Scale and Edge Detection with Topological Derivatives

  • Guozhi Dong
  • Markus Grasmair
  • Sung Ha Kang
  • Otmar Scherzer
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7893)


A typical task of image segmentation is to partition a given image into regions of homogeneous property. In this paper we focus on the problem of further detecting scales of discontinuities of the image. The approach uses a recently developed iterative numerical algorithm for minimizing the Mumford-Shah functional which is based on topological derivatives. For the scale selection we use a squared norm of the gradient at edge points. During the iteration progress, the square norm, as a function varied with iteration numbers, provides information about different scales of the discontinuity sets. For realistic image data, the graph of the norm function is regularized by using total variation minimization to provide stable separation. We present the details of the algorithm and document various numerical experiments.


Mumford-Shah Functional Topological Derivatives Scale Selection Total Variational Filtering 


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© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Guozhi Dong
    • 1
  • Markus Grasmair
    • 1
    • 2
  • Sung Ha Kang
    • 3
  • Otmar Scherzer
    • 1
    • 4
  1. 1.Computational Science CenterUniversity of ViennaWienAustria
  2. 2.Catholic University Eichstätt–IngolstadtEichstättGermany
  3. 3.School of MathematicsGeorgia Institute of TechnologyAtlantaUSA
  4. 4.Johann Radon Institute for Computational and Applied Mathematics (RICAM)Austrian Academy of SciencesLinzAustria

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