Approximately matching polygonal curves with respect to the Fréchet distance

Authors:
Axel Mosig;Michael Clausen
Affiliations:
Lehrstuhl für Bioinformatik, Universität Leipzig, D-04103 Leipzig, Germany;Institut für Informatik III, Universität Bonn, D-53117 Bonn, Germany
Venue:
Computational Geometry: Theory and Applications - Special issue on the 19th European workshop on computational geometry - EuroCG 03
Year:
2005

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Abstract

In this paper we present approximate algorithms for matching two polygonal curves with respect to the Fréchet distance. We define a discrete version of the Fréchet distance as a distance measure between polygonal curves and show that this discrete version is bounded by the continuous version of the Fréchet distance.For the task of matching with respect to the discrete Fréchet distance, we develop an algorithm that is based on intersecting certain subsets of the transformation group under consideration. Our algorithm for matching two point sequences of lengths m and n under the group of rigid motions has a time complexity of O(m2n2) for matching under the discrete Fréchet distance and can be modified for matching subcurves, closed curves and finding longest common subcurves, Group theoretical considerations allow us to eliminate translation components of affine transformations and to consider matching under arbitrary linear algebraic groups.