PRINCIPAL COMPONENT NEURONS IN A REALISTIC VISUAL ENVIRONMENT

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 fir st principal component of the visual environment. In this paper we ana lyse the form of the principal components of natural images. which hav e been preprocessed by centre-surround filters, analogous to those fou nd in the retina. The receptive fields are localized by a small circul ar boundary. We show that the ratio between the size of the receptive field and the size of the preprocessing filter determines the structur e of the receptive field. We also show that the receptive field is dep endent on the non-rotationally-symmetric components of the correlation function. The derivation relies on results about the correlation func tion of natural images in both the radially-symmetric and non-symmetri c cases.