Selection of alpha for alpha-hull in R2

摘要

For finding the shape of a planar set, Edelsbrunner, Kirkpatrick and Seidel introduced the concept of α-hulls as a natural generalization of convex hulls. While the α-hull is elegant and efficient to compute, it still suffers from a major drawback, i.e. the single parameter, namely α, must nevertheless be tuned. This paper deals with finding a way to overcome this drawback, i.e. we proposed here a selection criterion of α for α-hulls corresponding to a point set in R2. The selection criterion of α is based on the concept of minimum spanning trees and certain existing results. The effectiveness of the proposed selection criterion is demonstrated on some artificially generated data sets. The convergence (with sample size) of the α-hull, based on the proposed selection criterion for α, to the original pattern class has also been verified using symmetric difference, the Hausdorff metric, and a similarity metric.