Matching Point Sets with Respect to the Earth Mover’s Distance

  • Sergio Cabello
  • Panos Giannopoulos
  • Christian Knauer
  • Günter Rote
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3669)


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 FPTAS and polynomial-time (2 + ε)-approximation algorithms for the minimum Euclidean EMD between A and B under translations and rigid motions.


Approximation Algorithm Rigid Motion Match Point Alignment Rotation Partial Assignment 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Sergio Cabello
    • 1
  • Panos Giannopoulos
    • 2
  • Christian Knauer
    • 2
  • Günter Rote
    • 2
  1. 1.Department of MathematicsIMFMLjubljanaSlovenia
  2. 2.Institut für InformatikFreie Universität BerlinBerlinGermany

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