Title: A metric model for the functional architecture of the visual cortex,
Abstract: The purpose of this work is to construct a model for the functional
architecture of the primary visual cortex (V1), based on a structure of metric
measure space induced by the underlying organization of receptive profiles
(RPs) of visual cells. In order to account for the horizontal connectivity of
V1 in such a context, a diffusion process compatible with the geometry of the
space is defined following the classical approach of K.-T. Sturm. The
construction of our distance function does neither require any group
parameterization of the family of RPs, nor involve any differential structure.
As such, it adapts to non-parameterized sets of RPs, possibly obtained through
numerical procedures; it also allows to model the lateral connectivity arising
from non-differential metrics such as the one induced on a pinwheel surface by
a family of filters of vanishing scale. On the other hand, when applied to the
classical framework of Gabor filters, this construction yields a distance
approximating the sub-Riemannian structure proposed as a model for V1 by G.
Citti and A. Sarti [J Math Imaging Vis 24: 307 (2006)], thus showing itself to
be consistent with existing cortex models.