Discrete pattern recognition by fitting onto a continuous function

This article outlines an original method for matching discrete structures when atom correspondences are unknown. This method avoids the current atom-by-atom treatment (and its inherent combinatorial problems) and considers the structures to be compared in their totality. The basic idea is to first obtain the atom correspondences by fitting one of the two discrete structures onto a spline approximation of the other, rather than optimizing in discrete space, and, second, to overlap the two discrete structures on the basis of the proposed assignment. As starting data, the method requires only the Cartesian coordinates of the two structures. No connectivity information, neither atom labeling nor matching tolerance is required. This method can readily handle matches of molecules with a few hundred atoms. It is able to search for a given 3D pattern as well as for a pattern common to two structures.