10 research outputs found
The constitution of visual perceptual units in the functional architecture of V1
Scope of this paper is to consider a mean field neural model which takes into
account the functional neurogeometry of the visual cortex modelled as a group
of rotations and translations. The model generalizes well known results of
Bressloff and Cowan which, in absence of input, accounts for hallucination
patterns. The main result of our study consists in showing that in presence of
a visual input, the eigenmodes of the linearized operator which become stable
represent perceptual units present in the image. The result is strictly related
to dimensionality reduction and clustering problems
Local and global gestalt laws: A neurally based spectral approach
A mathematical model of figure-ground articulation is presented, taking into
account both local and global gestalt laws. The model is compatible with the
functional architecture of the primary visual cortex (V1). Particularly the
local gestalt law of good continuity is described by means of suitable
connectivity kernels, that are derived from Lie group theory and are neurally
implemented in long range connectivity in V1. Different kernels are compatible
with the geometric structure of cortical connectivity and they are derived as
the fundamental solutions of the Fokker Planck, the Sub-Riemannian Laplacian
and the isotropic Laplacian equations. The kernels are used to construct
matrices of connectivity among the features present in a visual stimulus.
Global gestalt constraints are then introduced in terms of spectral analysis of
the connectivity matrix, showing that this processing can be cortically
implemented in V1 by mean field neural equations. This analysis performs
grouping of local features and individuates perceptual units with the highest
saliency. Numerical simulations are performed and results are obtained applying
the technique to a number of stimuli.Comment: submitted to Neural Computatio
Geometry and dimensionality reduction of feature spaces in primary visual cortex
Some geometric properties of the wavelet analysis performed by visual neurons
are discussed and compared with experimental data. In particular, several
relationships between the cortical morphologies and the parametric dependencies
of extracted features are formalized and considered from a harmonic analysis
point of view
Cortical spatio-temporal dimensionality reduction for visual grouping
The visual systems of many mammals, including humans, is able to integrate
the geometric information of visual stimuli and to perform cognitive tasks
already at the first stages of the cortical processing. This is thought to be
the result of a combination of mechanisms, which include feature extraction at
single cell level and geometric processing by means of cells connectivity. We
present a geometric model of such connectivities in the space of detected
features associated to spatio-temporal visual stimuli, and show how they can be
used to obtain low-level object segmentation. The main idea is that of defining
a spectral clustering procedure with anisotropic affinities over datasets
consisting of embeddings of the visual stimuli into higher dimensional spaces.
Neural plausibility of the proposed arguments will be discussed
From receptive profiles to a metric model of V1
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