@article {Lempitsky2012,
	title = {Branch-and-mincut: Global optimization for image segmentation with high-level priors},
	journal = {Journal of Mathematical Imaging and Vision},
	volume = {44},
	number = {3},
	year = {2012},
	pages = {315{\textendash}329},
	abstract = {Efficient global optimization techniques such as graph cut exist for energies corresponding to binary image segmentation from low-level cues. However, introducing a high-level prior such as a shape prior or a color-distribution prior into the segmentation process typically results in an energy that is much harder to optimize. The main contribution of the paper is a new global optimization framework for a wide class of such energies. The framework is built upon two powerful techniques: graph cut and branch-and-bound. These techniques are unified through the derivation of lower bounds on the energies. Being computable via graph cut, these bounds are used to prune branches within a branchand-bound search. We demonstrate that the new framework can compute globally optimal segmentations for a variety of segmentation scenarios in a reasonable time on a modern CPU. These scenarios include unsupervised segmentation of an object undergoing 3D pose change, category-specific shape segmentation, and the segmentation under intensity/color priors defined by Chan-Vese and GrabCut functionals. {\textcopyright} Springer Science+Business Media, LLC 2011.},
	keywords = {Branch-and-bound, Global optimization, Graph Cuts, Image segmentation, Shape priors},
	issn = {09249907},
	doi = {10.1007/s10851-012-0328-0},
	author = {Lempitsky, Victor and Blake, Andrew and Carsten Rother}
}
@article {Lempitsky2010a,
	title = {Fusion moves for markov random field optimization},
	journal = {IEEE Transactions on Pattern Analysis and Machine Intelligence},
	volume = {32},
	number = {8},
	year = {2010},
	pages = {1392{\textendash}1405},
	abstract = {The efficient application of graph cuts to Markov Random Fields (MRFs) with multiple discrete or continuous labels remains an open question. In this paper, we demonstrate one possible way of achieving this by using graph cuts to combine pairs of suboptimal labelings or solutions. We call this combination process the fusion move. By employing recently developed graph-cut-based algorithms (so-called QPBO-graph cut), the fusion move can efficiently combine two proposal labelings in a theoretically sound way, which is in practice often globally optimal. We demonstrate that fusion moves generalize many previous graph-cut approaches, which allows them to be used as building blocks within a broader variety of optimization schemes than were considered before. In particular, we propose new optimization schemes for computer vision MRFs with applications to image restoration, stereo, and optical flow, among others. Within these schemes the fusion moves are used 1) for the parallelization of MRF optimization into several threads, 2) for fast MRF optimization by combining cheap-to-compute solutions, and 3) for the optimization of highly nonconvex continuous-labeled MRFs with 2D labels. Our final example is a nonvision MRF concerned with cartographic label placement, where fusion moves can be used to improve the performance of a standard inference method (loopy belief propagation). {\textcopyright} 2006 IEEE.},
	keywords = {Combinatorial algorithms, Computer vision, Graph algorithms, Image restoration., Markov random fields, Motion, Stereo},
	issn = {01628828},
	doi = {10.1109/TPAMI.2009.143},
	author = {Lempitsky, Victor and Carsten Rother and Roth, Stefan and Blake, Andrew}
}
@article {Lempitsky2010,
	title = {Fusion moves for markov random field optimization},
	journal = {IEEE Transactions on Pattern Analysis and Machine Intelligence},
	volume = {32},
	number = {8},
	year = {2010},
	pages = {1392{\textendash}1405},
	abstract = {The efficient application of graph cuts to Markov Random Fields (MRFs) with multiple discrete or continuous labels remains an open question. In this paper, we demonstrate one possible way of achieving this by using graph cuts to combine pairs of suboptimal labelings or solutions. We call this combination process the fusion move. By employing recently developed graph-cut-based algorithms (so-called QPBO-graph cut), the fusion move can efficiently combine two proposal labelings in a theoretically sound way, which is in practice often globally optimal. We demonstrate that fusion moves generalize many previous graph-cut approaches, which allows them to be used as building blocks within a broader variety of optimization schemes than were considered before. In particular, we propose new optimization schemes for computer vision MRFs with applications to image restoration, stereo, and optical flow, among others. Within these schemes the fusion moves are used 1) for the parallelization of MRF optimization into several threads, 2) for fast MRF optimization by combining cheap-to-compute solutions, and 3) for the optimization of highly nonconvex continuous-labeled MRFs with 2D labels. Our final example is a nonvision MRF concerned with cartographic label placement, where fusion moves can be used to improve the performance of a standard inference method (loopy belief propagation). {\textcopyright} 2006 IEEE.},
	keywords = {Combinatorial algorithms, Computer vision, Graph algorithms, Image restoration., Markov random fields, Motion, Stereo},
	issn = {01628828},
	doi = {10.1109/TPAMI.2009.143},
	author = {Lempitsky, Victor and Carsten Rother and Roth, Stefan and Blake, Andrew}
}
@conference {Lempitsky2009,
	title = {Image segmentation with a bounding box prior},
	booktitle = {Proceedings of the IEEE International Conference on Computer Vision},
	year = {2009},
	pages = {277{\textendash}284},
	abstract = {User-provided object bounding box is a simple and popular interaction paradigm considered by many existing interactive image segmentation frameworks. However, these frameworks tend to exploit the provided bounding box merely to exclude its exterior from consideration and sometimes to initialize the energy minimization. In this paper, we discuss how the bounding box can be further used to impose a powerful topological prior, which prevents the solution from excessive shrinking and ensures that the user-provided box bounds the segmentation in a sufficiently tight way. The prior is expressed using hard constraints incorporated into the global energy minimization framework leading to an NP-hard integer program. We then investigate the possible optimization strategies including linear relaxation as well as a new graph cut algorithm called pinpointing. The latter can be used either as a rounding method for the fractional LP solution, which is provably better than thresholding-based rounding, or as a fast standalone heuristic. We evaluate the proposed algorithms on a publicly available dataset, and demonstrate the practical benefits of the new prior both qualitatively and quantitatively. {\textcopyright}2009 IEEE.},
	isbn = {9781424444205},
	doi = {10.1109/ICCV.2009.5459262},
	author = {Lempitsky, Victor and Kohli, Pushmeet and Carsten Rother and Sharp, Toby}
}
@conference {Lempitsky2008,
	title = {FusionFlow: Discrete-continuous optimization for optical flow estimation},
	booktitle = {26th IEEE Conference on Computer Vision and Pattern Recognition, CVPR},
	year = {2008},
	abstract = {Accurate estimation of optical flow is a challenging task, which often requires addressing difficult energy optimization problems. To solve them, most top-performing methods rely on continuous optimization algorithms. The modeling accuracy of the energy in this case is often traded for its tractability. This is in contrast to the related problem of narrow-baseline stereo matching, where the top-performing methods employ powerful discrete optimization algorithms such as graph cuts and message-passing to optimize highly non-convex energies. In this paper, we demonstrate how similar non-convex energies can be formulated and optimized discretely in the context of optical flow estimation. Starting with a set of candidate solutions that are produced by fast continuous flow estimation algorithms, the proposed method iteratively fuses these candidate solutions by the computation of minimum cuts on graphs. The obtained continuous-valued fusion result is then further improved using local gradient descent. Experimentally, we demonstrate that the proposed energy is an accurate model and that the proposed discrete-continuous optimization scheme not only finds lower energy solutions than traditional discrete or continuous optimization techniques, but also leads to flow estimates that outperform the current state-of-the-art. {\textcopyright}2008 IEEE.},
	isbn = {9781424422432},
	doi = {10.1109/CVPR.2008.4587751},
	author = {Lempitsky, Victor and Roth, Stefan and Carsten Rother}
}
@conference {Lempitsky2008b,
	title = {Image segmentation by branch-and-mincut},
	booktitle = {Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)},
	volume = {5305 LNCS},
	number = {PART 4},
	year = {2008},
	pages = {15{\textendash}29},
	abstract = {Efficient global optimization techniques such as graph cut exist for energies corresponding to binary image segmentation from low-level cues. However, introducing a high-level prior such as a shape prior or a color-distribution prior into the segmentation process typically results in an energy that is much harder to optimize. The main contribution of the paper is a new global optimization framework for a wide class of such energies. The framework is built upon two powerful techniques: graph cut and branch-and-bound. These techniques are unified through the derivation of lower bounds on the energies. Being computable via graph cut, these bounds are used to prune branches within a branch-and-bound search. We demonstrate that the new framework can compute globally optimal segmentations for a variety of segmentation scenarios in a reasonable time on a modern CPU. These scenarios include unsupervised segmentation of an object undergoing 3D pose change, category-specific shape segmentation, and the segmentation under intensity/color priors defined by Chan-Vese and GrabCut functionals. {\textcopyright} 2008 Springer Berlin Heidelberg.},
	isbn = {3540886923},
	issn = {03029743},
	doi = {10.1007/978-3-540-88693-8-2},
	author = {Lempitsky, Victor and Blake, Andrew and Carsten Rother}
}
@conference {Lempitsky2008a,
	title = {Image segmentation by branch-and-mincut},
	booktitle = {Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)},
	volume = {5305 LNCS},
	number = {PART 4},
	year = {2008},
	pages = {15{\textendash}29},
	abstract = {Efficient global optimization techniques such as graph cut exist for energies corresponding to binary image segmentation from low-level cues. However, introducing a high-level prior such as a shape prior or a color-distribution prior into the segmentation process typically results in an energy that is much harder to optimize. The main contribution of the paper is a new global optimization framework for a wide class of such energies. The framework is built upon two powerful techniques: graph cut and branch-and-bound. These techniques are unified through the derivation of lower bounds on the energies. Being computable via graph cut, these bounds are used to prune branches within a branch-and-bound search. We demonstrate that the new framework can compute globally optimal segmentations for a variety of segmentation scenarios in a reasonable time on a modern CPU. These scenarios include unsupervised segmentation of an object undergoing 3D pose change, category-specific shape segmentation, and the segmentation under intensity/color priors defined by Chan-Vese and GrabCut functionals. {\textcopyright} 2008 Springer Berlin Heidelberg.},
	isbn = {3540886923},
	issn = {03029743},
	doi = {10.1007/978-3-540-88693-8-2},
	author = {Lempitsky, Victor and Blake, Andrew and Carsten Rother}
}
@conference {Lempitsky2007,
	title = {LogCut - Efficient graph cut optimization for markov random fields},
	booktitle = {Proceedings of the IEEE International Conference on Computer Vision},
	year = {2007},
	abstract = {Markov Random Fields (MRFs) are ubiquitous in low-level computer vision. In this paper, we propose a new approach to the optimization of multi-labeled MRFs. Similarly to α-expansion it is based on iterative application of binary graph cut. However, the number of binary graph cuts required to compute a labelling grows only logarithmically with the size of label space, instead of linearly. We demonstrate that for applications such as optical flow, image restoration, and high resolution stereo, this gives an order of magnitude speed-up, for comparable energies. Iterations are performed by "fusion" of solutions, done with QPBO which is related to graph cut but can deal with non-submodularity. At convergence, the method achieves optima on a par with the best competitors, and sometimes even exceeds them. {\textcopyright}2007 IEEE.},
	doi = {10.1109/ICCV.2007.4408907},
	author = {Lempitsky, Victor and Carsten Rother and Blake, Andrew}
}
@conference {Rother2007a,
	title = {Optimizing binary MRFs via extended roof duality},
	booktitle = {Proceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition},
	year = {2007},
	abstract = {Many computer vision applications rely on the efficient optimization of challenging, so-called non-submodular, binary pairwise MRFs. A promising graph cut based approach for optimizing such MRFs known as "roof duality" was recently introduced into computer vision. We study two methods which extend this approach. First, we discuss an efficient implementation of the "probing" technique introduced recently by Boros et al. [5]. It simplifies the MRF while preserving the global optimum. Our code is 400-700 faster on some graphs than the implementation of [5]. Second, we present a new technique which takes an arbitrary input labeling and tries to improve its energy. We give theoretical characterizations of local minima of this procedure. We applied both techniques to many applications, including image segmentation, new view synthesis, superresolution, diagram recognition, parameter learning, texture restoration, and image deconvolution. For several applications we see that we are able to find the global minimum very efficiently, and considerably outperform the original roof duality approach. In comparison to existing techniques, such as graph cut, TRW, BP, ICM, and simulated annealing, we nearly always find a lower energy. {\textcopyright} 2007 IEEE.},
	isbn = {1424411807},
	issn = {10636919},
	doi = {10.1109/CVPR.2007.383203},
	author = {Carsten Rother and Kolmogorov, Vladimir and Lempitsky, Victor and Szummer, Martin}
}
@article {Rother2007,
	title = {Optimizing Binary MRFs via Extended Roof Duality Technical Report MSR-TR-2007-46},
	journal = {Computing},
	year = {2007},
	abstract = {Many computer vision applications rely on the efficient optimization of challenging, so-called non-submodular, binary pairwise MRFs. A promising graph cut based approach for optimizing such MRFs known as "roof duality" was recently introduced into computer vision. We study two methods which extend this approach. First, we discuss an efficient implementation of the "probing" technique introduced recently by Boros et al. [8]. It simplifies the MRF while preserving the global optimum. Our code is 400-700 faster on some graphs than the implementation of [8]. Second , we present a new technique which takes an arbitrary input labeling and tries to improve its energy. We give theoretical characterizations of local minima of this procedure. We applied both techniques to many applications, including image segmentation, new view synthesis, super-resolution, diagram recognition, parameter learning, texture restoration, and image deconvolution. For several applications we see that we are able to find the global minimum very efficiently, and considerably outperform the original roof duality approach. In comparison to existing techniques , such as graph cut, TRW, BP, ICM, and simulated annealing, we nearly always find a lower energy.},
	url = {http://research.microsoft.com/vision/cambridge/},
	author = {Carsten Rother and Kolmogorov, Vladimir and Lempitsky, Victor and Szummer, Martin}
}
