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frechet-distance
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Streaming algorithms for line simplification
, Article 23rd Annual Symposium on Computational Geometry, SCG'07, Gyeongju, 6 June 2007 through 8 June 2007 ; 2007 , Pages 175-183 ; 1595937056 (ISBN); 9781595937056 (ISBN) ; De Berg, M ; Hachenberger, P ; Zarei, A ; Sharif University of Technology
2007
Abstract
We study the following variant of the well-known line-simpli- ficationproblem: we are getting a possibly infinite sequence of points p 0,p1,p2,... in the plane defining a polygonal path, and as wereceive the points we wish to maintain a simplification of the pathseen so far. We study this problem in a streaming setting, where weonly have a limited amount of storage so that we cannot store all thepoints. We analyze the competitive ratio of our algorithms, allowingresource augmentation: we let our algorithm maintain a simplificationwith 2k (internal) points, and compare the error of oursimplification to the error of the optimal simplification with k points. We obtain the algorithms with O(1)...
Distinguishing Image Similarities Using Frechet Metric
, M.Sc. Thesis Sharif University of Technology ; Mahdavi-Amiri, Nezam (Supervisor)
Abstract
Automatic recognition of input characters and distinguishing image similarities have been of high interest specially as computer systems have become widely popular in industries and businesses. In this thesis, we present a method based on the Frechet distance for automatic character and image recognition. Frechet distance is a measure of similarity between polygon curves. The presented approach in this thesis is based on the work of Maheshvari,et.al.We first provide a literature review on the existing techniques, emphasizing the superior performance of rule-based algorithms, and introducing the different types of Frechet distances based on the characteristics of the input geometry. Then, we...
Time Optimization in Speed-Constrained Frechet Distance
, M.Sc. Thesis Sharif University of Technology ; Zarrabi-Zadeh, Hamid Reza (Supervisor)
Abstract
The Frechet distance is a well-known geometric measure for evaluating the similarity of two polygonal curves. This distance is also known as dog-leash distance, as one can intuitively imagine the distance as the minimum length of a leash needed for a person to walk his/her dog, each walking along one of the curves from beginning to the end, without backtracking. The Frechet distance has several applications e.g., in computer graphics, computer vision, handwriting recognition and GIS.
In the standard denition of the Frechet distance, there is no limit on the speed of the motion on each of the curves. In 2009, Maheshwari et al. introduced a new variant of the Frechet distance in which each...
In the standard denition of the Frechet distance, there is no limit on the speed of the motion on each of the curves. In 2009, Maheshwari et al. introduced a new variant of the Frechet distance in which each...
Improved algorithms for partial curve matching
, Article Algorithmica ; Vol. 69, issue. 3 , 2014 , p. 641-657 ; Sack, J. R ; Shahbaz, K ; Zarrabi-Zadeh, H ; Sharif University of Technology
Abstract
We revisit the problem of deciding whether a given curve resembles some part of a larger curve under a fixed Fréchet distance, achieving a running time of O(nm), for n and m being the number of segments in the two curves. This improves the long-standing result of Alt and Godau by an O(log(nm)) factor. Our solution is based on constructing a simple data structure which we call free-space map. Using this data structure, we obtain improved algorithms for several variants of the Fréchet distance problem, including the Fréchet distance between two closed curves, and the so-called minimum/maximum walk problems. We also improve the map matching algorithm of Alt et al. for the particular case in...