Simplifying 3D polygonal chains under the discrete Fréchet distance

Authors:
Sergey Bereg;Minghui Jiang;Wencheng Wang;Boting Yang;Binhai Zhu
Affiliations:
Department of Computer Science, University of Texas at Dallas, Richardson, TX;Department of Computer Science, Utah State University, Logan, UT;Institute of Software, Chinese Academy of Sciences, Beijing, China;Department of Computer Science, University of Regina, Regina, Saskatchewan, Canada;Department of Computer Science, Montana State University, Bozeman, MT
Venue:
LATIN'08 Proceedings of the 8th Latin American conference on Theoretical informatics
Year:
2008

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Abstract

A well-known measure to characterize the similarity of two polygonal chains is the famous Fréchet distance. In this paper, for the first time, we consider the problem of simplifying 3D polygonal chains under the discrete Fréchet distance. We present efficient polynomial time algorithms for simplifying a single chain, including the first near-linear O(n log n) time exact algorithm for the continuous min-# fitting problem. Our algorithms generalize to any fixed dimension d 3. Motivated by the ridge-based model simplification we also consider simplifying a pair of chains simultaneously and we show that one version of the general problem is NP-complete.