Optimizing Binary MRFs with Higher Order Cliques

  • Asem M. Ali
  • Aly A. Farag
  • Georgy L. Gimel’farb
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5304)


Widespread use of efficient and successful solutions of Computer Vision problems based on pairwise Markov Random Field (MRF) models raises a question: does any link exist between the pairwise and higher order MRFs such that the like solutions can be applied to the latter models? This work explores such a link for binary MRFs that allow us to represent Gibbs energy of signal interaction with a polynomial function. We show how a higher order polynomial can be efficiently transformed into a quadratic function. Then energy minimization tools for the pairwise MRF models can be easily applied to the higher order counterparts. Also, we propose a method to analytically estimate the potential parameter of the asymmetric Potts prior. The proposed framework demonstrates very promising experimental results of image segmentation and can be used to solve other Computer Vision problems.


Markov Random Field Neighborhood System Clique Size Computer Vision Problem Quadratic Energy 
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 2008

Authors and Affiliations

  • Asem M. Ali
    • 1
  • Aly A. Farag
    • 1
  • Georgy L. Gimel’farb
    • 2
  1. 1.Computer Vision and Image Processing LaboratoryUniversity of LouisvilleUSA
  2. 2.Department of Computer ScienceThe University of AucklandNew Zealand

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