  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.
