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. Earth Movers Distance
For some reason, our brains are unable to tune out half a conversation. Researchers believe this is because we can't predict the speech pattern of a halfalogue the way we can with a monologue or two-way conversation -- making it harder to ignore.