# Similarity of polygonal curves in the presence of outliers

@article{Carufel2014SimilarityOP, title={Similarity of polygonal curves in the presence of outliers}, author={Jean-Lou De Carufel and Amin Gheibi and Anil Maheshwari and J{\"o}rg-R{\"u}diger Sack and Christian Scheffer}, journal={ArXiv}, year={2014}, volume={abs/1212.1617} }

## 16 Citations

On Computing the k-Shortcut Fréchet Distance

- Mathematics, Computer ScienceICALP
- 2022

A complexity analysis for the shortcut Fréchet distance, where one is allowed to take shortcuts along one of the curves, similar to the edit distance for sequences, and shows that efficient approximate decider algorithms are possible, even when k is large.

Applied Similarity Problems Using Frechet Distance

- Computer Science, MathematicsArXiv
- 2013

This thesis presents a data structure that encapsulates all the information available in the free-space diagram, yet it is capable of answering more general type of queries efficiently, and improves the map matching algorithm for the case when the map is a directed acyclic graph.

Computing the Fréchet distance with shortcuts is NP-hard

- Computer ScienceSoCG
- 2014

It is shown that, in the general case, the problem of computing the shortcut Fréchet distance is NP-hard, the first hardness result for a variant of the Fréchechet distance between two polygonal curves in the plane.

Minimum backward fréchet distance

- Computer Science, MathematicsSIGSPATIAL/GIS
- 2014

We propose a new measure to capture similarity between polygonal curves, called the minimum backward Fréchet distance. It is a natural optimization on the weak Fréchet distance, a variant of the…

More Flexible Curve Matching via the Partial Fréchet Similarity

- Computer ScienceInt. J. Comput. Geom. Appl.
- 2016

We study a modified version of the partial Frechet similarity that is motivated by real world applications, e.g. the analysis of spectroscopic data in the context of astroinformatics and the analysis…

Discrete Geometric Path Analysis in Computational Geometry

- Computer Science, Mathematics
- 2016

This thesis provides a technique that makes it possible to apply the existing approximation algorithms for triangulations to arrangements of lines and proposes a new measure to capture similarity between polygonal curves, called the Minimum Backward Frechet Distance (MBFD).

The Prefix Fréchet Similarity

- Computer ScienceWALCOM
- 2019

This is the first efficient algorithm for computing exactly the whole profile of a parametrized Frechet distance, i.e., the complete functional relation between \(\delta \) and the prefix Frechet similarity of T and \(T'\).

A note on the unsolvability of the weighted region shortest path problem

- MathematicsComput. Geom.
- 2014

The Discrete and Semicontinuous Fréchet Distance with Shortcuts via Approximate Distance Counting and Selection

- Computer ScienceTALG
- 2015

A variant of the Fréchet distance with shortcuts is considered, which captures the similarity between (sampled) curves in the presence of outliers, and can be applied to optimization problems for which the decision procedure is very fast but standard techniques like parametric search makes the optimization algorithm substantially slower.

## References

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This paper develops an approximation algorithm that, in O((n + m)/ε) time, computes a (1 − ε)-approximation to the optimal partial Fréchet similarity between two polygonal curves of size n and m, respectively.

Exact algorithms for partial curve matching via the Fréchet distance

- Computer Science, MathematicsSODA
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This paper presents the first exact algorithm that runs in polynomial time to compute fδ(P, Q), the partial Frechet similarity between P and Q, under the L1 and L∞ norms.

Applied Similarity Problems Using Frechet Distance

- Computer Science, MathematicsArXiv
- 2013

This thesis presents a data structure that encapsulates all the information available in the free-space diagram, yet it is capable of answering more general type of queries efficiently, and improves the map matching algorithm for the case when the map is a directed acyclic graph.

Computing the Fréchet distance with shortcuts is NP-hard

- Computer ScienceSoCG
- 2014

It is shown that, in the general case, the problem of computing the shortcut Fréchet distance is NP-hard, the first hardness result for a variant of the Fréchechet distance between two polygonal curves in the plane.

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As a measure for the resemblance of curves in arbitrary dimensions we consider the so-called Frechet-distance, which is compatible with parametrizations of the curves. For polygonal chains P and Q…

A note on the unsolvability of the weighted region shortest path problem

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- 2014

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Let S be a subdivision of the plane into polygonal regions, where each region has an associated positive weight. The weighted region shortest path problem is to determine a shortest path in S between…

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Galoois methods are applied to certain fundamental geometric optimization problems whose exact computational complexity has been an open problem for a long time and show that the classic Weber problem, along with the line-restricted Weber problem and itsthree-dimensional version are in general not solvable by radicals over the field of rationals.

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This work establishes criteria that a “median trajectory” should meet, and presents two different methods to construct a median for a set of input trajectories, and suggests that the second method, using homotopy, performs considerably better.