International Journal of Computer Vision

, Volume 82, Issue 3, pp 302–324

Robust Higher Order Potentials for Enforcing Label Consistency


    • Microsoft Research
  • L’ubor Ladický
    • Oxford Brookes University
  • Philip H. S. Torr
    • Oxford Brookes University

DOI: 10.1007/s11263-008-0202-0

Cite this article as:
Kohli, P., Ladický, L. & Torr, P.H.S. Int J Comput Vis (2009) 82: 302. doi:10.1007/s11263-008-0202-0


This paper proposes a novel framework for labelling problems which is able to combine multiple segmentations in a principled manner. Our method is based on higher order conditional random fields and uses potentials defined on sets of pixels (image segments) generated using unsupervised segmentation algorithms. These potentials enforce label consistency in image regions and can be seen as a generalization of the commonly used pairwise contrast sensitive smoothness potentials. The higher order potential functions used in our framework take the form of the Robust Pn model and are more general than the Pn Potts model recently proposed by Kohli et al. We prove that the optimal swap and expansion moves for energy functions composed of these potentials can be computed by solving a st-mincut problem. This enables the use of powerful graph cut based move making algorithms for performing inference in the framework. We test our method on the problem of multi-class object segmentation by augmenting the conventional crf used for object segmentation with higher order potentials defined on image regions. Experiments on challenging data sets show that integration of higher order potentials quantitatively and qualitatively improves results leading to much better definition of object boundaries. We believe that this method can be used to yield similar improvements for many other labelling problems.


Discrete energy minimizationMarkov and conditional random fieldsObject recognition and segmentation
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© Springer Science+Business Media, LLC 2009