@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}
}
@article {Kolmogorov2006,
	title = {Probabilistic fusion of stereo with color and contrast for bilayer segmentation},
	journal = {IEEE Transactions on Pattern Analysis and Machine Intelligence},
	volume = {28},
	number = {9},
	year = {2006},
	pages = {1480{\textendash}1492},
	abstract = {This paper describes models and algorithms for the real-time segmentation of foreground from background layers in stereo video sequences. Automatic separation of layers from color/contrast or from stereo alone is known to be error-prone. Here, color, contrast, and stereo matching information are fused to infer layers accurately and efficiently. The first algorithm, Layered Dynamic Programming (LDP), solves stereo in an extended six-state space that represents both foreground/background layers and occluded regions. The stereo-match likelihood is then fused with a contrast-sensitive color model that is learned on-the-fly and stereo disparities are obtained by dynamic programming. The second algorithm, Layered Graph Cut (LGC), does not directly solve stereo. Instead, the stereo match likelihood is marginalized over disparities to evaluate foreground and background hypotheses and then fused with a contrast-sensitive color model like the one used in LDP. Segmentation is solved efficiently by ternary graph cut. Both algorithms are evaluated with respect to ground truth data and found to have similar performance, substantially better than either stereo or color/contrast alone. However, their characteristics with respect to computational efficiency are rather different. The algorithms are demonstrated in the application of background substitution and shown to give good quality composite video output. {\textcopyright} 2006 IEEE.},
	keywords = {3D/stereo scene analysis, Computer vision, Dynamic programming, Image processing and computer vision, Parameter learning},
	issn = {01628828},
	doi = {10.1109/TPAMI.2006.193},
	url = {http://research.microsoft.com/vision/cambridge},
	author = {Kolmogorov, Vladimir and Criminisi, Antonio and Blake, Andrew and Cross, Geoffrey and Carsten Rother}
}
