<title>Ordering-oriented Hopfield network and its application in stereo vision</title>

Abstract

The Traveling Salesman Problem (TSP) is a well known problem which can be solved using Hopfield Networks. The TSP solution with Hopfield Networks is based on the uniqueness constraint. This is, each city must be visited once and only once while trying to minimize the traveling distance. But in the real world applications, usually there are other equally important constraints needed to be considered. For example, an ordering constraint in how cities are to be visited. This paper describes a Hopfield neural network that can solve a new class of optimization problems, called 'The Picking Stone Problem (PSP)'. The PSP requires not only the uniqueness but also the ordering constraints. The neural network implementation to solve PSP tends to turn on neurons which satisfy the ordering constraint and this constraint is essential in solving stereo correspondence problem in binocular vision. In this paper we define the PSP, formulate its computational complexity, propose the ordering-oriented neural network architecture, discuss the performance of the proposed network by both the traditional way and a new initialization method, then finally apply the network to incorporate with all the major stereo vision constraints to solve the stereo correspondence problem. The implementation and the performance of the ordering-oriented neural networks are investigated in detail and experimental results applying this technique to solve the stereo correspondence problem on real images are presented.