Frank R. Schmidt

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.

@InProceedings\{STCB07,
  author       = "Schmidt, Frank R. and T{\"o}ppe, Eno and Cremers, Daniel and Boykov, Yuri",
  title        = "Intrinsic Mean for Semimetrical Shape Retrieval via Graph Cuts",
  booktitle    = "Pattern Recognition (Proc. DAGM)",
  series       = "LNCS",
  volume       = "4713",
  pages        = "446--455",
  month        = "Sep",
  year         = "2007",
  publisher    = "Springer",
  address      = "Heidelberg, Germany",
  url          = "http://frank-r-schmidt.de/Publications/2007/STCB07"
}