Filters








156 Hits in 4.3 sec

Geodesic Fréchet Distance Inside a Simple Polygon [article]

Atlas F. Cook IV, Carola Wenk
2008 arXiv   pre-print
We present the first algorithm for the geodesic Fréchet distance between two polygonal curves A and B inside a simple bounding polygon P.  ...  Results are also presented for the geodesic Fréchet distance in a polygonal domain with obstacles and the geodesic Hausdorff distance for sets of points or sets of line segments inside a simple polygon  ...  ij(ε) b ij(ε) ε a ij(ε) b kj(ε) C kj c) Distance ÙÖ Ö Ø Ð Ú ÐÙ × Ó Ø Ö Ø ×Ø Ò ÓÖÓÐÐ ÖÝ º¾º Ì Ö ×Ô ÓÒ ÐÐ ÓÙÖ ÓÙÒ Ö × Ó Ö ×Ô ÐÐ Ò ÓÙÒ Ò O(log k) Ø Ñ Ý ÓÑÔÙØ Ò t 1 Ò t 2 ÓÖ ÓÙÒ Öݺ º¾º Ó × Ö Ø × ÓÒ ÈÖÓ Ð  ... 
arXiv:0802.2846v1 fatcat:l2n3oybxu5hplcra4teqzrx5sq

Geodesic Fréchet distance inside a simple polygon

Atlas F. Cook IV, Carola Wenk
2010 ACM Transactions on Algorithms  
We present the first algorithm for the geodesic Fréchet distance between two polygonal curves A and B inside a simple polygon P .  ...  Our work is different because we measure all distances using geodesics inside a simple polygon P , where a geodesic is a path that avoids all obstacles and cannot be shortened by slight perturbations [  ...  Geodesic Fréchet Distance Runtime Theorem 4: The exact geodesic Fréchet distance between two polygonal curves A and B inside a simple bounding polygon P can be computed in O(k + N 2 log kN log N ) expected  ... 
doi:10.1145/1868237.1868247 fatcat:34bns3us2fbrvnjq5kjb3di4ri

Walking your dog in the woods in polynomial time

Erin Wolf Chambers, Éric Colin de Verdière, Jeff Erickson, Sylvain Lazard, Francis Lazarus, Shripad Thite
2008 Proceedings of the twenty-fourth annual symposium on Computational geometry - SCG '08  
We describe a polynomial-time algorithm to compute the homotopic Fréchet distance between two given polygonal curves in the plane minus a given set of obstacles, which are either points or polygons.  ...  We propose a natural extension of Fréchet distance to more general metric spaces, which requires the leash itself to move continuously over time.  ...  This continuity requirement is satisfied automatically for curves inside a simple polygon, but not in more general environments like convex polyhedra.  ... 
doi:10.1145/1377676.1377694 dblp:conf/compgeom/ChambersVELLT08 fatcat:b7kuo5qnrrbwrn2n5iz7gtsndu

Homotopic Fréchet distance between curves or, walking your dog in the woods in polynomial time

Erin Wolf Chambers, Éric Colin de Verdière, Jeff Erickson, Sylvain Lazard, Francis Lazarus, Shripad Thite
2010 Computational geometry  
We describe a polynomial-time algorithm to compute the homotopic Fréchet distance between two given polygonal curves in the plane minus a given set of polygonal obstacles.  ...  We propose a natural extension of Fréchet distance to more general metric spaces, which requires the leash itself to move continuously over time.  ...  Acknowledgments This research was initiated during a visit to INRIA Lorraine in Nancy, made possible by a UIUC-CNRS-INRIA travel grant.  ... 
doi:10.1016/j.comgeo.2009.02.008 fatcat:vqtemc2z6nffxd7si62be32s7u

How to Stay Socially Distant: A Geometric Approach [article]

Omrit Filtser, Mayank Goswami, Joseph S.B. Mitchell, Valentin Polishchuk
2022 arXiv   pre-print
We then consider social distance width among polygons, which measures the minimum distance that two agents can maintain while restricted to travel in or on the boundary of the same polygon.  ...  We first study the social distance width of two polygonal curves in one and two dimensions, providing conditional lower bounds and matching algorithms.  ...  We then consider social distance width among polygons, which measures the minimum distance that two agents can maintain while restricted to travel in or on the boundary of the same polygon.  ... 
arXiv:2203.04548v1 fatcat:iv42zsg5kbcwxmbrmzininpobu

Fréchet Distance Problems in Weighted Regions [article]

Yam Ki Cheung, Ovidiu Daescu
2010 arXiv   pre-print
In both cases, we give algorithms for finding a (1+epsilon)-factor approximation of the Fr\'echet distance between two polygonal curves.  ...  We also consider the Fr\'echet distance between two polygonal curves among polyhedral obstacles in R^3 and present a (1+epsilon)-factor approximation algorithm.  ...  They gave the first polynomial-time algorithm for computing the Fréchet distance between simple polygons. In the second category, the distance between two points is the geodesic distance.  ... 
arXiv:1004.4901v1 fatcat:ygs2tbsk7vfvrkhrcvg4ah5smq

Development of a metric and the methods for quantitative estimation of the segmentation of biomedical images

Oleh Berezsky, Mykhailo Zarichnyi, Oleh Pitsun
2017 Eastern-European Journal of Enterprise Technologies  
Here and hereafter, d denotes the geodesic distance inside the tree, that is, d(t, t 0 ) indicates the length of the arc inside T, which connects t and t 0 . Mapping of root trees.  ...  In paper [17] , authors show an algorithm for computing the Fréchet distance for surfaces, which are represented by simple polygons. The algorithm has polynomial complexity.  ...  S k a c h k o v  ... 
doi:10.15587/1729-4061.2017.119493 fatcat:viqnkj5srfd6znvrvar7ixufd4

Applied Similarity Problems Using Frechet Distance [article]

Kaveh Shahbaz
2013 arXiv   pre-print
We also study this problem in the setting where the polygonal curves are inside a simple polygon.  ...  As the last part of this thesis, given a point set S and a polygonal curve P in R^d, we study the problem of finding a polygonal curve Q through S, which has a minimum Frechet distance to P.  ...  Geodesic Fréchet Distance In [28] , Cook and Wenk described an algorithm for the geodesic Fréchet distance between two polygonal curves P and Q inside a simple polygon K.  ... 
arXiv:1307.6628v1 fatcat:ayxp6ajgnzga7pcnz4urfgrugy

Locally correct Fréchet matchings

Kevin Buchin, Maike Buchin, Wouter Meulemans, Bettina Speckmann
2018 Computational geometry  
The Fréchet 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 Fréchet distance a Fréchet matching.  ...  We prove that at least one such a matching exists for two polygonal curves and give an algorithm to compute it.  ...  The Fréchet distance is the maximal distance between two matched points minimized over all monotonous matchings of the curves. We call a matching resulting in the Fréchet distance a Fréchet matching.  ... 
doi:10.1016/j.comgeo.2018.09.002 fatcat:ppwzxzef6zdlzh6fxyifd6p6yu

How to walk your dog in the mountains with no magic leash

Sariel Har-Peled, Amir Nayyeri, Mohammad Salavatipour, Anastasios Sidiropoulos
2012 Proceedings of the 2012 symposuim on Computational Geometry - SoCG '12  
We describe a O(log n)-approximation algorithm for computing the homotopic Frechét distance between two polygonal curves that lie on the boundary of a triangulated topological disk.  ...  Surprisingly, it is not even known if computing either the homotopic Frechét distance, or the minimum height of a homotopy, is in NP.  ...  [EGH + 02] considered the Frechét distance inside a simple polygon as a way to facilitate sweeping it efficiently.  ... 
doi:10.1145/2261250.2261269 dblp:conf/compgeom/Har-PeledNSS12 fatcat:hkoomihgwvbkjhjg2iduhacc3a

How to Walk Your Dog in the Mountains with No Magic Leash

Sariel Har-Peled, Amir Nayyeri, Mohammad Salavatipour, Anastasios Sidiropoulos
2015 Discrete & Computational Geometry  
We describe a O(log n)-approximation algorithm for computing the homotopic Frechét distance between two polygonal curves that lie on the boundary of a triangulated topological disk.  ...  Surprisingly, it is not even known if computing either the homotopic Frechét distance, or the minimum height of a homotopy, is in NP.  ...  [EGH + 02] considered the Frechét distance inside a simple polygon as a way to facilitate sweeping it efficiently.  ... 
doi:10.1007/s00454-015-9737-3 fatcat:s7y6pxj2i5h3rp777deqjbbaxq

How to Walk Your Dog in the Mountains with No Magic Leash [article]

Sariel Har-Peled, Amir Nayyeri, Mohammad Salavatipour, Anastasios Sidiropoulos
2015 arXiv   pre-print
We describe a O( n )-approximation algorithm for computing the homotopic distance between two polygonal curves that lie on the boundary of a triangulated topological disk.  ...  Surprisingly, it is not even known if computing either the homotopic distance, or the minimum height of a homotopy, is in NP.  ...  [EGH + 02] considered the Fréchet distance inside a simple polygon as a way to facilitate sweeping it efficiently.  ... 
arXiv:1401.7042v2 fatcat:remyhych2nb4ldfgrmumfl2gde

Computing Optimal Homotopies over a Spiked Plane with Polygonal Boundary

Benjamin Burton, Erin Chambers, Marc Van Kreveld, Wouter Meulemans, Tim Ophelders, Bettina Speckmann, Marc Herbstritt
2017 European Symposium on Algorithms  
The algorithm combines structural properties of homotopies arising from the geometry with methodology for computing Fréchet distances.  ...  In this paper, we examine this problem in a geometric setting, where we consider the boundary of a polygonal domain with spikes, point obstacles that can be crossed at an additive cost.  ...  The former is a variant where the leashes must stay inside a polygonal boundary and remain geodesic, but no obstacles are present inside the polygon [13] .  ... 
doi:10.4230/lipics.esa.2017.23 dblp:conf/esa/BurtonCKMOS17 fatcat:tltyqyrvafeqrlitqfqim4fzru

Page 3736 of Mathematical Reviews Vol. , Issue 98F [page]

1998 Mathematical Reviews  
A simple piecewise linear Markov transformation on an interval is considered.  ...  i.e. there exists a positive constant € such that distinct orbits eventually separate by a distance of at least ¢.  ... 

Simple Curve Embedding [article]

Jessica Sherette, Carola Wenk
2013 arXiv   pre-print
, as well as under weak Frechet distance if S is a terrain.  ...  Given a curve f and a surface S, how hard is it to find a simple curve f' in S that is the most similar to f?  ...  Acknowledgements The authors thank Sariel Har-Peled, Anne Driemel, and Benjamin Raichel for initial discussion of the simple curve embedding problem.  ... 
arXiv:1303.0821v1 fatcat:kkrd3xnf4zdi3konbfqdntc3by
« Previous Showing results 1 — 15 out of 156 results