Fusion moves for markov random field optimization

Victor Lempitsky, Carsten Rother, Stefan Roth, Andrew Blake

Research output: Contribution to journalArticlepeer-review

168 Citations (Scopus)


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).

Original languageEnglish
Article number5166447
Pages (from-to)1392-1405
Number of pages14
JournalIEEE Transactions on Pattern Analysis and Machine Intelligence
Issue number8
Publication statusPublished - 2010
Externally publishedYes


  • Combinatorial algorithms
  • Computer vision
  • Graph algorithms
  • Image restoration.
  • Markov random fields
  • Motion
  • Stereo


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