@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}
}
@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}
}
@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}
}
