A continuous max-flow approach to potts model

Authors:
Jing Yuan;Egil Bae;Xue-Cheng Tai;Yuri Boykov
Affiliations:
Computer Science Department, University of Western Ontario, London Ontario, Canada;Department of Mathematics, University of Bergen, Norway;Department of Mathematics, University of Bergen, Norway and Division of Mathematical Sciences, School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore;Computer Science Department, University of Western Ontario, London Ontario, Canada
Venue:
ECCV'10 Proceedings of the 11th European conference on Computer vision: Part VI
Year:
2010

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Abstract

We address the continuous problem of assigning multiple (unordered) labels with the minimum perimeter. The corresponding discrete Potts model is typically addressed with a-expansion which can generate metrication artifacts. Existing convex continuous formulations of the Potts model use TV-based functionals directly encoding perimeter costs. Such formulations are analogous to 'min-cut' problems on graphs. We propose a novel convex formulation with a continous 'max-flow' functional. This approach is dual to the standard TV-based formulations of the Potts model. Our continous max-flow approach has significant numerical advantages; it avoids extra computational load in enforcing the simplex constraints and naturally allows parallel computations over different labels. Numerical experiments show competitive performance in terms of quality and significantly reduced number of iterations compared to the previous state of the art convex methods for the continuous Potts model.