Determining the similarity of point patterns using internal, nonmetric representations: preliminary results

Point patterns can be represented by rank ordered lists of interpoint distances. This use of ordinal (i.e. nonmetric) information, combined with the independence of the representation from any coordinate system, means that the resulting representation, and reconstruction as well, is indifferent to scale, translation, rotation, and reflection. This paper focuses on establishing a measure of similarity between non-identical patterns of P points. In doing so, it considers two cases. The first, and simpler, includes an a priori specification of the point correspondences between the two patterns; in the second no such a priori specification is made and it thus requires first determining the best assignment of point correspondences