This paper shows that the continuous shearlet transform, a novel directional multiscale transform recently introduced by the authors and their collaborators, provides a precise geometrical characterization for the boundary curves of very general planar regions. This study is motivated by imaging applications, where such boundary curves represent edges of images. The shearlet approach is able to...

Given the Finsler structure (M, F) on a manifold M, a Riemannian structure (M, h) and a linear connection on M are defined. They are obtained as the " average " of the Finsler structure and the Chern connection. This linear connection is the Levi-Civita connection of the Riemannian metric h. The relation between parallel transport of the Chern connection and the Levi-Civita connection of h are ...

We show, using purely classical considerations and logical extrapolation of results belonging to point particle theories, that the metric background field in which a string propagates must satisfy an Einstein or an Einstein–like equation. Additionally, there emerge restrictions on the worldsheet curvature, which seems to act as a source for spacetime gravity, even in the absence of other matter...

In a prospective study we measured the intraocular pressure (IOP), the central corneal thickness (CCT) and the central corneal curvature in 172 myopic eyes before and after LASIK treatment. We find a significant decrease in intraocular pressure. Statistical evaluation reveals a linear correlation between the IOP decrease and the amount of stromal ablation. The IOP and corneal curvature are meas...

The novel apparatus described here was developed to investigate the thermo-mechanical behavior of metallic films on a substrate by acquiring the wafer curvature. It comprises an optical module producing and measuring an array of parallel laser beams, a high resolution scanning stage, a rapid thermal processing (RTP) chamber and several accessorial gas control modules. Unlike most traditional sy...

Although coherence scanning interferometry (CSI) is capable of measuring surface topography with sub-nanometre precision, it is well known that the performance of measuring instruments depends strongly on the local tilt and curvature of the sample surface. Based on 3D linear systems theory, however, a recent analysis of fringe generation in CSI provides a method to characterize the performance ...

It is well known that no non-trivial Killing vector field exists on a compact Riemannian manifold of negative Ricci curvature; analogously, no non-trivial harmonic one-form exists on a compact manifold of positive Ricci curvature. One can consider the following, more general, problem. By reducing the assumption on the Ricci curvature to one on the scalar curvature, such vanishing theorems canno...

PURPOSE To determine criteria for keratoconus or postoperative LASIK ectasia progression or improvement based on Pentacam HR (Oculus Optikgeräte GmbH) measured steepest corneal curvature. METHODS Sixty-one eyes from 41 patients with keratoconus or postoperative LASIK ectasia were evaluated. Each eye was measured 5 times with the Pentacam HR during the same clinic visit and the random measurem...