An investigation of spatial receptive fields of complex cells in the primary visual cortex

One of the main concerns of visual neuroscience is to understand how information is processed by the neural circuits in the visual system. Since the historic experiments of Hubel and Wiesel, many more aspects of visual information processing in the brain have been discovered using experimental approaches. However, a lot of computations underlying such processing remain unclear or even unknown. In the retina and the lateral geniculate nucleus, the basic computations have been identified by measuring the responses of neurons to simple visual stimuli such as gratings and oriented bars. However, in higher areas of the visual pathway, e.g. the cortical visual areas, many neurons (including complex cells) cannot be characterised entirely based on their responses to simple stimuli. The complex cells in the visual cortex do not exhibit linear receptive field properties. Hence, the failure of linear receptive field models to describe the behaviour of such neurons leads neuroscientists to seek more plausible quantitative models. Efficient coding is a computational hypothesis about sensory systems. Recently developed models based on the efficient coding hypothesis were able to capture certain properties of complex cells in the primary visual cortex. The Independent feature Subspace Analysis (ISA) model and the covariance model are such examples of these models. The ISA model employs the notion of the energy model in describing the responses of complex cells, whereas the covariance model is based on a recent speculation that complex cells tend to encode the second-order statistical dependencies of the visual input. In this thesis, the parametric technique of the generalised quadratic model (GQM) in conjunction with white Gaussian noise stimulation is used to identify the spatial receptive fields of complex cells in cat primary visual cortex. The validity of the identified receptive field filters are verified by measuring their performance in predicting the responses to test stimuli using correlation coefficients. The findings suggest that a majority of the complex cells in cat primary visual cortex are best described using a linear and one or more quadratic receptive field filters, which are classified as mixed complex cells. We observed that some complex cells exhibit linear as well as quadratic dependencies on an identified filter of their receptive fields. This often introduces a significant shift in the feature-contrast responses of these cells, which results in violations of the polarity invariance property of complex cells. Lastly, a quantitative comparison is performed between the experiment and theory using statistical analysis of the population of the cells’ receptive fields identified by experiment and those predicted by the efficient coding models. For this, motivated by the experimental findings for complex cells, a modification of the ISA model that incorporates a linear term is introduced. The simulated model receptive fields of the modified ISA and the covariance model are then used to draw comparison to the experimental data. While the modified ISA and the covariance models are comparable in predicting the complex cell receptive fields characteristics in the primary visual cortex, the latter shows more capable in explaining the observed intra-receptive field inhomogeneity of complex cells, including differences in orientation preference and ratio spatial frequency for the receptive field filters of the same cell. However, the major discrepancies between theory and experiment lie in the orientation bandwidth and spatial frequency bandwidth of the receptive field filters, where the population of the predicted model receptive field filters demonstrate much narrower bandwidths. These findings, thereby, suggest the sub-optimality of the experimental receptive field filters in terms of the efficiency of the code.