Results 1  10
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111
Anthropomorphic Image Reconstruction via Hypoelliptic Diffusion
 SIAM Journal on Control and Optimization, Volume 50, Issue
, 2012
"... Abstract. In this paper we study a model of geometry of vision due to Petitot, Citti and Sarti. One of the main features of this model is that the primary visual cortex V1 lifts an image from R2 to the bundle of directions of the plane. Neurons are grouped into orientation columns, each of them corr ..."
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Cited by 9 (4 self)
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corresponding to a point of this bundle. In this model a corrupted image is reconstructed by minimizing the energy necessary for the activation of the orientation columns corresponding to regions in which the image is corrupted. The minimization process gives rise to an hypoelliptic heat equation on the bundle
Author manuscript, published in "submitted (2012) submitted" Curve cuspless reconstruction via subRiemannian geometry
, 2013
"... We consider the problem of minimizing ∫ ℓ ξ2 + K2 (s) ds for a planar curve having fixed 0 initial and final positions and directions. The total length ℓ is free. Here s is the variable of arclength parametrization, K(s) is the curvature of the curve and ξ> 0 a parameter. This problem comes from ..."
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a model of geometry of vision due to Petitot, Citti and Sarti. We study existence of local and global minimizers for this problem. We prove that if for a certain choice of boundary conditions there is no global minimizer, then there is neither a local minimizer nor a geodesic. We finally give
Parallel Algorithm and Software for Image Inpainting via SubRiemannian Minimizers on the Group of Rototranslations
, 2012
"... Abstract. The paper is devoted to an approach for image inpainting developed on the basis of neurogeometry of vision and subRiemannian geometry. Inpainting is realized by completing damaged isophotes (level lines of brightness) by optimal curves for the leftinvariant subRiemannian problem on the ..."
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Cited by 2 (0 self)
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Abstract. The paper is devoted to an approach for image inpainting developed on the basis of neurogeometry of vision and subRiemannian geometry. Inpainting is realized by completing damaged isophotes (level lines of brightness) by optimal curves for the leftinvariant subRiemannian problem
Tausk, Variational Aspects of the Geodesics Problem in subRiemannian Geometry
 Journal of Geometry and Physics
"... ABSTRACT. We study the local geometry of the space of horizontal curves with endpoints freely varying in two given submanifolds P and Q of a manifold M endowed with a distribution D ⊂ T M. We give a different proof, that holds in a more general context, of a result by Bismut [2, Theorem 1.17] statin ..."
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Cited by 3 (1 self)
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.17] stating that the normal extremizers that are not abnormal are critical points of the subRiemannian action functional. We use the Lagrangian multipliers method in a Hilbert manifold setting, which leads to a characterization of the abnormal extremizers (critical points of the endpoint map) as curves where
unknown title
, 2013
"... A corticalinspired geometry for contour perception and motion integration ..."
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A corticalinspired geometry for contour perception and motion integration
HYPOELLIPTIC DIFFUSION AND HUMAN VISION: A SEMIDISCRETE NEW TWIST ON THE PETITOT THEORY
"... Abstract. This paper is devoted to present an algorithm implementing the theory of neurogeometry of vision, described by Jean Petitot in his book. We propose a new ingredient, namely working on the group of translations and discrete rotations SE(2, N). We focus on the theoretical and numerical aspec ..."
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Cited by 3 (2 self)
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aspects of integration of an hypoelliptic diffusion equation on this group. Our main tool is the generalized Fourier transform. We provide a complete numerical algorithm, fully parallellizable. The main objective is the validation of the neurobiological model.
On the Geometry of Diffusion Operators and Stochastic Flows
, 1998
"... this article. However in Theorem 1.3.9 we show how they are related to the behaviour of parallel translations with respect to associated semiconnections. In chapter 2 we concentrate on a generator A given in Hormander form, and its associated stochastic differential equation (s.d.e.). A first resu ..."
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Cited by 26 (9 self)
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result is Theorem 2.1.1 which shows in particular that (for dimM ? 1) any elliptic diffusion operator can be written as a sum of squares with no first order term, or equivalently that any elliptic diffusion is given by a Stratonovich equation with no drift term. The extension A
The Geometry of Filtering (Preliminary Version)
"... Filtering is the science of finding the law of a process given a partial observation of it. The main objects we study here are diffusion processes. These are naturally associated with second order linear differential operators which are semielliptic and so introduce a possibly degenerate Riemannian ..."
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Filtering is the science of finding the law of a process given a partial observation of it. The main objects we study here are diffusion processes. These are naturally associated with second order linear differential operators which are semielliptic and so introduce a possibly degenerate Riemannian
Vision et Cognition Jeanny HERAULT (GIPSA/UJF)
, 2010
"... Perception Visuelle, faits et modèles Modèles neurogéométriques de Vision Anthropomorphic image reconstruction via hypoelliptic diffusion Modèles cognitifs de l'attention visuelle Sur les mécanismes mis en œuvre par le système nerveux central Analyse en composantes indépendantes visuelles Spars ..."
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Perception Visuelle, faits et modèles Modèles neurogéométriques de Vision Anthropomorphic image reconstruction via hypoelliptic diffusion Modèles cognitifs de l'attention visuelle Sur les mécanismes mis en œuvre par le système nerveux central Analyse en composantes indépendantes visuelles
Results 1  10
of
111