Related papers: Conformal models for hypercolumns in the primary v…

The initial sections of the paper give a concise presentation, specially designed for a mathematically oriented audience, of some of the most basic facts on the functional architecture of early vision. Such information is usually scattered…

The brain processes visual inputs having structure over a large range of spatial scales. The precise mechanisms or algorithms used by the brain to achieve this feat are largely unknown and an open problem in visual neuroscience. In…

We consider the evolution model proposed in [9, 6] to describe illusory contrast perception phenomena induced by surrounding orientations. Firstly, we highlight its analogies and differences with the widely used Wilson-Cowan equations [48],…

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…

This paper investigates the online estimation of neural activity within the primary visual cortex (V1) in the framework of observability theory. We focus on a low-dimensional neural fields modeling hypercolumnar activity to describe…

Classical models describe primary visual cortex (V1) as a filter bank of orientation-selective linear-nonlinear (LN) or energy models, but these models fail to predict neural responses to natural stimuli accurately. Recent work shows that…

Primary visual cortex (V1) is the first stage of cortical image processing, and a major effort in systems neuroscience is devoted to understanding how it encodes information about visual stimuli. Within V1, many neurons respond selectively…

In this paper we propose a neurogeometrical model of the behaviour of cells of the arm area of the primary motor cortex (M1). We will mathematically express as a fiber bundle the hypercolumnar organization of this cortical area, first…

There has been great progress in understanding of anatomical and functional microcircuitry of the primate cortex. However, the fundamental principles of cortical computation - the principles that allow the visual cortex to bind retinal…

Convolutional neural networks (CNNs) have recently emerged as promising models of the ventral visual stream, despite their lack of biological specificity. While current state-of-the-art models of the primary visual cortex (V1) have surfaced…

We present a review of known models and a new simple mathematical modelling for border completion in the visual cortex V1 highlighting the striking analogies with bicycle rear wheel motions in the plane.

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…

For a hypersurface V of a conformal space, we introduce a conformal differential invariant I = h^2/g, where g and h are the first and the second fundamental forms of V connected by the apolarity condition. This invariant is called the…

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…

Neurons in cortical areas often integrate signals from different origins. In the primary visual cortex (V1), neural responses are modulated by non-visual context such as the animal's position. However, the spatial profile of these position…

This paper gives an overview of a theory for modelling the interaction between geometric image transformations and receptive field responses for a visual observer that views objects and spatio-temporal events in the environment. This…

A convolution model which accounts for neural activity dynamics in the primary visual cortex is derived and used to detect visually salient contours in images. Image inputs to the model are modulated by long-range horizontal connections,…

Accurate predictive models of the visual cortex neural response to natural visual stimuli remain a challenge in computational neuroscience. In this work, we introduce V1T, a novel Vision Transformer based architecture that learns a shared…

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…

Microscopic analysis of histological sections is considered the "gold standard" to verify structural parcellations in the human brain. Its high resolution allows the study of laminar and columnar patterns of cell distributions, which build…