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

Sergio Cabello, Panos Giannopoulos, Christian Knauer, Günter Rote
2005 Lecture Notes in Computer Science  
Let A and B be two 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] .  ... 
doi:10.1007/11561071_47 fatcat:tsca65csmrfszf3geiuivdmssa

Matching point sets with respect to the Earth Mover's Distance

Sergio Cabello, Panos Giannopoulos, Christian Knauer, Günter Rote
2008 Computational geometry  
Let A and B be two 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] .  ... 
doi:10.1016/j.comgeo.2006.10.001 fatcat:znoja3fx4bbhfcpumwss6fgcfa

Summable Reparameterizations of Wasserstein Critics in the One-Dimensional Setting [article]

Christopher Grimm, Yuhang Song, Michael L. Littman
2017 arXiv   pre-print
This paper looks particularly at this 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.  ... 
arXiv:1709.06533v1 fatcat:6lsmlqxr2ncibeawg2j2pfxg2y

Video-Based Face Recognition Using Earth Mover's Distance [chapter]

Jiangwei Li, Yunhong Wang, Tieniu Tan
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.  ... 
doi:10.1007/11527923_24 fatcat:l6yazy6e5zhqlibry5n62svkn4

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

Jiangwei Li, Yunhong Wang, Tieniu Tan
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".  ... 
doi:10.1007/978-3-540-30548-4_26 fatcat:sj5hoz6gxfhevbvmhdfcc7sshy

Earth Mover's Distance Minimization for Unsupervised Bilingual Lexicon Induction

Meng Zhang, Yang Liu, Huanbo Luan, Maosong Sun
2017 Proceedings of the 2017 Conference on Empirical Methods in Natural Language Processing  
By viewing word embedding spaces as distributions, we propose 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).  ... 
doi:10.18653/v1/d17-1207 dblp:conf/emnlp/ZhangLLS17 fatcat:clsjrmjob5abhkppvryumfrp2q

Circular Earth Mover's Distance for the comparison of local features

Julien Rabin, Julie Delon, Yann Gousseau
2008 Pattern Recognition (ICPR), Proceedings of the International Conference on  
In this contribution, we present an adaptation of 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  ... 
doi:10.1109/icpr.2008.4761372 dblp:conf/icpr/RabinDG08a fatcat:5esjkfgxvjb6dji6b3svz2yz2e

Robust hand gesture recognition based on finger-earth mover's distance with a commodity depth camera

Zhou Ren, Junsong Yuan, Zhengyou Zhang
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.  ... 
doi:10.1145/2072298.2071946 dblp:conf/mm/RenYZ11 fatcat:bsznat7qtrgqhdr7zerdhkch4y

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

Chi Zhang, Yujun Cai, Guosheng Lin, Chunhua Shen
2020 2020 IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR)  
We adopt 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  ... 
doi:10.1109/cvpr42600.2020.01222 dblp:conf/cvpr/ZhangCLS20 fatcat:xs6l3agykfg77pxlkopzpaj2sm

A Linear Time Histogram Metric for Improved SIFT Matching [chapter]

Ofir Pele, Michael Werman
2008 Lecture Notes in Computer Science  
In this paper we present a new 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.  ... 
doi:10.1007/978-3-540-88690-7_37 fatcat:i7rit25ncjh2lewos3wollb6ym

Towards Fully 8-bit Integer Inference for the Transformer Model

Ye Lin, Yanyang Li, Tengbo Liu, Tong Xiao, Tongran Liu, Jingbo Zhu
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  ... 
doi:10.24963/ijcai.2020/516 dblp:conf/ijcai/ChenLXPMC20 fatcat:meqdgmlcg5e7vc2mcodlu5hnjy

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

Sergio Cabello, Panos Giannopoulos, Christian Knauer
2006 Lecture Notes in Computer Science  
This shows that, unless FPT = W[1], 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.  ... 
doi:10.1007/11847250_16 fatcat:ftfickzctbccjdkdgxkf2hjmcy

On the parameterized complexity of d-dimensional point set pattern matching

Sergio Cabello, Panos Giannopoulos, Christian Knauer
2008 Information Processing Letters  
This shows that, unless FPT = W[1], 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.  ... 
doi:10.1016/j.ipl.2007.08.003 fatcat:622yn35rrzgl3h6sucheftaugy

Using Earth Mover's Distance in the Bag-of-Visual-Words Model for Mathematical Symbol Retrieval

Simone Marinai, Beatrice Miotti, Giovanni Soda
2011 2011 International Conference on Document Analysis and Recognition  
In this paper, 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.  ... 
doi:10.1109/icdar.2011.263 dblp:conf/icdar/MarinaiMS11a fatcat:ellug4cyjvcblga7derminrigm

DeepEMD: Differentiable Earth Mover's Distance for Few-Shot Learning [article]

Chi Zhang, Yujun Cai, Guosheng Lin, Chunhua Shen
2022 arXiv   pre-print
We employ 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 (  ... 
arXiv:2003.06777v4 fatcat:7lkdfct5dvhovnplxyukmdsgze
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