SELECTION OF ALPHA FOR ALPHA-HULL IN R-2

For finding the shape of a planar set, Edelsbrunner, Kirkpatrick and S eidel introduced the concept of alpha-hulls as a natural generalizatio n of convex hulls. While the alpha-hull is elegant and efficient to co mpute, it still suffers from a major drawback, i.e. the single paramet er, namely alpha, must nevertheless be tuned. This paper deals with fi nding a way to overcome this drawback, i.e. we proposed here a selecti on criterion of alpha for alpha-hulls corresponding to a point set in R-2. The selection criterion of alpha is based on the concept of minim um spanning trees and certain existing results. The effectiveness of t he proposed selection criterion is demonstrated on some artificially g enerated data sets. The convergence (with sample size) of the alpha-hu ll, based on the proposed selection criterion for alpha, to the origin al pattern class has also been verified using symmetric difference, th e Hausdorff metric, and a similarity metric. (C) 1997 Pattern Recognit ion Society. Published by Elsevier Science Ltd.