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

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

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

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

A Structured Model of Video Reproduces Primary Visual Cortical Organisation

The visual system must learn to infer the presence of objects and features in the world from the images it encounters, and as such it must, either implicitly or explicitly, model the way these elements interact to create the image. Do the response properties of cells in the mammalian visual system reflect this constraint? To address this question, we constructed a probabilistic model in which the identity and attributes of simple visual elements were represented explicitly and learnt the parameters of this model from unparsed, natural video sequences. After learning, the behaviour and grouping of variables in the probabilistic model corresponded closely to functional and anatomical properties of simple and complex cells in the primary visual cortex (V1). In particular, feature identity variables were activated in a way that resembled the activity of complex cells, while feature attribute variables responded much like simple cells. Furthermore, the grouping of the attributes within the model closely parallelled the reported anatomical grouping of simple cells in cat V1. Thus, this generative model makes explicit an interpretation of complex and simple cells as elements in the segmentation of a visual scene into basic independent features, along with a parametrisation of their moment-by-moment appearances. We speculate that such a segmentation may form the initial stage of a hierarchical system that progressively separates the identity and appearance of more articulated visual elements, culminating in view-invariant object recognition

Oscillations, metastability and phase transitions in brain and models of cognition

Neuroscience is being practiced in many different forms and at many different organizational levels of the Nervous System. Which of these levels and associated conceptual frameworks is most informative for elucidating the association of neural processes with processes of Cognition is an empirical question and subject to pragmatic validation. In this essay, I select the framework of Dynamic System Theory. Several investigators have applied in recent years tools and concepts of this theory to interpretation of observational data, and for designing neuronal models of cognitive functions. I will first trace the essentials of conceptual development and hypotheses separately for discerning observational tests and criteria for functional realism and conceptual plausibility of the alternatives they offer. I will then show that the statistical mechanics of phase transitions in brain activity, and some of its models, provides a new and possibly revealing perspective on brain events in cognition

Spatio-temporal models of the functional architecture of the visual cortex

In this work I tried to explore many aspects of cognitive visual science, each one based on different academic fields, proposing mathematical models capable to reproduce both neuro-physiological and phenomenological results that were described in the recent literature. The structure of my thesis is mainly composed of three chapters, corresponding to the three main areas of research on which I focused my work. The results of each work put the basis for the following, and their ensemble form an homogeneous and large-scale survey on the spatio-temporal properties of the architecture of the visual cortex of mammals

Dynamic coordination in brain and mind

Our goal here is to clarify the concept of 'dynamic coordination', and to note major issues that it raises for the cognitive neurosciences. In general, coordinating interactions are those that produce coherent and relevant overall patterns of activity, while preserving the essential individual identities and functions of the activities coordinated. 'Dynamic coordination' is the coordination that is created on a moment-by-moment basis so as to deal effectively with unpredictable aspects of the current situation. We distinguish different computational goals for dynamic coordination, and outline issues that arise concerning local cortical circuits, brain systems, cognition, and evolution. Our focus here is on dynamic coordination by widely distributed processes of self-organisation, but we also discuss the role of central executive processes