Correlations, Competition and Optimality: Modelling the Development of Topography and Ocular Dominance

iAbstract There is strong biological evidence that the same mechanisms underly the formation of both topography and ocular dominance in the visual system. However, previous computational models of visual development do not satisfactorily address both of these phenomena simultaneously. In this thesis we discuss in detail several models of visual development, focussing particularly on the form of correlations within and between eyes. Firstly, we analyse the ªcorrelationalº model for ocular dominance development recently proposed in [Miller et al 1989]. This model was originally presented for the case of identical correlations within each eye and zero correlations between the eyes. We relax these assumptions by introducing perturbative correlations within and between eyes, and show that (a) the system is unstable to non-identical perturbations in each eye, and (b) the addition of small positive correlations between the eyes, or small negative correlations within an eye, can cause binocular solutions to be favoured over monocular solutions. Secondly, we extend the elastic net model of [Goodhill 1988, Goodhill & Willshaw 1990] for the development of topography and ocular dominance, in particular considering its behaviour in the two-dimensional case. We give both qualitative and quantitative comparisons with the performance of an algorithm based on the self-organizing feature map of Kohonen, and show that in general the elastic net performs better. In additio