HISTOGRAMS DISTANCE.

A metric is defined on the space of multidimensional histograms. Such histograms store in the xth location the number of events with feature vector x; examples are gray level histograms and co-occurrence matrices of digital images. Given two multidimensional histograms, each is 'unfolded' and a minimum distance pairing is performed using a distance metric on the feature vectors x. The sum of the distances in the minimal pairing is used as the 'match distance' between the histograms. This distance is shown to be a metric, and in the one dimensional case is equal to the absolute difference of the two cumulative distribution functions. Among other applications, it facilitates direct computation of the distance between co-occurrence matrices or between point patterns. An example is also given for the use of this metric in grey-level quantization in a halftone-like manner.