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Shape Distances for Binary Image Segmentation

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Perspectives in Shape Analysis

Part of the book series: Mathematics and Visualization ((MATHVISUAL))

Abstract

Shape distances are an important measure to guide the task of shape classification. In this chapter we show that the right choice of shape similarity is also important for the task of image segmentation, even at the absence of any shape prior. To this end, we will study three different shape distances and explore how well they can be used in a trust region framework. In particular, we explore which distance can be easily incorporated into trust region optimization and how well these distances work for theoretical and practical examples.

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Notes

  1. 1.

    Since we are only interested in the minimizer, we removed constant terms from the energy.

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Author information

Authors and Affiliations

  1. Computer Science Department and BIOSS Centre for Biological Signalling Studies, University of Freiburg, Georges-Köhler Allee 52, Freiburg, Germany

    Frank R. Schmidt & Thomas Brox

  2. Computer Science Department, University of Western Ontario, London, ON, Canada

    Lena Gorelick & Yuri Boykov

  3. École de Technologie Supérieure, University of Quebec, Montreal, QC, Canada

    Ismail Ben Ayed

Authors
  1. Frank R. Schmidt
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  2. Lena Gorelick
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  3. Ismail Ben Ayed
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  4. Yuri Boykov
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  5. Thomas Brox
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Corresponding author

Correspondence to Frank R. Schmidt .

Editor information

Editors and Affiliations

  1. Institute for Applied Mathematics and Scientific Computing, Brandenburg University of Technology, Cottbus, Germany

    Michael Breuß

  2. Israel Institute of Technology Technion, Haifa, Israel

    Alfred Bruckstein

  3. School of Electrical and Computer Engineering, National Technical University of Athens, Athens, Greece

    Petros Maragos

  4. INRIA, Grenoble Rhône-Alpes, Saint Ismier, France

    Stefanie Wuhrer

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© 2016 Springer International Publishing Switzerland

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Schmidt, F.R., Gorelick, L., Ayed, I.B., Boykov, Y., Brox, T. (2016). Shape Distances for Binary Image Segmentation. In: Breuß, M., Bruckstein, A., Maragos, P., Wuhrer, S. (eds) Perspectives in Shape Analysis. Mathematics and Visualization. Springer, Cham. https://doi.org/10.1007/978-3-319-24726-7_6

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