Cortical feature maps via geometric models.

We present a new model for feature map formation in the primary visual cortex, building on dimension reduction/wire length minimization techniques. We create a model space of feature parameters, endowed with various geometries picked to reflect physical or experimental data and search for a map from the parameter space to the cortical sheet which minimizes distortions. Upon simulating these maps, we find a family of Riemannian and sub-Riemannian geometries which give rise to feature maps which reflect known experimental data concerning (1) the qualitative arrangement of orientation maps and (2) the distribution of connections. One of the main findings is that experimental data showing both elongated and non-elongated connection patterns are represented within our family of models.