Probabilistic matching of planar regions

Authors:
Helmut Alt;Ludmila Scharf;Daria Schymura
Affiliations:
Institut für Informatik, Freie Universität Berlin, Berlin, Germany;Institut für Informatik, Freie Universität Berlin, Berlin, Germany;Institut für Informatik, Freie Universität Berlin, Berlin, Germany
Venue:
Computational Geometry: Theory and Applications
Year:
2010

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Abstract

We analyze a probabilistic algorithm for matching shapes modeled by planar regions under translations and rigid motions (rotation and translation). Given shapes A and B, the algorithm computes a transformation t such that with high probability the area of overlap of t(A) and B is close to maximal. In the case of polygons, we give a time bound that does not depend significantly on the number of vertices, but on perimeter and area of the shapes and, in the case of rigid motions, also on the diameter.