FAST GENERALIZED 2-DIMENSIONAL HEAP FOR HAUSDORFF AND EARTH MOVER'S DISTANCE

A method of measuring distance between two distributions of data points in a space is described. The distances between data points are ordered in a plurality of heaps stored within 2-D heaps, which is constructed by giving heap structure to a list of one-dimensional heaps. Each plurality of heaps is ordered so that the minimum distance is the root node. The plurality of heaps within the 2-D heaps are ordered to determine the maximum of the root nodes. The maximum of the 2-D heaps are compared to determine the Hausdorff distance which is the greater of the maximums. The corresponding heaps are removed from their respective 2-D heaps. The Hausdorff distance is utilized in a set of calculations to generate an EMD. Determining the Hausdorff distance and generating the EMD is repeated until no more earths and no more holes remain. After all earths are moved to all holes, the work is established, and the similarity of the plurality of images is determined.