Approximate envelope minimization for curvature regularity

Authors:
Stefan Heber;Rene Ranftl;Thomas Pock
Affiliations:
Institute for Computer Graphics and Vision, Graz University of Technology, Graz, Austria;Institute for Computer Graphics and Vision, Graz University of Technology, Graz, Austria;Institute for Computer Graphics and Vision, Graz University of Technology, Graz, Austria
Venue:
ECCV'12 Proceedings of the 12th international conference on Computer Vision - Volume Part III
Year:
2012

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Abstract

We propose a method for minimizing a non-convex function, which can be split up into a sum of simple functions. The key idea of the method is the approximation of the convex envelopes of the simple functions, which leads to a convex approximation of the original function. A solution is obtained by minimizing this convex approximation. Cost functions, which fulfill such a splitting property are ubiquitous in computer vision, therefore we explain the method based on such a problem, namely the non-convex problem of binary image segmentation based on Euler's Elastica.