The aim of this paper is to present a new framework for regularization by diffusion. The methods we develop in the sequel can be used to smooth multichannel images, multichannel image sequences (videos), vector fields and orthonormal frame fields in any dimension.1 From a mathematical viewpoint, we deal with vector bundles over Riemannian manifolds and socalled generalized Laplacians. Sections ...

We employ the relationship between contact structures and Beltrami fields derived in part I of this series to construct a steady nonsingular solution to the Euler equations on a Riemannian S whose flowlines trace out closed curves of all possible knot and link types. Using careful contact-topological controls, we can make such vector fields realanalytic and transverse to the tight contact struc...

We draw connections between the field of contact topology (the study of totally nonintegrable plane distributions) and the study of Beltrami fields in hydrodynamics on Riemannian manifolds in dimension three. We demonstrate an equivalence between Reeb fields (vector fields which preserve a transverse nowhere-integrable plane field) up to scaling and rotational Beltrami fields (nonzero fields pa...

Abstract. In this paper we study multiscale analyses for images defined on Riemannian manifolds and extend the axiomatic approach proposed by Álvarez, Guichard, Lions, and Morel to this general case. This covers the case of twoand three-dimensional images and video sequences. After obtaining the general classification, we consider the case of morphological scale spaces, which are given in terms...

Critics of psychological measurement have accused quantitative psychologists ignoring the empirical hypothesis that phenomena are (Michell), or claimed it is impossible in principle to find out whether actually (Trendler). By drawing on Bennett and Hacker (2003), I argue both criticisms do not go far enough because they sidestep fundamental conceptual problem debate: It give concrete formulatio...

The scalar wave equation for a potential in a curved space time, i.e., the Laplace-Beltrami equation has been studied in this work. An action principle is used to derive a finite element algorithm for determining the modes of propagation inside a waveguide of arbitrary shape. Generalizing this idea, the Maxwell theory in a curved space time determines a set of linear partial differential equati...