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44
An Experimental Comparison of MinCut/MaxFlow Algorithms for Energy Minimization in Vision
 IEEE TRANSACTIONS ON PATTERN ANALYSIS AND MACHINE INTELLIGENCE
, 2001
"... After [10, 15, 12, 2, 4] minimum cut/maximum flow algorithms on graphs emerged as an increasingly useful tool for exact or approximate energy minimization in lowlevel vision. The combinatorial optimization literature provides many mincut/maxflow algorithms with different polynomial time compl ..."
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Cited by 791 (48 self)
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After [10, 15, 12, 2, 4] minimum cut/maximum flow algorithms on graphs emerged as an increasingly useful tool for exact or approximate energy minimization in lowlevel vision. The combinatorial optimization literature provides many mincut/maxflow algorithms with different polynomial time complexity. Their practical efficiency, however, has to date been studied mainly outside the scope of computer vision. The goal of this paper
What energy functions can be minimized via graph cuts
 IEEE Transactions on Pattern Analysis and Machine Intelligence
, 2004
"... Abstract—In the last few years, several new algorithms based on graph cuts have been developed to solve energy minimization problems in computer vision. Each of these techniques constructs a graph such that the minimum cut on the graph also minimizes the energy. Yet, because these graph construction ..."
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Cited by 690 (21 self)
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Abstract—In the last few years, several new algorithms based on graph cuts have been developed to solve energy minimization problems in computer vision. Each of these techniques constructs a graph such that the minimum cut on the graph also minimizes the energy. Yet, because these graph constructions are complex and highly specific to a particular energy function, graph cuts have seen limited application to date. In this paper, we give a characterization of the energy functions that can be minimized by graph cuts. Our results are restricted to functions of binary variables. However, our work generalizes many previous constructions and is easily applicable to vision problems that involve large numbers of labels, such as stereo, motion, image restoration, and scene reconstruction. We give a precise characterization of what energy functions can be minimized using graph cuts, among the energy functions that can be written as a sum of terms containing three or fewer binary variables. We also provide a generalpurpose construction to minimize such an energy function. Finally, we give a necessary condition for any energy function of binary variables to be minimized by graph cuts. Researchers who are considering the use of graph cuts to optimize a particular energy function can use our results to determine if this is possible and then follow our construction to create the appropriate graph. A software implementation is freely available.
Computing Visual Correspondence with Occlusions using Graph Cuts
"... Several new algorithms for visual correspondence based on graph cuts [7, 14, 17] have recently been developed. While these methods give very strong results in practice, they do not handle occlusions properly. Specifically, they treat the two input images asymmetrically, and they do not ensure that a ..."
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Cited by 265 (11 self)
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Several new algorithms for visual correspondence based on graph cuts [7, 14, 17] have recently been developed. While these methods give very strong results in practice, they do not handle occlusions properly. Specifically, they treat the two input images asymmetrically, and they do not ensure that a pixel corresponds to at most one pixel in the other image. In this paper, we present a new method which properly addresses occlusions, while preserving the advantages of graph cut algorithms. We give experimental results for stereo as well as motion, which demonstrate that our method performs well both at detecting occlusions and computing disparities.
Multicamera Scene Reconstruction via Graph Cuts
 in European Conference on Computer Vision
, 2002
"... We address the problem of computing the 3dimensional shape of an arbitrary scene from a set of images taken at known viewpoints. ..."
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Cited by 255 (10 self)
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We address the problem of computing the 3dimensional shape of an arbitrary scene from a set of images taken at known viewpoints.
Computing geodesics and minimal surfaces via graph cuts
 in International Conference on Computer Vision
, 2003
"... Geodesic active contours and graph cuts are two standard image segmentation techniques. We introduce a new segmentation method combining some of their benefits. Our main intuition is that any cut on a graph embedded in some continuous space can be interpreted as a contour (in 2D) or a surface (in 3D ..."
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Cited by 179 (22 self)
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Geodesic active contours and graph cuts are two standard image segmentation techniques. We introduce a new segmentation method combining some of their benefits. Our main intuition is that any cut on a graph embedded in some continuous space can be interpreted as a contour (in 2D) or a surface (in 3D). We show how to build a grid graph and set its edge weights so that the cost of cuts is arbitrarily close to the length (area) of the corresponding contours (surfaces) for any anisotropic Riemannian metric. There are two interesting consequences of this technical result. First, graph cut algorithms can be used to find globally minimum geodesic contours (minimal surfaces in 3D) under arbitrary Riemannian metric for a given set of boundary conditions. Second, we show how to minimize metrication artifacts in existing graphcut based methods in vision. Theoretically speaking, our work provides an interesting link between several branches of mathematicsdifferential geometry, integral geometry, and combinatorial optimization. The main technical problem is solved using CauchyCrofton formula from integral geometry. 1.
Graph Partition by SwendsenWang Cuts
, 2003
"... Vision tasks, such as segmentation, grouping, recognition, can be formulated as graph partition problems. The recent literature witnessed two popular graph cut algorithms: the Ncut using spectral graph analysis and the minimumcut using the maximum flow algorithm. This paper presents a third major a ..."
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Cited by 62 (16 self)
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Vision tasks, such as segmentation, grouping, recognition, can be formulated as graph partition problems. The recent literature witnessed two popular graph cut algorithms: the Ncut using spectral graph analysis and the minimumcut using the maximum flow algorithm. This paper presents a third major approach by generalizing the SwendsenWang method – a well celebrated algorithm in statistical mechanics. Our algorithm simulates ergodic, reversible Markov chain jumps in the space of graph partitions to sample a posterior probability. At each step, the algorithm splits, merges, or regroups a sizable subgraph, and achieves fast mixing at low temperature enabling a fast annealing procedure. Experiments show it converges in 230 seconds in a PC for image segmentation. This is 400 times faster than the singlesite update Gibbs sampler, and 2040 times faster than the DDMCMC algorithm. The algorithm can optimize over the number of models and works for general forms of posterior probabilities, so it is more general than the existing graph cut approaches.
Stereo correspondence by dynamic programming on a tree
 IEEE CVPR, Vol II
, 2005
"... Dynamic programming on a scanline is one of the oldest and still popular methods for stereo correspondence. While efficient, its performance is far from the state of the art because the vertical consistency between the scanlines is not enforced. We reexamine the use of dynamic programming for stere ..."
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Cited by 40 (0 self)
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Dynamic programming on a scanline is one of the oldest and still popular methods for stereo correspondence. While efficient, its performance is far from the state of the art because the vertical consistency between the scanlines is not enforced. We reexamine the use of dynamic programming for stereo correspondence by applying it to a tree structure, as opposed to the individual scanlines. The nodes of this tree are all the image pixels, but only the “most important” edges of the 4 connected neighbourhood system are included. Thus our algorithm is truly a global optimization method because disparity estimate at one pixel depends on the disparity estimates at all the other pixels, unlike the scanline based methods. We evaluate our algorithm on the benchmark Middlebury database. The algorithm is very fast, it takes only a fraction of a second for a typical image. The results are considerably better than that of the scanline based methods. While the results are not the state of the art, our algorithm offers a good trade off in terms of accuracy and computational efficiency. 1
Graph Cuts in Vision and Graphics: Theories and Applications
 “MATH. MODELS OF C.VISION: THE HANDBOOK”, EDTS. PARAGIOS, CHEN, FAUGERAS
"... Combinatorial mincut algorithms on graphs emerged as an increasingly useful tool for problems in vision. Typically, the use of graphcuts is motivated by one of the following two reasons. Firstly, graphcuts allow geometric interpretation; under certain conditions a cut on a graph can be seen as a ..."
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Cited by 20 (2 self)
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Combinatorial mincut algorithms on graphs emerged as an increasingly useful tool for problems in vision. Typically, the use of graphcuts is motivated by one of the following two reasons. Firstly, graphcuts allow geometric interpretation; under certain conditions a cut on a graph can be seen as a hypersurface in ND space embedding the corresponding graph. Thus, many applications in vision and graphics use mincut algorithms as a tool for computing optimal hypersurfaces. Secondly, graphcuts also work as a powerful energy minimization tool for a fairly wide class of binary and nonbinary energies that frequently occur in early vision. In some cases graph cuts produce globally optimal solutions. More generally, there are iterative graphcut based techniques that produce provably good approximations which (were empirically shown to) correspond to highquality solutions in practice. Thus, another large group of applications use graphcuts as an optimization technique for lowlevel vision problems based on global energy formulations. This chapter is intended as a tutorial illustrating these two aspects of graphcuts in the context of problems in computer vision and graphics. We explain general theoretical properties that motivate the use of graph cuts, as well as, show their limitations.
Surface reconstruction by propagating 3d stereo data in multiple 2d images
 In Proceedings of the European Conference on Computer Vision
, 2004
"... Abstract. We present a novel approach to surface reconstruction from multiple images. The central idea is to explore the integration of both 3D stereo data and 2D calibrated images. This is motivated by the fact that only robust and accurate feature points that survived the geometry scrutiny of mult ..."
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Cited by 11 (2 self)
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Abstract. We present a novel approach to surface reconstruction from multiple images. The central idea is to explore the integration of both 3D stereo data and 2D calibrated images. This is motivated by the fact that only robust and accurate feature points that survived the geometry scrutiny of multiple images are reconstructed in space. The density insufficiency and the inevitable holes in the stereo data should be filled in by using information from multiple images. The idea is therefore to first construct small surface patches from stereo points, then to progressively propagate only reliable patches in their neighborhood from images into the whole surface using a bestfirst strategy. The problem reduces to searching for an optimal local surface patch going through a given set of stereo points from images. This constrained optimization for a surface patch could be handled by a local graphcut that we develop. Real experiments demonstrate the usability and accuracy of the approach. 1