Sergio Cabello, Panos Giannopoulos, Christian Knauer, and Günter Rote:

Matching point sets with respect to the earth mover's distance

  1. In: Abstracts of the 21st European Workshop on Computational Geometry, Eindhoven, March 2005, pp. 57-60.
  2. In: "Algorithms - ESA 2005", Proc. Thirteenth Annual European Symposium on Algorithms, Palma de Mallorca, 2005. Editors: Gerth Stolting Brodal and Stefano Leonardi. Lecture Notes in Computer Science 3669, Springer-Verlag, 2005, pp. 520-531. doi:10.1007/11561071_47
  3. Computational Geometry, Theory and Applications 39 (2008), pp. 118-133. doi:10.1016/j.comgeo.2006.10.001


The Earth Mover's Distance (EMD) between two weighted point sets (point distributions) is a distance measure commonly used in computer vision for color-based image retrieval and shape matching. It measures the minimum amount of work needed to transform one set into the other one by weight transportation. We study the following shape matching problem: Given two weighted point sets A and B in the plane, compute a rigid motion of A that minimizes its Earth Mover's Distance to B. No algorithm is known that computes an exact solution to this problem. We present simple FPTASs and polynomial-time (2+ε)-approximation algorithms for the minimum Euclidean EMD between A and B under translations and rigid motions.
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