Article ID Journal Published Year Pages File Type
414814 Computational Geometry 2008 16 Pages PDF
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.

Related Topics
Physical Sciences and Engineering Computer Science Computational Theory and Mathematics