Mathematics > Metric Geometry
[Submitted on 15 Mar 2018 (v1), last revised 11 Oct 2019 (this version, v3)]
Title:From receptive profiles to a metric model of V1
View PDFAbstract: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.
Submission history
From: Noemi Montobbio [view email][v1] Thu, 15 Mar 2018 14:42:50 UTC (9,453 KB)
[v2] Thu, 21 Feb 2019 16:07:11 UTC (4,896 KB)
[v3] Fri, 11 Oct 2019 12:31:07 UTC (4,896 KB)
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