Left-invariant PDE-evolutions on the roto-translation group SE(2)(and their resolvent equations) have been widely studied in the fields of cortical modeling and image analysis. They include hypo-elliptic diffusion (for contour enhancement) proposed by Citti & Sarti, and Petitot, and they include the direction process (for contour completion) proposed by Mumford. This paper presents a thorough study and comparison of the many numerical approaches, which, remarkably, are missing in the literature. Existing numerical approaches can be classified into 3 categories: Finite difference methods, Fourier based methods (equivalent to SE(2)-Fourier methods), and stochastic methods (Monte Carlo simulations). There are also 3 types of exact solution...
In this article we study both left-invariant (convection-)diffusions and left-invariant Hamilton-Jac...
HARDI (High Angular Resolution Diffusion Imaging) is a recent magnetic resonance imaging (MRI) techn...
Abstract. In this paper we study a model of geometry of vision due to Petitot, Citti and Sarti. One ...
Left-invariant PDE-evolutions on the roto-translation group SE(2)(and their resolvent equations) hav...
Abstract. Left-invariant PDE-evolutions on the roto-translation group SE(2) (and their resolvent equ...
We provide the explicit solutions of linear, left-invariant, diffusion equations and the correspondi...
Abstract. This paper presents a semi-discrete alternative to the theory of neurogeometry of vision, ...
In previous work we studied linear and nonlinear left-invariant diffusion equations on the 2D Euclid...
In previous work we studied linear and nonlinear left-invariant diffusion equations on the 2D Euclid...
We provide the explicit solutions of linear, left-invariant, (convection)-diffusion equations and th...
This paper presents a semi-discrete alternative to the theory of neurogeometry of vision, due to Cit...
In this article we study both left-invariant (convection-)diffusions and left-invariant Hamilton-Jac...
By means of a special type of wavelet unitary transform we construct an orientation score from a gre...
In this article we study both left-invariant (convection-)diffusions and left-invariant Hamilton-Jac...
HARDI (High Angular Resolution Diffusion Imaging) is a recent magnetic resonance imaging (MRI) techn...
Abstract. In this paper we study a model of geometry of vision due to Petitot, Citti and Sarti. One ...
Left-invariant PDE-evolutions on the roto-translation group SE(2)(and their resolvent equations) hav...
Abstract. Left-invariant PDE-evolutions on the roto-translation group SE(2) (and their resolvent equ...
We provide the explicit solutions of linear, left-invariant, diffusion equations and the correspondi...
Abstract. This paper presents a semi-discrete alternative to the theory of neurogeometry of vision, ...
In previous work we studied linear and nonlinear left-invariant diffusion equations on the 2D Euclid...
In previous work we studied linear and nonlinear left-invariant diffusion equations on the 2D Euclid...
We provide the explicit solutions of linear, left-invariant, (convection)-diffusion equations and th...
This paper presents a semi-discrete alternative to the theory of neurogeometry of vision, due to Cit...
In this article we study both left-invariant (convection-)diffusions and left-invariant Hamilton-Jac...
By means of a special type of wavelet unitary transform we construct an orientation score from a gre...
In this article we study both left-invariant (convection-)diffusions and left-invariant Hamilton-Jac...
HARDI (High Angular Resolution Diffusion Imaging) is a recent magnetic resonance imaging (MRI) techn...
Abstract. In this paper we study a model of geometry of vision due to Petitot, Citti and Sarti. One ...