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Related papers: Discrete Frechet distance for closed curves

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The discrete Fr{\'e}chet distance is a measure of similarity between point sequences which permits to abstract differences of resolution between the two curves, approximating the original Fr{\'e}chet distance between curves. Such distance…

Computational Geometry · Computer Science 2018-06-05 Jérémy Barbay

The article analyzes similarity of closed polygonal curves with respect to the Frechet metric, which is stronger than the well-known Hausdorff metric and therefore is more appropriate in some applications. An algorithm is described that…

Computational Geometry · Computer Science 2015-05-18 M. Schlesinger , E. Vodolazskiy , V. Yakovenko

The Frechet distance is a metric to compare two curves, which is based on monotonous matchings between these curves. We call a matching that results in the Frechet distance a Frechet matching. There are often many different Frechet…

Computational Geometry · Computer Science 2012-06-28 Kevin Buchin , Maike Buchin , Wouter Meulemans , Bettina Speckmann

The article analyzes similarity of closed polygonal curves in Frechet metric, which is stronger than the well-known Hausdorff metric and therefore is more appropriate in some applications. An algorithm that determines whether the Frechet…

Computational Geometry · Computer Science 2014-09-17 M. I. Schlesinger , E. V. Vodolazskiy , V. M. Yakovenko

Computing the Fr\'echet distance between two polygonal curves takes roughly quadratic time. In this paper, we show that for a special class of curves the Fr\'echet distance computations become easier. Let $P$ and $Q$ be two polygonal curves…

Computational Geometry · Computer Science 2019-08-28 Joachim Gudmundsson , Majid Mirzanezhad , Ali Mohades , Carola Wenk

The discrete Fr\'echet distance is a useful similarity measure for comparing two sequences of points $P=(p_1,\ldots, p_m)$ and $Q=(q_1,\ldots,q_n)$. In many applications, the quality of the matching can be improved if we let $Q$ undergo…

Computational Geometry · Computer Science 2015-01-16 Rinat Ben Avraham , Haim Kaplan , Micha Sharir

The \emph{Fr\'echet distance} is a well studied similarity measures between curves. The \emph{discrete Fr\'echet distance} is an analogous similarity measure, defined for a sequence $A$ of $m$ points and a sequence $B$ of $n$ points, where…

Computational Geometry · Computer Science 2016-09-09 Rinat Ben Avraham , Omrit Filtser , Haim Kaplan , Matthew J. Katz , Micha Sharir

We introduce the discrete Fr\'echet gap and its variants as an alternative measure of similarity between polygonal curves. We believe that for some applications the new measure (and its variants) may better reflect our intuitive notion of…

Computational Geometry · Computer Science 2015-06-17 Omrit Filtser , Matthew J. Katz

Let $m$ and $n$ be the numbers of vertices of two polygonal curves in $\mathbb{R}^d$ for any fixed $d$ such that $m \leq n$. Since it was known in 1995 how to compute the Fr\'{e}chet distance of these two curves in $O(mn\log (mn))$ time, it…

Computational Geometry · Computer Science 2024-10-21 Siu-Wing Cheng , Haoqiang Huang

The Fr\'echet distance is a commonly used similarity measure between curves. It is known how to compute the continuous Fr\'echet distance between two polylines with $m$ and $n$ vertices in $\mathbb{R}^d$ in $O(mn (\log \log n)^2)$ time;…

Computational Geometry · Computer Science 2022-08-29 Thijs van der Horst , Marc van Kreveld , Tim Ophelders , Bettina Speckmann

It is unlikely that the discrete Fr\'echet distance between two curves of length $n$ can be computed in strictly subquadratic time. We thus consider the setting where one of the curves, $P$, is known in advance. In particular, we wish to…

Computational Geometry · Computer Science 2024-04-08 Boris Aronov , Tsuri Farhana , Matthew J. Katz , Indu Ramesh

The Fr\'echet distance is a similarity measure between two curves $A$ and $B$: Informally, it is the minimum length of a leash required to connect a dog, constrained to be on $A$, and its owner, constrained to be on $B$, as they walk…

Computational Geometry · Computer Science 2012-04-25 Pankaj K. Agarwal , Rinat Ben Avraham , Haim Kaplan , Micha Sharir

The Fr\'echet distance is a popular similarity measure between curves. For some applications, it is desirable to match the curves under translation before computing the Fr\'echet distance between them. This variant is called the Translation…

Computational Geometry · Computer Science 2021-08-13 Joachim Gudmundsson , André van Renssen , Zeinab Saeidi , Sampson Wong

All known algorithms for the Fr\'echet distance between curves proceed in two steps: first, they construct an efficient oracle for the decision version; second, they use this oracle to find the optimum from a finite set of critical values.…

Computational Geometry · Computer Science 2016-08-11 Kevin Buchin , Maike Buchin , Rolf van Leusden , Wouter Meulemans , Wolfgang Mulzer

We study the shortcut Fr\'{e}chet distance, a natural variant of the Fr\'{e}chet distance, that allows us to take shortcuts from and to any point along one of the curves. The classic Fr\'echet distance is a bottle-neck distance measure and…

Computational Geometry · Computer Science 2013-12-05 Maike Buchin , Anne Driemel , Bettina Speckmann

Let $P$ be a polygon with $k$ vertices. Let $R$ and $B$ be two simple, interior disjoint curves on the boundary of $P$, with $n$ and $m$ vertices. We show how to compute the Fr\'echet distance between $R$ and $B$ using the geodesic…

Computational Geometry · Computer Science 2025-04-21 Thijs van der Horst , Marc van Kreveld , Tim Ophelders , Bettina Speckmann

The discrete Fr\'echet distance is a popular measure for comparing polygonal curves. An important variant is the discrete Fr\'echet distance under translation, which enables detection of similar movement patterns in different spatial…

Data Structures and Algorithms · Computer Science 2021-10-13 Karl Bringmann , Marvin Künnemann , André Nusser

$\renewcommand{\Re}{{\rm I\!\hspace{-0.025em} R}} \newcommand{\eps}{{\varepsilon}} \newcommand{\SetX}{\mathsf{X}} \newcommand{\VorX}[1]{\mathcal{V} \pth{#1}} \newcommand{\Polygon}{\mathsf{P}} \newcommand{\Space}{\overline{\mathsf{m}}}…

Computational Geometry · Computer Science 2015-04-30 Boris Aronov , Sariel Har-Peled , Christian Knauer , Yusu Wang , Carola Wenk

We propose sublinear algorithms for probabilistic testing of the discrete and continuous Fr\'echet distance - a standard similarity measure for curves. We assume the algorithm is given access to the input curves via a query oracle: a query…

Computational Geometry · Computer Science 2025-09-05 Peyman Afshani , Maike Buchin , Anne Driemel , Marena Richter , Sampson Wong

The Fr\'echet distance is a computational mainstay for comparing polygonal curves. The Fr\'echet distance under translation, which is a translation invariant version, considers the similarity of two curves independent of their location in…

Computational Geometry · Computer Science 2025-01-23 Lotte Blank , Jacobus Conradi , Anne Driemel , Benedikt Kolbe , André Nusser , Marena Richter
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