FIAS Scientific Report 2011 - Frankfurt Institute for Advanced Studies ...

Power spectra of the natural input to the visual system explain retinal coding
Collaborators: D. Pamplona 1 , J. Triesch 1 , C. A. Rothkopf 1
1 Frankfurt Institute for Advanced Studies
The statistics of the natural environment have been characterized to gain insight in the processing of natural
stimuli based on the efficient coding hypothesis. The statistical regularities present in these images have been
measured and neurons have been shown to reduce the redundancy present in these stimuli. This analysis reveals
that retinal Ganglion cells’ properties can be related to the second order dependencies present in natural images.
While such analysis has used the convenient assumption that natural image data is isotropic across the visual
field, giving up on this assumption has reveal important dependencies reflected by their neuronal coding. Here
we consider and quantify precisely the second order dependencies in images of natural environments due to the
imaging properties of a model eye.
First, we generated artificial scenes with three-dimensional edge elements and quantified the resulting distributions
of orientations by applying the perspective projection onto a spherical surface. These distributions show a
strong influence of the imaging process on the statistics of the input to the visual system. Secondly, image data
from a naturalistic virtual environment was obtained. The second order statistics were computed as a function
of eccentricity and radial distance from the center of projection. This analysis confirms strong dependencies of
the second order statistics on the position across the visual field. Finally, we repeated the analysis to commonly
used natural image databases including the van Hateren database and quantified the second order dependencies
as function of the position across the visual field using a new generalized parameterization of the power spectra.
We conclude by providing a detailed quantitative analysis of the second order statistical dependencies of the
natural input to the visual system and making novel predictions of the retinal Ganglion cells’ profiles as function
of their position across the visual field.
Left: Naturalistic virtual reality image covering 120 degrees of field of view and a region corresponding to 26 degrees
of eccentricity. Center: Profile power spectra for different directions across the visual field. Right: Distribution of the
projections on the principal components of power spectra depending on the position and scene. On the left column are
the first four principal components, the rows are average coefficients of projection of three scenes categories: coast, street
and tall building.
Related publication in 2011:
1) D. Pamplona, J. Triesch, C. A. Rothkopf, Predicting Ganglion Cells Variability, COSYNE - Computational
and Systems Neuroscience, February 24-27, 2011, Salt Lake City, Utah, USA.
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