Left-invariant parabolic evolutions on $SE(2)$ and contour enhancement via invertible orientation scores Part I: Linear left-invariant diffusion equations on $SE(2)$

Left-invariant Parabolic Evolutions on Se(2) and Contour Enhancement via Invertible Orientation Scores Part I: Linear Left-invariant Diffusion Equations on Se(2)

We provide the explicit solutions of linear, left-invariant, diffusion equations and the corresponding resolvent equations on the 2D-Euclidean motion group SE(2) = R T. These parabolic equations are forward Kolmogorov equations for well-known stochastic processes for contour enhancement and contour completion. The solutions are given by group convolution with the corresponding Green’s functions...

Left-invariant Parabolic Evolutions on Se(2) and Contour Enhancement via Invertible Orientation Scores Part I: Linear Left-invariant Diffusion Equations

We provide the explicit solutions of linear, left-invariant, diffusion equations and the corresponding resolvent equations on the 2D-Euclidean motion group SE(2) = R T. These parabolic equations are forward Kolmogorov equations for well-known stochastic processes for contour enhancement and contour completion. The solutions are given by group convolution with the corresponding Green’s functions...

Left-invariant Parabolic Evolutions on Se(2) and Contour Enhancement via Invertible Orientation Scores Part Ii: Nonlinear Left-invariant Diffusions on Invertible Orientation Scores

By means of a special type of wavelet unitary transform we construct an orientation score from a grey-value image. This orientation score is a complex-valued function on the 2D Euclidean motion group SE(2) and gives us explicit information on the presence of local orientations in an image. As the transform between image and orientation score is unitary we can relate operators on images to opera...

Left-invariant Stochastic Evolution Equations on SE(2) and its Applications to Contour Enhancement and Contour Completion via Invertible Orientation Scores

We provide the explicit solutions of linear, left-invariant, (convection)-diffusion equations and the corresponding resolvent equations on the 2D-Euclidean motion group SE(2) = RoT. These diffusion equations are forward Kolmogorov equations for well-known stochastic processes for contour enhancement and contour completion. The solutions are given by groupconvolution with the corresponding Green...

Topologically Left Invariant Mean on Dual Semigroup Algebras