Computational Models Relating Properties of Visual Neurons to Natural Stimulus Statistics

The topic of this thesis is mathematical modeling of computations taking place in the visual system, the largest sensory system in the primate brain. While a great deal is known about how certain visual neurons respond to stimuli, a very profound question is why they respond as they do. Here this question is approached by formulating models of computation which might underlie the observed response properties. The main motivation is to improve our understanding of how the brain functions. A better understanding of the computational underpinnings of the visual system may also yield advances in medical technology or computer vision, such as development of visual prostheses, or design of computer vision algorithms. In this thesis several models of computation are examined. An underlying assumption in this work is that the statistical properties of visual stimuli are related to the structure of the visual system. The relationship has formed through the mechanisms of evolution and development. A model of computation specifies this relationship between the visual system and stimulus statistics. Such a model also contains free parameters which correspond to properties of visual neurons. The experimental evaluation of a model consists of estimation of these parameters from a large amount of natural visual data, and comparison of the resulting parameter values against neurophysiological knowledge of the properties of the neurons, or results obtained with other models. The main contribution of this thesis is the introduction of new models of computation in the primary visual cortex. The results obtained with these models suggest that one defining feature of the computations performed by a class of neurons called simple cells, is that the output of a neuron consists of periods of intense neuronal activity. It also seems that the activity levels of nearby simple cells are positively correlated over short time intervals. In addition, the probability of the occurrence of such regions of intense activity in the joint space of time and cortical area seems to be small. Another contribution of the thesis is the examination of the relationship between two previous computational models, namely independent component analysis and local spatial frequency analysis. This examination suggests that results obtained with independent component analysis share some important properties with wavelets, in the way their localization in space and frequency depends on their average spatial frequency.