ENG 
ESP Session S13 - Harmonic Analysis, Fractal Geometry, and Applications
Friday, July 16, 12:10 ~ 12:40 UTC-3
Learning group representations in brain's visual cortex
Davide Barbieri
Universidad Autónoma de Madrid, Spain - This email address is being protected from spambots. You need JavaScript enabled to view it.
Human vision has inspired several advances in harmonic analysis, especially wavelet analysis, and it has been the main source of heuristics for the development of neural network architectures devoted to image processing. One of the most studied neural structures in brain's visual cortex is area V1, where neurons perform a wavelet-like analysis that is generally considered to be associated with the group structure of rotations and translations. It is indeed possible to model part of the perceptual behavior of the network of neural cells in V1 as a projection of the image onto one, or more, orbits of that group, and consequently associate to each neuron in V1 a parameter of the group. However, due to the physical constraint of having a neural displacement onto a two dimensional layer, the group is not fully, nor uniformly, represented in V1. The represented subset of the group has however a characteristic geometric structure, that has been modeled over the physiological measurements of what are called orientation preference maps. A natural question posed by this empirical observation is whether the missing part of the group, and of the corresponding wavelet coefficients, has perceptual consequences, and if, on the other hand, it is possible to recover or estimate in some stable way the missing information. The ability to perform such a task would allow one to effectively learn a full group representation from a partial set of well positioned detectors. We will propose such a mechanism, and briefly discuss its possible physical implementation.