In this work we show how to construct connectivity kernels induced by the
receptive profiles of simple cells of the primary visual cortex (V1). These
kernels are directly defined by the shape of such profiles: this provides a
metric model for the functional architecture of V1, whose global geometry is
determined by the reciprocal interactions between local elements. Our
construction adapts to any bank of filters chosen to represent a set of
receptive profiles, since it does not require any structure on the
parameterization of the family. The connectivity kernel that we define carries
a geometrical structure consistent with the well-known properties of long-range
horizontal connections in V1, and it is compatible with the perceptual rules
synthesized by the concept of association field. These characteristics are
still present when the kernel is constructed from a bank of filters arising
from an unsupervised learning algorithm.Comment: 25 pages, 18 figures. Added acknowledgement