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

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

*In: Abstracts of the 21st European Workshop on Computational
Geometry,
Eindhoven, March 2005, pp. 57-60.*
*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*
*
*Computational Geometry,
Theory and Applications 39 (2008), pp. 118-133.* doi:10.1016/j.comgeo.2006.10.001

### Abstract

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.
Last update: November 15, 2007.