Algorithms for Point Set Congruence.

摘要

The primary purpose of the project supported by this grant was to expand research in point matching, by applying the perturbation technique and the approximate algorithm paradigm to more complex problem formulations. During the tenure of the grant the investigator has successfully worked towards this goal. The main results of this research are contained in the paper 'Generalized approximate algorithms for point set congruence'. This paper is still undergoing revisions, and a copy of the most recent draft is included in this report. The paper introduces a device called the (e, k)-map, which is a more general measure of point set congruence than the one previously examined by the investigator. The paper discusses ways to construct the (e, k)-map. While the investigator's previous work was limited to equal cardinality, planar point sets, this current work has expanded attention both to Point sets of unequal cardinality and to point sets in higher dimensions. The investigator has even begun the study of projective congruence, in which one compares a 2-dimensional image with the family of projections of a 3-dimensional model..... Algorithms, Point set congruence, Pergurbation technique.