A connectionist model for convex-hull of a planar set.

Abstract

A neural network model is proposed for computation of the convex-hull of a finite planar set. The model is self-organizing in that it adapts itself to the hull-vertices of the convex-hull in an orderly fashion without any supervision. The proposed network consists of three layers of processors. The bottom layer computes the activation functions, the outputs of which are passed onto the middle layer. The middle layer is used for winner selection. These information are passed onto the topmost layer as well as fed back to the bottom layer. The network in the topmost layer self-organizes by labeling the hull-processors in an orderly fashion so that the final convex-hull is obtained from the topmost layer. Time complexities of the proposed model are analyzed and are compared with existing models of similar nature.