Howard Hughes Medical Institute, Center for Neural Science, and Courant Institute of Mathematical Sciences, New York University, USA
Wednesday 9 April 2008
Seminar Room B10 (Basement)
Alexandra House, 17 Queen Square, London, WC1N 3AR
Re-Examining the Local Statistics of Images and Their Implications for Early Visual Processing
A well-known series of results over the past 15 years has shown that the local statistical properties of natural images are best decomposed using local oriented operators. These operators, obtained using Independent Components Analysis (ICA) or maximization of response sparsity, have been held up as successful examples of predicting the form of early visual processing, especially the receptive field properties of neurons in area V1. But there are a number of peculiar aspects of these results. First, the responses of the obtained operators are far from independent, and are at most only slightly more sparse than those of random filters. Second, the description of V1 responses is primarily constructed on a substrate of linear filtering, and ignores the fact that the retina and LGN both contain significant nonlinear elements. I'll re-examine this problem, with a goal of efficiently encoding the image data by transforming to a new representation whose components are statistically independent, coupled with a regularizing principle that favors solutions that minimally distort the data. I'll argue that the local statistics of images are poorly fit by the source model associated with Independent Components Analysis, and should be described using elliptically symmetric densities. For this source model, I'll show that the optimal solution for generating independent responses consists of non-oriented (center-surround) filtering followed by a compressive nonlinearity, more closely analogous to the behaviors of retina than V1. And I'll show empirically that this transformation greatly outperforms ICA or sparse component methodologies in reducing redundancy.