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Markov random field modeling in computer vision
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Stereo Without Epipolar Lines: A Maximum-Flow Formulation
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Fast Approximate Energy Minimization via Graph Cuts
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A Taxonomy and Evaluation of Dense Two-Frame Stereo Correspondence Algorithms
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Occlusions, Discontinuities, and Epipolar Lines in Stereo
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An Experimental Comparison of Stereo Algorithms
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Interactive Organ Segmentation Using Graph Cuts
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Multi-camera Scene Reconstruction via Graph Cuts
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Segmentation by Grouping Junctions
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Markov Random Fields with Efficient Approximations
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What Energy Functions can be Minimized via Graph Cuts?
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A Maximum-Flow Formulation of the N-Camera Stereo Correspondence Problem
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Segmentation Given Partial Grouping Constraints
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"GrabCut": interactive foreground extraction using iterated graph cuts
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Adaptive Region-Based Video Registration
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A Surface Reconstruction Method Using Global Graph Cut Optimization
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International Journal of Computer Vision
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A Linear Programming Approach to Max-Sum Problem: A Review
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Object segmentation using graph cuts based active contours
Computer Vision and Image Understanding
MAP ZDF segmentation and tracking using active stereo vision: Hand tracking case study
Computer Vision and Image Understanding
Dynamosaicing: Mosaicing of Dynamic Scenes
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Minimal Aspect Distortion (MAD) Mosaicing of Long Scenes
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Simultaneous Segmentation and Pose Estimation of Humans Using Dynamic Graph Cuts
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Discriminative Learning of Max-Sum Classifiers
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Continuous Global Optimization in Multiview 3D Reconstruction
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EMMCVPR '09 Proceedings of the 7th International Conference on Energy Minimization Methods in Computer Vision and Pattern Recognition
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IPMI'07 Proceedings of the 20th international conference on Information processing in medical imaging
Co-segmentation of image pairs with quadratic global constraint in MRFs
ACCV'07 Proceedings of the 8th Asian conference on Computer vision - Volume Part II
Combinatorial optimization for electrode labeling of EEG caps
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MRF labeling with a graph-shifts algorithm
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Object segmentation in video via graph cut built on superpixels
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ECCV'12 Proceedings of the 12th European conference on Computer Vision - Volume Part IV
Discrete multi-material interface reconstruction for volume fraction data
EuroVis'08 Proceedings of the 10th Joint Eurographics / IEEE - VGTC conference on Visualization
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Proceedings of the 6th International Conference on Computer Vision / Computer Graphics Collaboration Techniques and Applications
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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 characterize the energy functions that can be minimized by graph cuts. Our results are restricted to energy functions with 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 present three main results: a necessary condition for any energy function that can be minimized by graph cuts; a sufficient condition for energy functions that can be written as a sum of functions of up to three variables at a time; and a general-purpose construction to minimize such an energy function. 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.