Approximate MRF Inference Using Bounded Treewidth Subgraphs

  • Alexander Fix
  • Joyce Chen
  • Endre Boros
  • Ramin Zabih
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7572)


Graph cut algorithms [9], commonly used in computer vision, solve a first-order MRF over binary variables. The state of the art for this NP-hard problem is QPBO [1,2], which finds the values for a subset of the variables in the global minimum. While QPBO is very effective overall there are still many difficult problems where it can only label a small subset of the variables. We propose a new approach that, instead of optimizing the original graphical model, instead optimizes a tractable sub-model, defined as an energy function that uses a subset of the pairwise interactions of the original, but for which exact inference can be done efficiently. Our Bounded Treewidth Subgraph (k-BTS) algorithm greedily computes a large weight treewidth-k subgraph of the signed graph, then solves the energy minimization problem for this subgraph by dynamic programming. The edges omitted by our greedy method provide a per-instance lower bound. We demonstrate promising experimental results for binary deconvolution, a challenging problem used to benchmark QPBO [2]: our algorithm performs an order of magnitude better than QPBO or its common variants [4], both in terms of energy and accuracy, and the visual quality of our output is strikingly better as well. We also obtain a significant improvement in energy and accuracy on a stereo benchmark with 2nd order priors [5], although the improvement in visual quality is more modest. Our method’s running time is comparable to QPBO.


Greedy Algorithm Original Graph Tree Decomposition Signed Graph Exact Inference 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Alexander Fix
    • 1
  • Joyce Chen
    • 1
  • Endre Boros
    • 2
  • Ramin Zabih
    • 1
  1. 1.Computer Science DepartmentCornell UniversityIthacaUSA
  2. 2.RUTCORRutgers UniversityNew BrunswickUSA

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