Locally correct Fréchet matchings

@article{Buchin2019LocallyCF,
  title={Locally correct Fr{\'e}chet matchings},
  author={Kevin Buchin and Maike Buchin and Wouter Meulemans and Bettina Speckmann},
  journal={Comput. Geom.},
  year={2019},
  volume={76},
  pages={1-18}
}

Generalized Dynamic Time Warping: Unleashing the Warping Power Hidden in Point-Wise Distances

TLDR
This work introduces the first conceptual framework called Generalized Dynamic Time Warping (GDTW) that supports now alignment (warping) of a large array of domain-specific distances in a uniform manner and is the first method that generalizes the ubiquitous DTW and "extends" its warping capabilities to a rich diversity of point-to-point distances.

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TLDR
It is proved that at least one Frechet matching exists for two polygonal curves and an O(N^3 log N) algorithm is given to compute it, where N is the total number of edges in both curves.

Lexicographic Fréchet matchings

TLDR
The Frechet distance between two curves is the maximum distance in a simultaneous traversal of the two curves and the goal is to minimize the time T during which the distance exceeds a threshold s, subject to upper speed constraints.

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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

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Given two simplicial complexes in Rd and start and end vertices in each complex, we show how to compute curves (in each complex) between these vertices, such that the weak Fréchet distance between

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Four Soviets Walk the Dog: Improved Bounds for Computing the Fréchet Distance

TLDR
This work gives a randomized algorithm to compute the Fréchet distance between two polygonal curves in time and shows that there exists an algebraic decision tree for the decision problem of depth, for some varepsilon > 0, which reveals an intriguing new aspect of this well-studied problem.

Computing the Discrete Fréchet Distance in Subquadratic Time

TLDR
This work presents the first subquadratic algorithm for computing the discrete Frechet distance between two sequences of points in the plane, and uses the geometry of the problem in a subtle way to encode legal positions of the frogs as states of a finite automaton.

Computing Discrete Fréchet Distance ∗

TLDR
A discrete variation of the Fréchet distance that provides good approximations of the continuous measure and can be efficiently computed using a simple algorithm is presented.

Computing the Fréchet Distance with a Retractable Leash

TLDR
This work presents a novel approach that avoids the detour through the decision version of the Fréchet distance between polygonal curves and gives the first quadratic time algorithm.

New Similarity Measures between Polylines with Applications to Morphing and Polygon Sweeping

TLDR
Two new related metrics, the geodesic width and the link width, for measuring the “distance” between two nonintersecting polylines in the plane are introduced and used to solve two problems: Compute a continuous transformation that “morphs” one polyline into another polyline and construct a corresponding morphing strategy.