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Locally Correct Fréchet Matchings [chapter]

Kevin Buchin, Maike Buchin, Wouter Meulemans, Bettina Speckmann
2012 Lecture Notes in Computer Science  
We propose to restrict the set of Fréchet matchings to "natural" matchings and to this end introduce locally correct Fréchet matchings.  ...  We also present an O(N 2 ) algorithm to compute a locally correct discrete Fréchet matching.  ...  Locally correct Fréchet matchings We introduce locally correct Fréchet matchings, for which the matching between any two matched subcurves is a Fréchet matching. Definition 1 (Local correctness).  ... 
doi:10.1007/978-3-642-33090-2_21 fatcat:h2jnvjcmf5hbvgesbhqt6hbi4e

Locally Correct Frechet Matchings [article]

Kevin Buchin, Maike Buchin, Wouter Meulemans, Bettina Speckmann
2012 arXiv   pre-print
We also present an O(N^2) algorithm to compute a locally correct discrete Frechet matching.  ...  We propose to restrict the set of Frechet matchings to "natural" matchings and to this end introduce locally correct Frechet matchings.  ...  Locally correct Fréchet matchings We introduce locally correct Fréchet matchings, for which the matching between any two matched subcurves is a Fréchet matching. Definition 1 (Local correctness).  ... 
arXiv:1206.6257v1 fatcat:pbaiju7stnfz5f6sanh3rwf63i

Locally correct Fréchet matchings

Kevin Buchin, Maike Buchin, Wouter Meulemans, Bettina Speckmann
2018 Computational geometry  
We propose to restrict the set of Fréchet matchings to "natural" matchings and to this end introduce locally correct Fréchet matchings.  ...  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.  ...  Locally correct matchings We introduce locally correct matchings, which are a Fréchet matching for any two matched subcurves.  ... 
doi:10.1016/j.comgeo.2018.09.002 fatcat:ppwzxzef6zdlzh6fxyifd6p6yu

Approximating the integral Fréchet distance

Anil Maheshwari, Jörg-Rüdiger Sack, Christian Scheffer
2018 Computational geometry  
Scheffer 26:3 that decreases the matched distance as quickly as possible."[2, p. 237]. The matching induced by π ab fulfils this requirement. S WAT 2 0 1 6 A. Maheshwari, J.-R. Sack, and C.  ...  Additionally, such a shortest path provides an optimal solution for the partial Fréchet similarity of segments for all leash lengths.  ...  A locally correct matching can be transformed into a locally optimal Fréchet matching in O(n). Generally, a locally optimal matching can be computed in O(n 3 log n). Proof.  ... 
doi:10.1016/j.comgeo.2018.01.001 fatcat:d6maaooh3vhcdlndokdr6hr5li

An Improved Map-Matching Technique Based on the Fréchet Distance Approach for Pedestrian Navigation Services

Yoonsik Bang, Jiyoung Kim, Kiyun Yu
2016 Sensors  
The Fréchet distance approach can provide reasonable matching results because two linear trajectories are parameterized with the time variable.  ...  The theory underlying this approach is based on the Fréchet distance, one of the measures of geometric similarity between two curves.  ...  Applying the Fréchet-distance-based method reduced the error and increased the number of correct matches.  ... 
doi:10.3390/s16101768 pmid:27782091 pmcid:PMC5087552 fatcat:u7osnyy3hnaahmyxqq3ii5zmqa

Approximating the Integral Fréchet Distance [article]

Anil Maheshwari and Jörg-Rüdiger Sack and Christian Scheffer
2015 arXiv   pre-print
The average Fréchet distance is defined as the integral Fréchet distance divided by the lengths of T_1 and T_2.  ...  The integral Fréchet distance defines the cost of a deformation as the integral of the distances between points that are related.  ...  [4] suggested to extend the definition of locally correct (Fréchet) matchings to "locally optimal" (Fréchet) matchings as future work.  ... 
arXiv:1512.03359v1 fatcat:sjwv2gjb3bfgljlgu34ejevzaq

A Reconstruction Method for Broken Contour Lines Based on Similar Contours

Chengming Li, Xiaoli Liu, Wei Wu, Zhiwei Hao
2018 ISPRS International Journal of Geo-Information  
Second, the discrete Fréchet distance is used to select a reference line and perform reconstruction. Finally, the actual data of Yunnan Province are utilized for verification.  ...  3064 7 Correct reconstruction of general broken contour lines 1225 8 Correct reconstruction of complex broken contour lines 1839 9 Reconstruction accuracy rate of the broken contour lines 93.5% broken  ...  [4, 5] optimized the minimum point pair method to refine the constraint criterion for breakpoint matching and used Newton's difference interpolation algorithm to complete the matching connection of  ... 
doi:10.3390/ijgi8010008 fatcat:jbqwapgncncnbfm7obpb6v5u5q

Discretized Approaches to Schematization [article]

Wouter Meulemans
2016 arXiv   pre-print
We investigate two approaches, simple map matching and connected face selection, based on commonly used similarity metrics.  ...  With the former, S is a simple cycle C in G and we quantify resemblance via the Fréchet distance.  ...  [8] introduced "locally correct Fréchet matchings" to counteract this flaw with the Fréchet distance. Can we extend this concept to simple map matching?  ... 
arXiv:1606.06488v1 fatcat:h33mxq7mobdyxlaars6v33novm

Skeleton-Based Recognition of Shapes in Images via Longest Path Matching [chapter]

Gulce Bal, Julia Diebold, Erin Wolf Chambers, Ellen Gasparovic, Ruizhen Hu, Kathryn Leonard, Matineh Shaker, Carola Wenk
2015 Association for Women in Mathematics Series  
We present two approaches: one based on map-matching techniques using the weak Fréchet distance, and one based on a multiscale curve metric after reducing the Voronoi graphs to their minimum spanning trees  ...  Inspired by prior work matching from a library using only the longest path in the medial axis [3], we extract medial axes from shapes with clean contours and seek to recognize these shapes within "noisy  ...  Matching via weak Fréchet distance Our first method of matching is based on map-matching via the weak Fréchet distance.  ... 
doi:10.1007/978-3-319-16348-2_6 fatcat:3bohrxgmong4dprv6lawo4y4hi

A Multisource Contour Matching Method Considering the Similarity of Geometric Features

GUO Wenyue,YU Anzhu,SUN Qun,LI Shaomei,XU Qing,WEN Bowei,LI Yuanfu
2020 Journal of Geodesy and Geoinformation Science  
It has been proved that the proposed contour matching strategy has a high matching precision and good applicability.  ...  The existing multi-source contour matching studies have focused on the matching methods with consideration of topological relations and similarity measurement based on spatial Euclidean distance, while  ...  0.11 ① Matching accuracy = Correct matching number Correct matching number+Error matching number ×100% Matching recall = Correct matching number Correct matching number+Unmatched number ×100  ... 
doi:10.11947/j.jggs.2020.0308 doaj:18397fbec73f40fc833416c8df2bca2c fatcat:3vahdkcq4zedpdwgtjfyr4whqe

Fuzzy c-Means Clustering for Persistence Diagrams [article]

Thomas Davies, Jack Aspinall, Bryan Wilder, Long Tran-Thanh
2021 arXiv   pre-print
Therefore to compute the weighted Fréchet mean, we need to find the correct bijections. We start by using the Hungarian algorithm to find an optimal matching between M k and each D j .  ...  ) states that an optimal matching at a point is also locally optimal.  ... 
arXiv:2006.02796v5 fatcat:jlvpub2upfeahcoyfgleb7jmiu

Intermittent Map Matching with the Discrete Fréchet Distance [article]

Tim Wylie, Binhai Zhu
2016 arXiv   pre-print
The map matching problem is usually approached with the Fr\'echet distance matching the edges of the path as well.  ...  In this paper we focus on the map matching problem where the goal is to find a path through a planar graph such that the path through the vertices closely matches a given polygonal curve.  ...  However, the methodologies can also be classified based on the problem definition where we have local/incremental methods, global methods, and statistical methods.  ... 
arXiv:1409.2456v2 fatcat:tb6fhntnazc7dcdgv5vx4mcwb4

Computing the Fréchet Distance with a Retractable Leash

Kevin Buchin, Maike Buchin, Rolf van Leusden, Wouter Meulemans, Wolfgang Mulzer
2016 Discrete & Computational Geometry  
We also get a (1+ε)-approximation of the Fréchet distance under the Euclidean metric, in quadratic time for any fixed ε > 0.  ...  This gives the first quadratic time algorithm for the Fréchet distance between polygonal curves in R^d under polyhedral distance functions (e.g., L_1 and L_∞).  ...  A Fréchet matching that induces a Fréchet matching for any two matched subcurves is called a locally correct Fréchet matching [11] .  ... 
doi:10.1007/s00454-016-9800-8 fatcat:okpbqvy7tvgqvlqbr76jimuyli

(2+ϵ)-ANN for time series under the Fréchet distance [article]

Anne Driemel, Ioannis Psarros
2021 arXiv   pre-print
In both cases, the answer is correct. Our first data structure achieves a (5+ϵ) approximation factor, uses space in n·𝒪(ϵ^-1)^k + 𝒪(nm) and has query time in 𝒪(k).  ...  We study approximate-near-neighbor data structures for time series under the continuous Fréchet distance.  ...  Suppose now that π(p i ) is a local minimum.  ... 
arXiv:2008.09406v5 fatcat:rb7rt2zk2za4fckkiqw7uxmwda

Part-to-Whole Registration of Histology and MRI Using Shape Elements

Jonas Pichat, Juan Eugenio Iglesias, Sotiris Nousias, Tarek Yousry
2017 2017 IEEE International Conference on Computer Vision Workshops (ICCVW)  
Because each level line is associated with many canonical curves (one for each shape element), matches are found when the Fréchet distance is minimum and below a certain threshold.  ...  When sufficient information comes in (1/4th), recognition becomes more successful: despite finding more false than true matches for piece 2, RANSAC was able to return the correct transformation-most of  ... 
doi:10.1109/iccvw.2017.21 dblp:conf/iccvw/PichatINY17 fatcat:fngyejcm3fcafnz7aizpsffno4
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