Approximate Envelope Minimization for Curvature Regularity

  • Stefan Heber
  • Rene Ranftl
  • Thomas Pock
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7585)


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.


Curvature segmentation convex conjugate convex envelope 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Stefan Heber
    • 1
  • Rene Ranftl
    • 1
  • Thomas Pock
    • 1
  1. 1.Institute for Computer Graphics and VisionGraz University of TechnologyGrazAustria

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