Geometrical matching of images: potential functions and moments

A theory for computational geometry appropriate for geometrical objects specified by point sets (in effect, binary images) is developed. The theory deals with the determination of the transformation that brings two images into registration, and the similarity of optimally registered sets. Several classes of geometric transformations are considered: translation, congruence, and similarity transformations. The theory is based on `potential functions,´ which are shift- and rotation-invariant set comparison functions that are generalizations of cross-correlation and set difference. These functions have the advantage of `action at a distance,´ which facilitates matching of nonoverlapping sets. The type of set comparison function that is admissable depends on the class of transformations under consideration. A relation between potential functions and the use of moments for registration is discovered