Tod S. Levitt
A significant problem in image understanding (IU) is to represent objects as models stored in a machine environment for IU systems to use in model driven pattern matching for object recognition. This paper presents a technique for autonomous machine description of objects presented as spatial data, i.e., data presented as point sets in Euclidean n-space. This general definition of objects as spatial data encompasses the cases of explicit listings of points, lines or other spatial features, objects defined by light pen in a CAD system, generalized cone representations, polygonal boundary representations, quad-trees, etc. The description technique decomposes an object into component sub-parts which are meaningful to a human being. It is based upon a measure of symmetry of point sets. Most spatial data has no global symmetry. In order to arrive at a reasonable description of a point set, we attempt to decompose the data into the fewest subsets each of which is as symmetric as possible. The technique is based upon statistics which capture the opposing goals of fewest pieces and most symmetry. An algorithm is proposed which operates sequentially in polynomial time to reach an optimal (but not necessarily unique) decomposition. The semantic content of the descriptions which the technique produces agrees with results of experiments on qualitative human perception of spatial data. In particular, the technique provides a step toward a quantitative measure of the old perceptual Gestalt school of psychology’s concept of "goodness of figure".