Abstract. A new morphological multiscale method in 3D image processing is presented which combines the image processing methodology based on nonlinear diffusion equations and the theory of geometric evolution problems. Its aim is to smooth level sets of a 3D image while simultaneously preserving geometric features such as edges and corners on the level sets. This is obtained by an anisotropic c...

Abstract. A new morphological multiscale method in 3D image processing is presented which combines the image processing methodology based on nonlinear diffusion equations and the theory of geometric evolution problems. Its aim is to smooth level sets of a 3D image while simultaneously preserving geometric features such as edges and corners on the level sets. This is obtained by an anisotropic c...

Data sets are often modeled as point clouds in R, for D large. It is often assumed that the data has some interesting low-dimensional structure, for example that of a d-dimensional manifold M, with d much smaller than D. When M is simply a linear subspace, one may exploit this assumption for encoding efficiently the data by projecting onto a dictionary of d vectors in R (for example found by SV...

Patients with bicuspid aortic valve (BAV) are more likely to develop a calcific aortic stenosis (CAS), as well as a number of other ailments, as compared to their cohorts with normal tricuspid aortic valves (TAV). It is currently unknown whether the increase in risk of CAS is caused by the geometric differences between the tricuspid and bicuspid valves or whether the increase in risk is caused ...

We provide a framework for structural multiscale geometric organization of graphs and subsets of Rn. We use diffusion semigroups to generate multiscale geometries in order to organize and represent complex structures. We show that appropriately selected eigenfunctions or scaling functions of Markov matrices, which describe local transitions, lead to macroscopic descriptions at different scales....

A special member of the emerging family of multiscale geometric transforms is the curvelet transform which was developed in the last few years in an attempt to overcome inherent limitations of traditional multistage representations such as wavelets. Mathematical is a set and lattice theoretic methodology for image analysis, which aims at quantitatively describing the geometrical structure of im...

Scaling laws for characteristic length scales (in time or in the model parameters) are both experimentally robust and accessible for rigorous analysis. In multiscale situations cross–overs between different scaling laws are observed. We give a simple example from micromagnetics. In soft ferromagnetic films, the geometric character of a wall separating two magnetic domains depends on the film th...