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Getting around a lower bound for the minimum Hausdorff distance

1998
*
Computational geometry
*

We consider

doi:10.1016/s0925-7721(97)00032-1
fatcat:zwbde6cxxbf7jdpdmdfgoqcfmu
*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*. ...##
###
Geometric pattern matching under Euclidean motion

1997
*
Computational geometry
*

We also show how to use our methods to substantially improve on existing algorithms

doi:10.1016/0925-7721(95)00047-x
fatcat:nuqmk7a5ffayhkmiebxvc6k4ni
*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 ...##
###
Two Dimensional Yau-Hausdorff Distance with Applications on Comparison of DNA and Protein Sequences

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 ...

##
###
A Metric for Polygon Comparison and Building Extraction Evaluation

2015
*
IEEE Geoscience and Remote Sensing Letters
*

Furthermore, we compare building polygons extracted from a digital surface model to

doi:10.1109/lgrs.2014.2330695
fatcat:6xhtgxzt4vbnnhpxvuqmliqwca
*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. ...##
###
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

2003
*
Proceedings of the nineteenth conference on Computational geometry - SCG '03
*

We propose efficient approximation algorithms

doi:10.1145/777792.777835
dblp:conf/compgeom/AgarwalHSW03
fatcat:4vnmhgmpljbkjgfn3aoe2noljq
*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 ...##
###
DOCUMENT IMAGE REGISTRATION FOR IMPOSED LAYER EXTRACTION

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. ...

##
###
Hausdorff distance under translation for points and balls

2003
*
Proceedings of the nineteenth conference on Computational geometry - SCG '03
*

We propose efficient approximation algorithms

doi:10.1145/777833.777835
fatcat:zukmxyi26femxcwnimovde2ww4
*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 ...##
###
Hausdorff distance under translation for points and balls

2010
*
ACM Transactions on Algorithms
*

We propose efficient approximation algorithms

doi:10.1145/1824777.1824791
fatcat:vjezj5gx6fdnpmckw3kh3ih7va
*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 ...##
###
The upper envelope of voronoi surfaces and its applications

1993
*
Discrete & Computational Geometry
*

We then discuss applications of

doi:10.1007/bf02189323
fatcat:mxigm66i4jft3gda5s7vasbfua
*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*...##
###
Minimum Partial-Matching and Hausdorff RMS-Distance under Translation: Combinatorics and Algorithms
[chapter]

2014
*
Lecture Notes in Computer Science
*

We consider

doi:10.1007/978-3-662-44777-2_9
fatcat:aqgakfngmnbu7p2ssfcbptqzlm
*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. ...##
###
Minimizing the Weighted Directed Hausdorff Distance between Colored Point Sets under Translations and Rigid Motions
[chapter]

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. ...

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

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*. ...

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

1996
*
Discrete & Computational Geometry
*

We exhibit lower-bound constructions

doi:10.1007/bf02716804
fatcat:g35kz6uh7jcnbgav46bp5dxwkq
*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. ...##
###
Partial-Matching and Hausdorff RMS Distance Under Translation: Combinatorics and Algorithms
[article]

2014
*
arXiv
*
pre-print

In addition, we show how to

arXiv:1411.7273v1
fatcat:ohx6lk4jrza5hc7tyezzrkx2ze
*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] . ...
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