Using multiscale top points in image matching

Earth Mover's Distance (EMD) reflects the minimal amount of work that must be performed to transform one distribution into the other by moving distribution mass around. Very efficient algorithms for calculating the EMD exist. In our experiments we have used an algorithm proposed by Rubner et al. Without going into details about the EMD and its implementation an intuitive view of the EMD is as follows:Given two distributions, one can be seen as a mass of earth properly spread in space, the other as a set of holes in that same space. Assuming that there is always at least as much earth as needed to fill all the holes (this can be achieved by switching what is called earth or holes if necessary), the EMD gives a measure of the least amount of work needed to fill the holes with earth. One unit of work corresponds to transporting a unit of earth by a unit distance.This means that apart from the distributions we want to match (e.g. the top points) a weight distribution} and a distance measure are important