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Approximate Envelope Minimization for Curvature Regularity
Stefan Heber, Rene Ranftl, and Thomas Pock
Institute for Computer Graphics and Vision, Graz University of Technology Inffeldgasse 16, A-8010, Graz, Austriastefan.heber@icg.tugraz.at
ranftl@icg.tugraz.at
pock@icg.tugraz.at
http://www.icg.tu-graz.ac.at
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.
Keywords: Curvature, segmentation, convex conjugate, convex envelope
LNCS 7585, p. 283 ff.
lncs@springer.com
© Springer-Verlag Berlin Heidelberg 2012