Statistics, models and learning in BCM theory of a natural visual environment

Recently, there has been a great deal of interest in the statistics of natural images from both biological and computational perspectives. From the biological side, it is widely believed that our visual system is adapted to deal efficiently with natural stimuli. Part of this adaptation is experience-dependent and occurs due to some general mechanism in the brain for modifying the synapses of a neuron as a function of the inputs to the neuron. A better understanding of natural scene statistics may thus provide insight into the role of the environment in the development of the nervous system.; Two basis properties of natural images are: (i) they are extremely non-Gaussian, with highly kurtotic distributions for almost any mean-0 filter response, and (ii) their statistics seem to be largely invariant to a change of scale or coarse-graining. A detailed study of small patches of natural images shows that the state space of such patches is very sparse and highly structured, with most of the high-contrast data concentrated in low-dimensional manifolds and clusters. An important question in vision is whether we can find stochastic models that capture the typical structures of natural images. We argue that many of the observed characteristics of natural images are, at least partly, due to the world being made up of objects in some generalized sense. We develop a simplified visual environment where an image is formed from a set of elementary shapes, whose locations and scale are sampled from a homogeneous Poisson process. These shapes partially occlude one another as they are laid down in layers. The image model, although very simple, seems to capture much of the low-level statistics of naturally occurring scenes. We finally test whether the BCM theory of synaptic plasticity and inputs from this artificial visual environment can account for the observed response properties of cortical cells in the primary visual cortex. The study is an attempt to better understand what patterns in the environment the brain learns to be sensitive to.