Related papers: A new perspective on border completion in visual c…

If a piece of the contour of a picture is missing to the eye vision, then the brain tends to complete it using some kind of sub-Riemannian geodesics of the unit tangent bundle of the plane, R2xS1. These geodesics can be obtained by lifting…

We consider a natural extension of the Petitot-Citti-Sarti model of the primary visual cortex. In the extended model, the curvature of contours is taking into account such that occluded contours are completed using sub-Riemannian geodesics…

We propose a differential geometric model of hypercolumns in the primary visual cortex V1 that combines features of the symplectic model of the primary visual cortex by A. Sarti, G. Citti and J. Petitot and of the spherical model of…

We relate the sub-Riemannian geometry on the group of rigid motions of the plane to `bicycling mathematics'. We show that this geometry's geodesics correspond to bike paths whose front tracks are either non-inflectional Euler elasticae or…

We propose a totally functional view of geometric matrix completion problem. Differently from existing work, we propose a novel regularization inspired from the functional map literature that is more interpretable and theoretically sound.…

The pattern formation in orientation and ocular dominance columns is one of the most investigated problems in the brain. From a known cortical structure, we build spin-like Hamiltonian models with long-range interactions of the Mexican hat…

We present a neuro-mathematical model for geometrical optical illusions (GOIs), a class of illusory phenomena that consists in a mismatch of geometrical properties of the visual stimulus and its associated percept. They take place in the…

In recent years, the interdisciplinary research between information science and neuroscience has been a hotspot. In this paper, based on recent biological findings, we proposed a new model to mimic visual information processing, motor…

We consider Wilson-Cowan-type models for the mathematical description of orientation-dependent Poggendorff-like illusions. Our modelling improves two previously proposed cortical-inspired approaches embedding the sub-Riemannian heat kernel…

Computational modeling helps neuroscientists to integrate and explain experimental data obtained through neurophysiological and anatomical studies, thus providing a mechanism by which we can better understand and predict the principles of…

Due to challenging applications such as collaborative filtering, the matrix completion problem has been widely studied in the past few years. Different approaches rely on different structure assumptions on the matrix in hand. Here, we focus…

Self-organization of orientation-wheels observed in the visual cortex is discussed from the view point of topology. We argue in a generalized model of Kohonen's feature mappings that the existence of the orientation-wheels is a consequence…

We study, theoretically and experimentally, a 1-parameter family of transformations and their limiting vector field on the space of plane polygons. These transformations are discrete analogs of completely integrable transformation on closed…

We provide a new and simple system of equations for the normal sub-Riemannian geodesics. These use a partial connection that we show is canonically available, given a choice of complement to the distribution. We also describe conditions…

We develop a neurogeometric model for the arm area of motor cortex, which encodes complex motor primitives, ranging from simple movement features like movement direction, to short hand trajectories, termed fragments, and ultimately to more…

We introduce a model for image morphing in the primary visual cortex V1 to perform completion of missing images in time. We model the output of simple cells through a family of Gabor filters and the propagation of the neural signal…

The monography considers the problem of constructing a Hamiltonian cycle in a complete graph. A rule for constructing a Hamiltonian cycle based on isometric cycles of a graph is established. An algorithm for constructing a Hamiltonian cycle…

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…

We model the functional architecture of the early stages of three-dimensional vision by extending the neurogeometric sub-Riemannian model for stereo-vision introduced in \cite{BCSZ23}. A new framework for correspondence is introduced that…

This thesis is concerned with extending the idea of geodesic completeness from pseudo-Riemannian to complex geometry: we take, however a completely holomorphicpoint of view; that is to say, a 'metric' will be a (meromorphic) symmetric…