Multi-scale 3-D Surface Description: Open and Closed Surfaces

A novel technique for multi-scale smoothing of a free-form 3-D surface is presented. Complete triangulated models of 3-D objects are constructed automatically and using a local parametrization technique, are then smoothed using a 2-D Gaussian filter. Our method for local parametrization makes use of semigeodesic coordinates as a natural and efficient way of sampling the local surface shape. The smoothing eliminates the surface noise together with high curvature regions such as sharp edges, therefore, sharp corners become rounded as the object is smoothed iteratively. Our technique for free-form 3-D multi-scale surface smoothing is independent of the underlying triangulation. It is also argued that the proposed technique is preferrable to volumetric smoothing or level set methods since it is applicable to incomplete surface data which occurs during occlusion. Our technique was applied to closed as well as open 3-D surfaces and the results are presented here

Multi-Scale Free-Form Surface Description and Curvature Estimation

A novel technique for multi-scale smoothing of a free-form 3-D surface is presented. Complete triangulated models of 3-D objects are constructed at our center [4] and using a local parametrization technique, are then smoothed using a 2-D Gaussian filter. Our method for local parametrization makes use of semigeodesic coordinates as a natural and efficient way of sampling the local surface shape. The smoothing eliminates the surface noise together with high curvature regions such as sharp edges, therefore, sharp corners become rounded as the object is smoothed iteratively. Our technique for free-form 3-D multi-scale surface smoothing is independent of the underlying triangulation. It is also argued that the proposed technique is preferrable to volumetric smoothing or level set methods since it is applicable to incomplete surface data which occurs during occlusion. The technique was applied to simple and complex 3-D objects and the results are presented here

On universal decoherence under gravity: a perspective through the Equivalence Principle

In Nature Phys. 11, 668 (2015) (Ref. [1]), a composite particle prepared in a pure initial quantum state and propagated in a uniform gravitational field is shown to undergo a decoherence process at a rate determined by the gravitational acceleration. By assuming Einstein's Equivalence Principle to be valid, we demonstrate, first in a Lorentz frame with accelerating detectors, and then directly in the Lab frame with uniform gravity, that the dephasing between the different internal states arise not from gravity but rather from differences in their rest mass, and the mass dependence of the de Broglie wave's dispersion relation. We provide an alternative view to the situation considered by Ref. [1], where we propose that gravity plays a kinematic role in the loss of fringe visibility by giving the detector a transverse velocity relative to the particle beam; visibility can be easily recovered by giving the screen an appropriate uniform velocity. We finally propose that dephasing due to gravity may in fact take place for certain modifications to the gravitational potential where the Equivalence Principle is violated.Comment: 5 pages, 3 figure

Quantum variational measurement in the next generation gravitational-wave detectors

A relatively simple method of overcoming the Standard Quantum Limit in the next-generation Advanced LIGO gravitational wave detector is considered. It is based on the quantum variational measurement with a single short (a few tens of meters) filter cavity. Estimates show that this method allows to reduce the radiation pressure noise at low frequencies ($<100 \mathrm{Hz}$) to the level comparable with or smaller than the low-frequency noises of non-quantum origin (mirrors suspension noise, mirrors internal thermal noise, and gravity gradients fluctuations).Comment: 12 pages, 4 figures; NSNS SNR estimates added; misprints correcte

Increasing future gravitational-wave detectors sensitivity by means of amplitude filter cavities and quantum entanglement

The future laser interferometric gravitational-wave detectors sensitivity can be improved using squeezed light. In particular, recently a scheme which uses the optical field with frequency dependent squeeze factor, prepared by means of a relatively short (~30 m) amplitude filter cavity, was proposed \cite{Corbitt2004-3}. Here we consider an improved version of this scheme, which allows to further reduce the quantum noise by exploiting the quantum entanglement between the optical fields at the filter cavity two ports.Comment: 10 pages, 7 figure