Intrinsic mean for semi-metrical shape retrieval via graph cuts

Authors:
Frank R. Schmidt;Eno Töppe;Daniel Cremers;Yuri Boykov
Affiliations:
Department of Computer Science, University of Bonn, Bonn, Germany;Department of Computer Science, University of Bonn, Bonn, Germany;Department of Computer Science, University of Bonn, Bonn, Germany;Computer Science Department, University of Western Ontario, London, ON, Canada
Venue:
Proceedings of the 29th DAGM conference on Pattern recognition
Year:
2007

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Abstract

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.