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Locally Correct Fréchet Matchings
[chapter]
2012
Lecture Notes in Computer Science
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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]
2012
arXiv
pre-print
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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
2018
Computational geometry
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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
2018
Computational geometry
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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
2016
Sensors
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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]
2015
arXiv
pre-print
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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
2018
ISPRS International Journal of Geo-Information
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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]
2016
arXiv
pre-print
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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]
2015
Association for Women in Mathematics Series
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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
2020
Journal of Geodesy and Geoinformation Science
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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 ...
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doi:10.11947/j.jggs.2020.0308
doaj:18397fbec73f40fc833416c8df2bca2c
fatcat:3vahdkcq4zedpdwgtjfyr4whqe
Fuzzy c-Means Clustering for Persistence Diagrams
[article]
2021
arXiv
pre-print
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2020 pre-print arXiv:2006.02796v4 fatcat:24zaiw2gtzeoxjlzim4pdjpi3aOther Versions
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]
2016
arXiv
pre-print
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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
2016
Discrete & Computational Geometry
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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]
2021
arXiv
pre-print
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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
2017
2017 IEEE International Conference on Computer Vision Workshops (ICCVW)
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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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