[7]-=-). However, when the graph G = (V, E) has a restricted form, the problem can be solved more e#ciently. For instance, with first-order snakes the graph is simply a chain, which enables a dynamic progra...

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... are given in terms of a similarity function between instances. Unlike other recent work based on energy minimization and random fields in machine learning (Blum & Chawla, 2001) and image processing (=-=Boykov et al., 2001-=-), we adopt Gaussian fields over a continuous state space rather than random fields over the discrete label set. This “relaxation” to a continuous rather than discrete sample space results in many att...

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...), whereas we are concerned with physical proximity between the items to be classied; indeed, in computer vision, modeling proximity information via graph cuts has led to very effective classication (=-=Boykov, Veksler, and Zabih, 1999-=-). 2.3 Cut-based classication Figure 2 shows a worked example of the concepts in this section. Suppose we have n items x 1 , . . . , x n to divide into two classes C 1 and C 2 , and we have access to ...

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...-hard problem, so researchers have focused on approximate minimization algorithms. The two most well-known techniques are graph cuts and belief propagation. The former one was introduced in the 1990s =-=[3]-=-, [9], [10], [15] and showed a major improvement over previously used simulated annealing [8]. To our knowledge, graph cuts are currently considered to be the most accurate minimization algorithm for ...

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...nealing [3], proved to be extremely inefficient. In the last few years, energy minimization approaches have had a renaissance, primarily due to powerful new optimization algorithms such as graph cuts =-=[4, 5]-=- and loopy belief propagation (LBP) [6]. The results, especially in stereo, have been dramatic; according to the widely-used Middlebury stereo benchmarks [7], almost all the top-performing stereo meth...

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...d energy function is reached. 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 compl...