Representing Shapes by Fitting Data using an Evolutionary Approach

An evolutionary approach has been introduced for representing shapes by optimal curve fitting to planar data raised from the outlines of the two dimensional shapes. The algorithm designed, consists of various phases towards the solution of the problem. The spline model used is a rational cubic spline. It is a C1 model possessing shape parameters in its description in such a way that one parameter is sitting between each two consecutive control points. These shape parameters provide interval tension control and have been utilized to obtain an optimal curve fit to data raised from the outlines of the planar shapes. Detecting corners, from amongst the data points, is one of the important phases in the design algorithm. It helps in many ways including keeping permanent genes in the chromosomes, capturing a pleasant looking spline fitting data. In case of too large data, it provides a data reduction concept. The chromosomes have been constructed by considering the candidates of the locations of knots, together with shape parameters, as genes. The knots to the corresponding corner points have been kept fixed to minimize the computation cost. The best model among the candidates is searched by using Akaike’s Information Criterion (AIC). The method automatically determines the appropriate number and location of knots together with optimal vector of shape parameter values.