Spatio-Chromatic Information available from different Neural Layers via Gaussianization

How much visual information about the retinal images can be extracted from the different layers of the visual pathway?. Separate subsystems (e.g. opponent channels, spatial filters, nonlinearities of the texture sensors) have been suggested to be organized for optimal information transmission. However, the efficiency of these different layers has not been measured when they operate together on colorimetrically calibrated natural images and using multivariate information-theoretic units over the joint spatio-chromatic array of responses. In this work we present a statistical tool to address this question in an appropriate (multivariate) way. Specifically, we propose an empirical estimate of the information transmitted by the system based on a recent Gaussianization technique that reduces the challenging multivariate PDF estimation problem to a set of simpler univariate estimations. Total correlation measured using the proposed estimator is consistent with predictions based on the analytical Jacobian of a standard spatio-chromatic model of the retina-cortex pathway. If the noise at certain representation is proportional to the dynamic range of the response, and one assumes sensors of equivalent noise level, transmitted information shows the following trends: (1) progressively deeper representations are better in terms of the amount of information about the input, (2) the transmitted information up to the cortical representation follows the PDF of natural scenes over the chromatic and achromatic dimensions of the stimulus space, (3) the contribution of spatial transforms to capture visual information is substantially bigger than the contribution of chromatic transforms, and (4) nonlinearities of the responses contribute substantially to the transmitted information but less than the linear transforms.