R Remco Duits

On the Axioms of Scale Space Theory

We consider alternative scale space representations beyond the well-established Gaussian case that satisfy all “reasonable” axioms. One of these turns out to be subject to a first order pseudo partial differential equation equivalent to the Laplace equation on the upper half plane {(x, s) ∈ ℝd × ℝ | s > 0}. We investigate this so-called Poisson scale space and show that it is indeed a viable alternative to Gaussian scale space. Poisson and Gaussian scale space are related via a one-parameter class of operationally well-defined intermediate representations generated by a fractional power of (minus) the spatial Laplace operator.

Image Analysis and Reconstruction using a Wavelet Transform Constructed from a Reducible Representation of the Euclidean Motion Group

Inspired by the early visual system of many mammalians we consider the construction of-and reconstruction from- an orientation score

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

{\it U_f}:\mathbb{R}^2 \times S^{1} \to \mathbb{C}

The explicit solutions of linear left-invariant second order stochastic evolution equations on the 2D Euclidean motion group

as a local orientation representation of an image,

α scale spaces on a bounded domain

f:\mathbb{R}^2 \to \mathbb{R}

On image reconstruction from multiscale top points

. The mapping