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The Fréchet Distance Unleashed: Approximating a Dog with a Frog

Authors Sariel Har-Peled , Benjamin Raichel , Eliot W. Robson

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  • Theory of computation → Computational geometry
Keywords
  • Curve similarity
  • Fréchet distance

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Abstract

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.

Cite As Get BibTex

Sariel Har-Peled, Benjamin Raichel, and Eliot W. Robson. The Fréchet Distance Unleashed: Approximating a Dog with a Frog. In 41st International Symposium on Computational Geometry (SoCG 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 332, pp. 54:1-54:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025) https://doi.org/10.4230/LIPIcs.SoCG.2025.54

Author Details

Sariel Har-Peled
  • Department of Computer Science, University of Illinois, Urbana, IL, USA
Benjamin Raichel
  • Department of Computer Science, University of Texas at Dallas, Richardson, TX, USA
Eliot W. Robson
  • Department of Computer Science, University of Illinois, Urbana, IL, USA

Funding

  • Har-Peled, Sariel: Work on this paper was partially supported by a NSF AF award CCF-2317241.
  • Raichel, Benjamin: Work on this paper was partially supported by NSF AF Award CCF-2311179.
  • Robson, Eliot W.: Work on this paper was partially supported by a NSF AF award CCF-2317241.

Supplementary Materials

References

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