EMD swMATH ID: 14902 Software Authors: Y. Rubner Description: Code for the Earth Movers Distance (EMD). This is an implementation of the Earth Movers Distance, as described in [1]. The EMD computes the distance between two distributions, which are represented by signatures. The signatures are sets of weighted features that capture the distributions. The features can be of any type and in any number of dimensions, and are defined by the user. The EMD is defined as the minimum amount of work needed to change one signature into the other. The notion of ”work” is based on the user-defined ground distance which is the distance between two features. The size of the two signatures can be different. Also, the sum of weights of one signature can be different than the sum of weights of the other (partial match). Because of this, the EMD is normalized by the smaller sum. The code is implemented in C, and is based on the solution for the Transportation problem as described in [2] Please let me know of any bugs you find, or any questions, comments, suggestions, and criticisms you have. If you find this code useful for your work, I would like very much to hear from you. Once you do, I’ll inform you of any improvements, etc. Also, an acknowledgment in any publication describing work that uses this code would be greatly appreciated. Homepage: http://robotics.stanford.edu/~rubner/emd/default.htm Related Software: SIFT; Wasserstein GAN; SIMPLIcity; VisualSEEk; PASCAL VOC; DOTmark; UCI-ml; NeTra; PRMLT; GitHub; ElemStatLearn; ROME; CUReT; MultiScaleOT; MNIST; PyTorch; darch; R; POT; PointNet Cited in: 205 Publications Standard Articles 1 Publication describing the Software, including 1 Publication in zbMATH Year The earth mover’s distance as a metric for image retrieval. Zbl 1012.68705Rubner, Yossi; Tomasi, Carlo; Guibas, Leonidas J. 2000 all top 5 Cited by 480 Authors 13 Peyré, Gabriel 7 Cuturi, Marco 6 Munk, Axel 6 Schmitzer, Bernhard 5 Rabin, Julien 4 Guibas, Leonidas John 4 Li, Wuchen 4 Mérigot, Quentin 3 Bonneel, Nicolas 3 Coifman, Ronald Raphaël 3 Delon, Julie 3 Leeb, William E. 3 Osher, Stanley Joel 3 Rohde, Gustavo K. 3 Rote, Günter 3 Slepčev, Dejan 3 Sommerfeld, Max 3 Talmon, Ronen 3 Yin, Wotao 3 Zemel, Yoav 2 Baier, Daniel 2 Bollt, Erik M. 2 Brossier, Romain 2 Chazal, Frédéric 2 Chizat, Lénaïc 2 Cloninger, Alexander 2 Coeurjolly, David 2 Cohen-Steiner, David 2 Cuevas, Antonio 2 Daubechies, Ingrid Chantal 2 Ding, Hu 2 Dsilva, Carmeline J. 2 Frost, Sarah 2 Geiß, Darius 2 Gousseau, Yann 2 Heitz, Matthieu 2 Jäger, Manfred 2 Kahn, Jonas 2 Kevrekidis, Ioannis George 2 Klatt, Marcel 2 Klein, Rolf-Dieter 2 Kolouri, Soheil 2 Koulouri, Alexandra 2 Lipman, Yaron 2 Lippi, Marco 2 Liu, Ying 2 Lu, Guojun 2 Métivier, Ludovic 2 Ostrovska, Sofiya 2 Ostrovskii, Mikhail Iosifovich 2 Ozolek, John A. 2 Papadakis, Nicolas 2 Passerini, Andrea 2 Penninger, Rainer 2 Puccetti, Giovanni 2 Rubner, Yossi 2 Ryu, Ernest K. 2 Shokoufandeh, Ali 2 Solomon, Justin 2 Tameling, Carla 2 Tomasi, Carlo 2 Veneroni, Marco 2 Vialard, François-Xavier 2 Weed, Jonathan 2 Yin, Penghang 2 Zhang, Dengsheng 1 Abellanas, Manuel 1 Abramov, Rafail V. 1 Ahmed, Nesreen K. 1 Alger, Jeffrey R. 1 Ammar, Amine 1 Amores, Jaume 1 Andersson, Helge I. 1 Andoni, Alexandr 1 Arroyo, Javier 1 Asano, Tetsuo 1 Aujol, Jean-François 1 Auricchio, Gennaro 1 Avendaño-Garrido, Martha Lorena 1 Avidan, Shai 1 Bach, Francis R. 1 Backhaus, Scott N. 1 Balzanella, Antonio 1 Bao, Michael 1 Bar-Hillel, Aharon 1 Barrena, Manuel 1 Bassetti, Federico 1 Basu, Saurav 1 Bauer, Martin 1 Beecks, Christian 1 Ben Chen, Mirela 1 Ben-Eliezer, Omri 1 Benamou, Jean-David 1 Bereg, Sergey N. 1 Berrendero, Jose Ramon 1 Berretti, Stefano 1 Bhandarkar, Suchendra M. 1 Bouguila, Nizar 1 Bretzner, Lars 1 Bronevich, Andrey G. ...and 380 more Authors all top 5 Cited in 109 Serials 17 Pattern Recognition 10 Journal of Mathematical Imaging and Vision 8 SIAM Journal on Imaging Sciences 6 SIAM Journal on Scientific Computing 6 International Journal of Computer Vision 5 Journal of Computational Physics 5 Applied and Computational Harmonic Analysis 5 Journal of Machine Learning Research (JMLR) 4 Journal of Scientific Computing 4 Computational Geometry 4 SIAM Journal on Mathematics of Data Science 3 Computer Aided Geometric Design 3 Bernoulli 3 Data Mining and Knowledge Discovery 3 Foundations of Computational Mathematics 3 Advances in Data Analysis and Classification. 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Académie des Sciences, Paris 1 SIAM Journal on Applied Dynamical Systems 1 Multiscale Modeling & Simulation 1 Quantum Information Processing 1 Communications in Mathematical Sciences 1 International Journal of Wavelets, Multiresolution and Information Processing 1 Mediterranean Journal of Mathematics 1 Computational Management Science 1 Statistical Methods and Applications 1 Mathematical Biosciences and Engineering 1 Journal of Shanghai Jiaotong University (Science) 1 The Kluwer International Series in Engineering and Computer Science 1 Communications in Mathematical Analysis 1 Mathematics in Computer Science 1 Mathematics and Financial Economics 1 Communications in Computational Physics 1 Statistical Analysis and Data Mining 1 Electronic Journal of Statistics 1 Foundations and Trends in Computer Graphics and Vision 1 Algorithms 1 MathematicS In Action ...and 9 more Serials all top 5 Cited in 37 Fields 96 Computer science (68-XX) 45 Numerical analysis (65-XX) 42 Statistics (62-XX) 38 Operations research, mathematical programming (90-XX) 34 Calculus of variations and optimal control; optimization (49-XX) 18 Information and communication theory, circuits (94-XX) 12 Biology and other natural sciences (92-XX) 11 Probability theory and stochastic processes (60-XX) 9 Combinatorics (05-XX) 8 Functional analysis (46-XX) 7 Partial differential equations (35-XX) 7 Dynamical systems and ergodic theory (37-XX) 6 Fluid mechanics (76-XX) 6 Geophysics (86-XX) 5 Differential geometry (53-XX) 5 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 5 Systems theory; control (93-XX) 4 General topology (54-XX) 3 Convex and discrete geometry (52-XX) 2 General and overarching topics; collections (00-XX) 2 Measure and integration (28-XX) 2 Harmonic analysis on Euclidean spaces (42-XX) 2 Global analysis, analysis on manifolds (58-XX) 2 Statistical mechanics, structure of matter (82-XX) 1 History and biography (01-XX) 1 Mathematical logic and foundations (03-XX) 1 Order, lattices, ordered algebraic structures (06-XX) 1 Real functions (26-XX) 1 Ordinary differential equations (34-XX) 1 Difference and functional equations (39-XX) 1 Approximations and expansions (41-XX) 1 Geometry (51-XX) 1 Algebraic topology (55-XX) 1 Manifolds and cell complexes (57-XX) 1 Mechanics of deformable solids (74-XX) 1 Classical thermodynamics, heat transfer (80-XX) 1 Quantum theory (81-XX) Citations by Year