Point pattern matching using a genetic algorithm and Voronoi tessellation

Point pattern matching problem consists in identifying similar point patterns in two point sets which differ one each other in scale, orientation angle or position. A new objective function for the problem of point pattern matching is proposed here. The function scores not only the exact matching situations between patterns, but also the inexact ones. It has only one global maximum in the desired solution, and hence implosion cases which occur for very low scale factors are avoided. An efficient algorithm for the evaluation of the objective function is proposed. The algorithm requires a preprocessing stage to label the Voronoi regions of one of the point sets. Then, a genetic algorithm is used to maximize the proposed objective function.