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This content will become publicly available on January 1, 2026

Title: The Fréchet Distance Unleashed: Approximating a Dog with a Frog
We show that a variant of the continuous Fréchet distance between polygonal curves can be computed using essentially the same algorithm used to solve the discrete version. The new variant is not necessarily monotone, but this shortcoming can be easily handled via refinement. Combined with a Dijkstra/Prim type algorithm, this leads to a realization of the Fréchet distance (i.e., a morphing) that is locally optimal (aka locally correct), that is both easy to compute, and in practice, takes near linear time on many inputs. The new morphing has the property that the leash is always as short as possible. These matchings/morphings are more natural, and are better than the ones computed by standard algorithms - in particular, they handle noise more graciously. This should make the Fréchet distance more useful for real world applications. We implemented the new algorithm, and various strategies to obtain fast practical performance. We performed extensive experiments with our new algorithm, and released publicly available (and easily installable and usable) Julia and Python packages. In particular, the Julia implementation, for computing the regular Fréchet distance, seems to be {significantly faster} than other currently available implementations. See Table 2.2. Our algorithms can be used to compute the almost-exact Fréchet distance between polygonal curves. Implementations and numerous examples are available here: https://frechet.xyz.  more » « less
Award ID(s):
2317241
PAR ID:
10611579
Author(s) / Creator(s):
; ;
Editor(s):
Aichholzer, Oswin; Wang, Haitao
Publisher / Repository:
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Date Published:
Volume:
332
ISSN:
1868-8969
ISBN:
978-3-95977-370-6
Page Range / eLocation ID:
54:1-54:13
Subject(s) / Keyword(s):
Curve similarity Fréchet distance Theory of computation → Computational geometry
Format(s):
Medium: X Size: 13 pages; 1020218 bytes Other: application/pdf
Size(s):
13 pages 1020218 bytes
Location:
Japan
Right(s):
Creative Commons Attribution 4.0 International license; info:eu-repo/semantics/openAccess
Sponsoring Org:
National Science Foundation
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