18 Apr 2017; IMS (UiTø), room U3=A016. 14:15-16:00.

Valentin Lychagin

“Invariants and the problem of image recognition for primary visual VI cortex”

After discovery by D. Hubel and T. Wiesel in 1956 (Nobel Prize at 1981) that VI cortex of mammals could be viewed as 2-dimensional manifold M equipped with 1-dimensional distribution D. Hubel, W. Hoffman and J. Petitot proposed to consider primary visual cortex VI as the contact 3-dimensional manifold PT*M. Different models for activity of visual neurons lead, in addition to contact structure, to different geometries on M. We'll discuss the metric (plane: E(2), sphere: SO(3)) and conformal (sphere: SL(2,C)) geometries. Then different (black-white) pictures correspond to different, up to transformations from the structure group, distributions on M. Differential invariants of the actions of the structure groups on sections of the bundle PT*M--->M give us the necessary information for recognition of distributions. We'll describe structures of the fields of differential invariants and show how to use them to recognise distributions.