A NOVEL CONNECTIONIST FRAMEWORK FOR COMPUTATION OF AN APPROXIMATE CONVEX-HULL OF A SET OF PLANAR POINTS, CIRCLES AND ELLIPSES

Abstract

We propose a two layer neural network for computation of an approximate convex-hull of a set of points or a set of circles/ellipses of different sizes. The algorithm is based on a very elegant concept — shrinking of a rubber band surrounding the set of planar objects. Logically, a set of neurons is placed on a circle (rubber band) surrounding the objects. Each neuron has a parameter vector associated with it. This may be viewed as the current position of the neuron. The given set of points/objects exerts a force of attraction on every neuron, which determines how its current position will be updated (as if, the force determines the direction of movement of the neuron lying on the rubber band). As the network evolves, the neurons (parameter vectors) approximate the convex-hull more and more accurately. The scheme can be applied to find the convex-hull of a planar set of circles or ellipses or a mixture of the two. Some properties related to the evolution of the algorithm are also presented.