Computing the Similarity Between Moving Curves

In this paper we study similarity measures for moving curves which can, for example, model changing coastlines or glacier termini. Points on a moving curve have two parameters, namely the position along the curve as well as time. We therefore focus on similarity measures for surfaces, specifically t...

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Bibliographic Details
Published inAlgorithms - ESA 2015 pp. 928 - 940
Main Authors Buchin, Kevin, Ophelders, Tim, Speckmann, Bettina
Format Book Chapter
LanguageEnglish
Published Berlin, Heidelberg Springer Berlin Heidelberg 12.11.2015
SeriesLecture Notes in Computer Science
Subjects
Decision Algorithm
Pareto Frontier
Simple Polygon
Transitive Closure
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Summary:In this paper we study similarity measures for moving curves which can, for example, model changing coastlines or glacier termini. Points on a moving curve have two parameters, namely the position along the curve as well as time. We therefore focus on similarity measures for surfaces, specifically the Fréchet distance between surfaces. While the Fréchet distance between surfaces is not even known to be computable, we show for variants arising in the context of moving curves that they are polynomial-time solvable or NP-complete depending on the restrictions imposed on how the moving curves are matched. We achieve the polynomial-time solutions by a novel approach for computing a surface in the so-called free-space diagram based on max-flow min-cut duality.
ISBN:3662483491
9783662483497
ISSN:0302-9743
1611-3349
DOI:10.1007/978-3-662-48350-3_77