seminar: Geometric Mathematical Models of the primary visual cortex
speaker: Scott Pauls (Dartmouth College, Department of Mathematics)abstract: Recently, Citti and Sarti have developed a model of the simple cell function of the primary visual cortex based on the sub-Riemannian roto-translation group. We will discuss applications of this model to two problems. The first, the problem of occlusion and disocclusion was initially addressed by Citti and Sarti who showed that, via the model, disocclusions are performed by solving the sub-Riemannian minimal surface problem. We will discuss recent results concerning the existence and properties of minimal surfaces in the roto-translation group with applications to digital image reconstruction. Second, we will address the problem of dimension reduction and wire-length minimization in the visual cortex. Here, we attempt to find mapping from the parameter space of neurons, in this case modeled by the roto-translation group, to the two dimensional surface of the cortex with as little distortion as possible. We will discuss numerical simulations which show that the sub-Riemannian roto-translation model is superior to, for example, a Euclidean model as it provides cortical maps similar to those found experimentally and, more importantly, reflect the axial specificity of horizontal connections revealed by Bosking et al.
timetable:
Thu 7 Sep, 14:00 - 15:00, Aula Dini
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