Fusion Moves for Markov Random Field Optimization

• Published in: IEEE transactions on pattern analysis and machine intelligence Vol. 32; no. 8; pp. 1392 - 1405
• Main Authors: Lempitsky, Victor, Rother, Carsten, Roth, Stefan, Blake, Andrew
• Format: Journal Article
• Language: English
• Published: Los Alamitos, CA IEEE 01.08.2010; IEEE Computer Society; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Algorithmics. Computability. Computer arithmetics; Algorithms; Application software; Applied sciences; Artificial intelligence; Belief propagation; combinatorial algorithms; Computer science; control theory; systems; Computer vision; Exact sciences and technology; graph algorithms; Graphs; Image motion analysis; Image restoration; Inference algorithms; Labeling; Labels; Magnetorheological fluids; Marking; Markov processes; Markov random fields; Mathematical models; motion; Optimization; Pattern recognition. Digital image processing. Computational geometry; stereo; Stereo vision; Studies; Theoretical computing; Markov process; Cartography; Computer vision; Non convex programming; combinatorial algorithms; Probabilistic approach; Stereo image processing; Image processing; motion; Combinatorial problem; Dynamic analysis; Inference; Layout problem; Image restoration; Optimization; Markov random fields; Credal approach; Graph cut; stereo; Pattern analysis; Artificial intelligence; Optical flow; Parallelization; graph algorithms
• ISSN: 0162-8828; 1939-3539; 1939-3539
• DOI: 10.1109/TPAMI.2009.143

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).