Intrinsic Mean for Semi-metrical Shape Retrieval Via Graph Cuts

  • Frank R. Schmidt
  • Eno Töppe
  • Daniel Cremers
  • Yuri Boykov
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4713)


We address the problem of describing the mean object for a set of planar shapes in the case that the considered dissimilarity measures are semi-metrics, i.e. in the case that the triangle inequality is generally not fulfilled. To this end, a matching of two planar shapes is computed by cutting an appropriately defined graph the edge weights of which encode the local similarity of respective contour parts on either shape. The cost of the minimum cut can be interpreted as a semi-metric on the space of planar shapes. Subsequently, we introduce the notion of a mean shape for the case of semi-metrics and show that this allows to perform a shape retrieval which mimics human notions of shape similarity.


Dynamic Time Warping Dissimilarity Measure Shape Space Shape Match Shape Retrieval 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2007

Authors and Affiliations

  • Frank R. Schmidt
    • 1
  • Eno Töppe
    • 1
  • Daniel Cremers
    • 1
  • Yuri Boykov
    • 2
  1. 1.Department of Computer Science, University of Bonn, Römerstr. 164, 53117 BonnGermany
  2. 2.Computer Science Department, University of Western Ontario, London, ONCanada

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