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Matching Point Sets with Respect to the Earth Mover's Distance
[chapter]

2005
*
Lecture Notes in Computer Science
*

Let A and B be two

doi:10.1007/11561071_47
fatcat:tsca65csmrfszf3geiuivdmssa
*sets*of m resp. n weighted*points*in*the*plane,*with*m ≤ n. ... We present (1 + ) and (2+ )-approximation algorithms for*the*minimum Euclidean*Earth**Mover's**Distance*between A and B under translations and rigid motions*respectively*. ...*The**Earth**Mover's**Distance*(EMD) is a similarity measure for weighted*point**sets**with*applications in colour-based image retrieval [7] , shape*matching*[7, 2, 1] and music score*matching*[9] . ...##
###
Matching point sets with respect to the Earth Mover's Distance

2008
*
Computational geometry
*

Let A and B be two

doi:10.1016/j.comgeo.2006.10.001
fatcat:znoja3fx4bbhfcpumwss6fgcfa
*sets*of m resp. n weighted*points*in*the*plane,*with*m ≤ n. ... We present (1 + ) and (2+ )-approximation algorithms for*the*minimum Euclidean*Earth**Mover's**Distance*between A and B under translations and rigid motions*respectively*. ...*The**Earth**Mover's**Distance*(EMD) is a similarity measure for weighted*point**sets**with*applications in colour-based image retrieval [7] , shape*matching*[7, 2, 1] and music score*matching*[9] . ...##
###
Summable Reparameterizations of Wasserstein Critics in the One-Dimensional Setting
[article]

2017
*
arXiv
*
pre-print

This paper looks particularly at this

arXiv:1709.06533v1
fatcat:6lsmlqxr2ncibeawg2j2pfxg2y
*matching*capability in*the*context of problems*with*one-dimensional outputs. ... We identify a class of function decompositions*with*properties that make them well suited*to**the*critic role in a leading approach*to*GANs known as Wasserstein GANs. ... For each of*the*GAN methods, training was conducted over 100, 000 iterations,*with*an estimate of*the**Earth*-*Mover's**distance*being computed*with**the*training data every 1000 iterations. ...##
###
Video-Based Face Recognition Using Earth Mover's Distance
[chapter]

2005
*
Lecture Notes in Computer Science
*

*The*

*set*of features is then compressed

*with*a signature, which is composed of numbers of

*points*and their corresponding weights. ... This metric makes use of

*Earth*

*Mover's*

*Distance*(EMD) as

*the*underlying similarity measurement between two distributions of face images. ... So

*the*

*match*problem turns

*to*be

*the*

*distance*measurement of two signatures.

*Earth*

*Mover's*

*Distance*(EMD) is proposed for this purpose. ...

##
###
Video-Based Face Recognition Using a Metric of Average Euclidean Distance
[chapter]

2004
*
Lecture Notes in Computer Science
*

*Earth*

*Mover's*

*Distance*is a recently proposed metric for geometric pattern

*matching*and it reflects

*the*average ground

*distance*between two distributions. ... This metric makes use of

*Earth*

*Mover's*

*Distance*(EMD) as

*the*underlying similarity measurement between videos. ... EMD is a measurement of

*the*minimal work needed

*to*fill

*the*holes

*with*

*earth*. This is

*the*reason why it is named "

*Earth*

*Mover's*

*Distance*". ...

##
###
Earth Mover's Distance Minimization for Unsupervised Bilingual Lexicon Induction

2017
*
Proceedings of the 2017 Conference on Empirical Methods in Natural Language Processing
*

By viewing word embedding spaces as distributions, we propose

doi:10.18653/v1/d17-1207
dblp:conf/emnlp/ZhangLLS17
fatcat:clsjrmjob5abhkppvryumfrp2q
*to*minimize their*earth**mover's**distance*, a measure of divergence between distributions. ... In addition, we reveal an interesting finding that*the**earth**mover's**distance*shows potential as a measure of language difference. ... This work is supported by*the*National Natural Science Foundation of China (No. 61522204),*the*973 Program (2014CB340501), and*the*National Natural Science Foundation of China (No. 61331013). ...##
###
Circular Earth Mover's Distance for the comparison of local features

2008
*
Pattern Recognition (ICPR), Proceedings of the International Conference on
*

In this contribution, we present an adaptation of

doi:10.1109/icpr.2008.4761372
dblp:conf/icpr/RabinDG08a
fatcat:5esjkfgxvjb6dji6b3svz2yz2e
*the**Earth**Mover's**Distance**to*onedimensional circular histograms. This*distance*, that we call CEMD, is used*to*compare SIFT-like descriptors. ...*The*chosen dissimilarity measure is of crucial importance for*the*overall performances of these algorithms and has*to*be both robust and computationally efficient. ... Acknowledgments*The*authors acknowledge*the*support of*the*French Agence Nationale de la Recherche (ANR), under grant BLAN07-2_183172, Optimal transport: Theory and applications*to*cosmological reconstruction ...##
###
Robust hand gesture recognition based on finger-earth mover's distance with a commodity depth camera

2011
*
Proceedings of the 19th ACM international conference on Multimedia - MM '11
*

*To*handle

*the*noisy hand shape obtained from

*the*Kinect sensor, we propose a novel

*distance*metric for hand dissimilarity measure, called Finger-

*Earth*

*Mover's*

*Distance*(FEMD). ... Compared

*to*

*the*entire human body,

*the*hand is a smaller object

*with*more complex articulations and more easily affected by segmentation errors. ... Finger-

*Earth*

*Mover's*

*Distance*In [9] , Rubner et al. presented a general and flexible metric, called

*Earth*

*Mover's*

*Distance*(EMD),

*to*measure

*the*

*distance*between signatures or histograms. ...

##
###
DeepEMD: Few-Shot Image Classification With Differentiable Earth Mover's Distance and Structured Classifiers

2020
*
2020 IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR)
*

We adopt

doi:10.1109/cvpr42600.2020.01222
dblp:conf/cvpr/ZhangCLS20
fatcat:xs6l3agykfg77pxlkopzpaj2sm
*the**Earth**Mover's**Distance*(EMD) as a metric*to*compute a structural*distance*between dense image representations*to*determine image relevance. ...*The*EMD generates*the*optimal*matching*flows between structural elements that have*the*minimum*matching*cost, which is used*to*represent*the*image*distance*for classification. ... Acknowledgements This research is supported by*the*National Research Foundation Singapore under its AI Singapore Programme (Award Number: AISG-RP-2018-003) and*the*MOE Tier-1 research grants: RG126/17 ...##
###
A Linear Time Histogram Metric for Improved SIFT Matching
[chapter]

2008
*
Lecture Notes in Computer Science
*

In this paper we present a new

doi:10.1007/978-3-540-88690-7_37
fatcat:i7rit25ncjh2lewos3wollb6ym
*Earth**Mover's**Distance*(EMD) variant. We show that it is a metric (unlike*the*original EMD [1] which is a metric only for normalized histograms). ... Moreover, it is a natural extension of*the*L1 metric. Second, we propose a linear time algorithm for*the*computation of*the*EMD variant,*with*a robust ground*distance*for oriented gradients. ...*The*ground*distance*between this supplier or demander*to*all other demanders or suppliers*respectively*is*set**to*be α times*the*maximum ground*distance*. ...##
###
Towards Fully 8-bit Integer Inference for the Transformer Model

2020
*
Proceedings of the Twenty-Ninth International Joint Conference on Artificial Intelligence
*

*with*

*the*floating

*point*baseline but requires nearly 4x less memory footprint. ... On

*the*other hand, previous systems still rely on 32-bit floating

*point*for certain functions in complex models (e.g., Softmax in Transformer), and make heavy use of quantization and de-quantization. ... Acknowledgments Proceedings of

*the*Twenty-Ninth International Joint Conference on Artificial Intelligence ...

##
###
On the Parameterized Complexity of d-Dimensional Point Set Pattern Matching
[chapter]

2006
*
Lecture Notes in Computer Science
*

This shows that, unless FPT = W[1],

doi:10.1007/11847250_16
fatcat:ftfickzctbccjdkdgxkf2hjmcy
*the*problem of finding an isometry of A that minimizes its directed Hausdorff*distance*, or its*Earth**Mover's**Distance*,*to*B, is not in FPT. ... Deciding whether two n-*point**sets*A, B ∈ R d are congruent is a fundamental problem in geometric pattern*matching*. ... Concluding remarks We have studied*the*parameterized complexity of a fundamental*point**set*pattern*matching*problem*with**respect**to**the*dimension. ...##
###
On the parameterized complexity of d-dimensional point set pattern matching

2008
*
Information Processing Letters
*

This shows that, unless FPT = W[1],

doi:10.1016/j.ipl.2007.08.003
fatcat:622yn35rrzgl3h6sucheftaugy
*the*problem of finding an isometry of A that minimizes its directed Hausdorff*distance*, or its*Earth**Mover's**Distance*,*to*B, is not in FPT. ... Deciding whether two n-*point**sets*A, B ∈ R d are congruent is a fundamental problem in geometric pattern*matching*. ... Concluding remarks We have studied*the*parameterized complexity of a fundamental*point**set*pattern*matching*problem*with**respect**to**the*dimension. ...##
###
Using Earth Mover's Distance in the Bag-of-Visual-Words Model for Mathematical Symbol Retrieval

2011
*
2011 International Conference on Document Analysis and Recognition
*

In this paper,

doi:10.1109/icdar.2011.263
dblp:conf/icdar/MarinaiMS11a
fatcat:ellug4cyjvcblga7derminrigm
*the**Earth**Mover's**Distance*(EMD) is used as a similarity measure in*the*mathematical symbol retrieval task.*The*approach is based on*the*Bag-of-Visual-Words model. ...*The*comparison between*the*latter vectors is performed*with**the*EMD which naturally allows*to*incorporate*the*topological organization of SOM clusters in*the**distance*computation. ...*EARTH**MOVER'S**DISTANCE*In this work, we propose*to*use*the*EMD*to*compute*the*similarity for SOM-based clustering. ...##
###
DeepEMD: Differentiable Earth Mover's Distance for Few-Shot Learning
[article]

2022
*
arXiv
*
pre-print

We employ

arXiv:2003.06777v4
fatcat:7lkdfct5dvhovnplxyukmdsgze
*the**Earth**Mover's**Distance*(EMD) as a metric*to*compute a structural*distance*between dense image representations*to*determine image relevance. ...*The*EMD generates*the*optimal*matching*flows between structural elements that have*the*minimum*matching*cost, which is used*to*calculate*the*image*distance*for classification. ... ACKNOWLEDGMENTS This research was supported by*the*National Research Foundation Singapore under its AI Singapore Programme (Award Number: AISG-RP-2018-003) and*the*MOE Tier-1 research grants: RG28/18 ( ...
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