Principal component neurons in a realistic visual environment

Abstract

The structure of receptive fields in the visual cortex is believed to be shaped by unsupervised learning. It has been shown that several of the forms of stabilized Hebbian learning rules are governed by the first principal component of the visual environment. In this paper we analyse the form of the principal components of natural images, which have been preprocessed by centre-surround filters, analogous to those found in the retina. The receptive fields are localized by a small circular boundary. We show that the ratio between the size of the receptive field and the size of the preprocessing filter determines the structure of the receptive field. We also show that the receptive field is dependent on the non-rotationally-symmetric components of the correlation function. The derivation relies on results about the correlation function of natural images in both the radially-symmetric and non-symmetric cases.