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Getting around a lower bound for the minimum Hausdorff distance

L.Paul Chew, Klara Kedem
1998 Computational geometry  
We consider the following geometric pattern matching problem: find the minimum Hausdorff distance between two point sets under translation with Ll or L~ as the underlying metric.  ...  We examine the question of whether one can get around this cubic lower bound, and show that under the Ll and L~ metrics, the time to compute the minimum Hausdorff distance between two point sets is O(n  ...  [6] , is based on the minimum Hausdorff distance between point sets in the plane under translation.  ... 
doi:10.1016/s0925-7721(97)00032-1 fatcat:zwbde6cxxbf7jdpdmdfgoqcfmu

Geometric pattern matching under Euclidean motion

L.Paul Chew, Michael T. Goodrich, Daniel P. Huttenlocher, Klara Kedem, Jon M. Kleinberg, Dina Kravets
1997 Computational geometry  
We also show how to use our methods to substantially improve on existing algorithms for finding the minimum Hausdorff distance under Euclidean motion.  ...  We establish upper bounds on the combinatorial complexity of this subproblem in model-based computer vision, when the sets A and B contain points, line segments, or (filled-in) polygons.  ...  In particular, if A is a set of m points in the plane and if B is a set of n points in the plane, then we show how to find the one-way minimum Hausdorff distance under Euclidean motion in O(m3n 2 log 2  ... 
doi:10.1016/0925-7721(95)00047-x fatcat:nuqmk7a5ffayhkmiebxvc6k4ni

Two Dimensional Yau-Hausdorff Distance with Applications on Comparison of DNA and Protein Sequences

Kun Tian, Xiaoqian Yang, Qin Kong, Changchuan Yin, Rong L. He, Stephen S.-T. Yau, Yang Zhang
2015 PLoS ONE  
The Yau-Hausdorff method can be used for measuring the similarity of DNA sequences based on two important tools: the Yau-Hausdorff distance and graphical representation of DNA sequences.  ...  The complexity of this method is lower than that of any other two dimensional minimum Hausdorff algorithm.  ...  The minimum Hausdorff distance between two one-dimensional point sets A and B under translation is defined as H 1 ðA; BÞ ¼ min t2R hðA þ t; BÞ ð 3Þ where h(A+t,B) is the Hausdorff distance between A and  ... 
doi:10.1371/journal.pone.0136577 pmid:26384293 pmcid:PMC4575136 fatcat:nkd3ta5orzfnzoxiun4qnddvca

A Metric for Polygon Comparison and Building Extraction Evaluation

Janja Avbelj, Rupert Muller, Richard Bamler
2015 IEEE Geoscience and Remote Sensing Letters  
Furthermore, we compare building polygons extracted from a digital surface model to the reference building polygons by computing PoLiS, Hausdorff and Chamfer distances.  ...  What is more, Hausdorff and Chamfer distances overrate the dissimilarity when one polygon has more vertices than the other.  ...  ACKNOWLEDGMENT The authors would like to thank the city of Munich, Department of Environment and Health for providing the reference building footprints.  ... 
doi:10.1109/lgrs.2014.2330695 fatcat:6xhtgxzt4vbnnhpxvuqmliqwca

Page 2227 of Mathematical Reviews Vol. , Issue 92d [page]

1992 Mathematical Reviews  
{For the entire collection see MR 92a:68002.} 92d:68114 68U05 68T10 Rote, Giinter (A-TGRZ) Computing the minimum Hausdorff distance between two-point sets on a line under translation. Inform.  ...  Summary: “Given two sets of points on a line, we want to translate one of them so that their Hausdorff distance (the maximum of the distances from a point in either of the sets to the nearest point in  ... 

Hausdorff distance under translation for points and balls

Pankaj K. Agarwal, Sariel Har-Peled, Micha Sharir, Yusu Wang
2003 Proceedings of the nineteenth conference on Computational geometry - SCG '03  
We propose efficient approximation algorithms for computing the minimum rms and the minimum summed Hausdorff distances under translation, between two point sets in R d .  ...  We also consider the problem in the standard setting, by computing the Hausdorff distance between the unions of the two sets (as point sets).  ...  [4] present algorithms for approximating the minimum Hausdorff distance under different families of transformations for sets of points or of segments in R 2 , and for sets of triangles in R 3 , using  ... 
doi:10.1145/777792.777835 dblp:conf/compgeom/AgarwalHSW03 fatcat:4vnmhgmpljbkjgfn3aoe2noljq

DOCUMENT IMAGE REGISTRATION FOR IMPOSED LAYER EXTRACTION

Surabhi Narayan, Sahana D Gowda
2017 ICTACT Journal on Image and Video Processing  
For every transformation of the input vertices, Minimum Hausdorff distance (MHD) is computed.  ...  Minimum Hausdorff distance identifies the rotation and scaling values by which the input image should be transformed to align it to the template.  ...  ACKNOWLEDGEMENT The authors acknowledge the support provided by VTU.  ... 
doi:10.21917/ijivp.2017.0205 fatcat:p5ns7tedc5egjf2k2ks7zsehxy

Hausdorff distance under translation for points and balls

Pankaj K. Agarwal, Sariel Har-Peled, Micha Sharir, Yusu Wang
2003 Proceedings of the nineteenth conference on Computational geometry - SCG '03  
We propose efficient approximation algorithms for computing the minimum rms and the minimum summed Hausdorff distances under translation, between two point sets in R d .  ...  We also consider the problem in the standard setting, by computing the Hausdorff distance between the unions of the two sets (as point sets).  ...  [4] present algorithms for approximating the minimum Hausdorff distance under different families of transformations for sets of points or of segments in R 2 , and for sets of triangles in R 3 , using  ... 
doi:10.1145/777833.777835 fatcat:zukmxyi26femxcwnimovde2ww4

Hausdorff distance under translation for points and balls

Pankaj K. Agarwal, Sariel Har-Peled, Micha Sharir, Yusu Wang
2010 ACM Transactions on Algorithms  
We propose efficient approximation algorithms for computing the minimum rms and the minimum summed Hausdorff distances under translation, between two point sets in R d .  ...  We also consider the problem in the standard setting, by computing the Hausdorff distance between the unions of the two sets (as point sets).  ...  [4] present algorithms for approximating the minimum Hausdorff distance under different families of transformations for sets of points or of segments in R 2 , and for sets of triangles in R 3 , using  ... 
doi:10.1145/1824777.1824791 fatcat:vjezj5gx6fdnpmckw3kh3ih7va

The upper envelope of voronoi surfaces and its applications

Daniel P. Huttenlocher, Klara Kedem, Micha Sharir
1993 Discrete & Computational Geometry  
We then discuss applications of the methods to the problems of finding the minimum Hausdorff distance under translation, between sets of points and segments.  ...  The upper envelope of a set of these Voronoi surfaces, each defined for a different set of sources, can be used to solve the problem of finding the minimum Hausdorff distance between two sets of points  ...  The minimum Hausdorff distance under translation between two sets of points in ~3 based on the L 2 metric (and the translation that achieves this minimum) can be computed in time O((pq)2(p + q)l+~) for  ... 
doi:10.1007/bf02189323 fatcat:mxigm66i4jft3gda5s7vasbfua

Minimum Partial-Matching and Hausdorff RMS-Distance under Translation: Combinatorics and Algorithms [chapter]

Rinat Ben-Avraham, Matthias Henze, Rafel Jaume, Balázs Keszegh, Orit E. Raz, Micha Sharir, Igor Tubis
2014 Lecture Notes in Computer Science  
We consider the RMS-distance (sum of squared distances between pairs of points) under translation between two point sets in the plane.  ...  In addition, we show how to compute a local minimum of the partial matching RMS-distance under translation, in polynomial time. RM S 1 (B, A) = RM S(A, B) + RM S(B, A).  ...  Minimum Hausdorff RMS-distance under translation in two dimensions.  ... 
doi:10.1007/978-3-662-44777-2_9 fatcat:aqgakfngmnbu7p2ssfcbptqzlm

Minimizing the Weighted Directed Hausdorff Distance between Colored Point Sets under Translations and Rigid Motions [chapter]

Christian Knauer, Klaus Kriegel, Fabian Stehn
2009 Lecture Notes in Computer Science  
The weighted Hausdorff distance, as introduced in this paper, takes the weights of the point sets into account.  ...  class T , compute the transformations t ∈ T that minimize the weighted directed Hausdorff distance of t(P ) to Q.  ...  An exact algorithm optimizing the Hausdorff distance under translations for points in the plane is presented in Section 5. A 2-approximation for translations in R d Theorem 1.  ... 
doi:10.1007/978-3-642-02270-8_13 fatcat:jedm2md2ovdalb24vqxrbrf5vy

Minimizing the weighted directed Hausdorff distance between colored point sets under translations and rigid motions

C. Knauer, K. Kriegel, F. Stehn
2011 Theoretical Computer Science  
The weighted Hausdorff distance, as introduced in this paper, takes the weights of the point sets into account.  ...  class T , compute the transformations t ∈ T that minimize the weighted directed Hausdorff distance of t(P ) to Q.  ...  In this paper we discuss the problem of matching two sequences of weighted point sets under the weighted directed Hausdorff distance.  ... 
doi:10.1016/j.tcs.2010.03.020 fatcat:6vvbrbmkw5cndhehzjde7k62vi

Lower bounds for the complexity of the graph of the Hausdorff distance as a function of transformation

W. J. Rucklidge
1996 Discrete & Computational Geometry  
We exhibit lower-bound constructions for both sets of points in the plane, and sets of points and line segments; we consider the graph of the directed Hausdorff distance under translation, rigid motion  ...  Algorithms.to find the minimum distance as one set is transformed have been described, but few lower bounds are known.  ...  Acknowledgments The ~ (n*) example shown in Section 3 is due to Paul Chew and Klara Kedem.  ... 
doi:10.1007/bf02716804 fatcat:g35kz6uh7jcnbgav46bp5dxwkq

Partial-Matching and Hausdorff RMS Distance Under Translation: Combinatorics and Algorithms [article]

Rinat Ben-Avraham, Matthias Henze, Rafel Jaume, Balázs Keszegh, Orit E. Raz, Micha Sharir, Igor Tubis
2014 arXiv   pre-print
In addition, we show how to compute a local minimum of the partial-matching RMS distance under translation, in polynomial time.  ...  We consider the RMS distance (sum of squared distances between pairs of points) under translation between two point sets in the plane, in two different setups.  ...  , and by the Hermann Minkowski-MINERVA Center for Geometry at Tel Aviv University. Igor Tubis was supported by the Deutsch Institute. A preliminary version of this paper has appeared in [6] .  ... 
arXiv:1411.7273v1 fatcat:ohx6lk4jrza5hc7tyezzrkx2ze
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