Related papers: Geometrical Optical Illusion via Sub-Riemannian Ge…
Geometric-optical illusions (GOI) are a subclass of a vast variety of visual illusions. A special class of GOIs originates from the superposition of a simple geometric figure ("target") with an array of non-intersecting curvilinear elements…
Visual distortions of perceived lengths, angles, or forms, are generally known as "geometric-optical illusions" (GOI). In the present paper we focus on a class of GOIs where the distortion of a straight line segment (the "target" stimulus)…
Geometrical optical illusions have been object of many studies due to the possibility they offer to understand the behaviour of low-level visual processing. They consist in situations in which the perceived geometrical properties of an…
In this paper, we propose a model of arm reaching movements expressed in terms of geodesics in a sub-Riemannian space. We will choose a set of kinematic variables to which motor cortical cells are selective with the purpose of modelling the…
We solve explicitly the geodesic equation for a wide class of (pseudo)-Riemannian homogeneous manifolds (G/H,m), including those with G compact, as well as non-compact semisimple Lie groups, under a simple algebraic condition for the metric…
Why does our visual system fail to reconstruct reality, when we look at certain patterns? Where do Geometrical illusions start to emerge in the visual pathway? How far should we take computational models of vision with the same visual…
Many phenomena are naturally characterized by measuring continuous transformations such as shape changes in medicine or articulated systems in robotics. Modeling the variability in such datasets requires performing statistics on Lie groups,…
The geometry of generative models serves as the basis for interpolation, model inspection, and more. Unfortunately, most generative models lack a principal notion of geometry without restrictive assumptions on either the model or the data…
A geodesic orbit manifold (GO manifold) is a Riemannian manifold (M,g) with the property that any geodesic in M is an orbit of a one-parameter subgroup of a group G of isometries of (M,g). The metric g is then called a G-GO metric in M. For…
The classical construction of the symplectic structure on the space of geodesic trajectories via Hamiltonian reduction fails in the pseudo-Riemannian setting due to a dimensional mismatch created by the null geodesics. This paper proposes a…
Geodesics on Riemannian manifolds are precisely the locally length-minimizing curves, but their explicit description via simple functions is rarely possible. Geodesics of the simplest form, such as lines on Euclidean space and great circles…
In this paper we first recall the definition of geometical model of the visual cortex, focusing in particular on the geometrical properties of horizontal cortical connectivity. Then we recognize that histograms of edges - co-occurrences are…
We consider the problem of visual imitation learning without human supervision (e.g. kinesthetic teaching or teleoperation), nor access to an interactive reinforcement learning (RL) training environment. We present a geometric perspective…
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…
In this work, we propose to study the global geometrical properties of generative models. We introduce a new Riemannian metric to assess the similarity between any two data points. Importantly, our metric is agnostic to the parametrization…
The geodesic equations for optical media whose refractive indices have a non-vanishing gradient are developed. It is shown that when those media are optically isotropic, the light paths will be mull geodesics of a spatial metric that is…
Contemporary deep learning models have achieved impressive performance in image classification by primarily leveraging statistical regularities within large datasets, but they rarely incorporate structured insights drawn directly from…
We investigate the rudiments of Riemannian geometry on orbit spaces $M/G$ for isometric proper actions of Lie groups on Riemannian manifolds. Minimal geodesic arcs are length minimising curves in the metric space $M/G$ and they can hit…
Geodesic orbit spaces (or g.o. spaces) are defined as those homogeneous Riemannian spaces $(M=G/H,g)$ whose geodesics are orbits of one-parameter subgroups of $G$. The corresponding metric $g$ is called a geodesic orbit metric. We study the…
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…