We homogenize the mechanical properties of a two-phase polymer composite, made polyurethane matrix containing porous spherical silicone-based inclusions, and designed to be used for wave control as local resonant insulator. First we consider homogenized energy an expression obtained by explicit method. Then, couple inclusions means second-order tangent Direct finite element simulations allow so...

ii Acknowledgements iii Contents 1 Introduction 1 1.

Understanding the geometry of gears with skew axes is a complex task, hard to grasp and to visualize. However, due to Study’s Principle of Transference, the geometric treatment based on dual vectors can be readily derived from that of the spherical case. This paper is based on Martin Disteli’s work and on the authors’ previous results where Camus’ concept of an auxiliary curve is extended to th...

The stereographic projection determines a bijection between the two-sphere, minus the North Pole, and the tangent plane at the South Pole. This correspondence induces a unitary map between the corresponding L2 spaces. This map in turn leads to equivalence between the continuous wavelet transform formalisms on the plane and on the sphere. More precisely, any plane wavelet may be lifted, by inver...

We discuss Spherical Needlets and their properties. Needlets are a form of spherical wavelets which do not rely on any kind of tangent plane approximation and enjoy good localization properties in both pixel and harmonic space; moreover needlets coefficients are asymptotically uncorrelated at any fixed angular distance, which makes their use in statistical procedures very promising. In view of ...

We recently introduced an algorithm for spherical parametrization and remeshing, which allows resampling of a genus-zero surface onto a regular 2D grid, a spherical geometry image. These geometry images offer several advantages for shape compression. First, simple extension rules extend the square image domain to cover the infinite plane, thereby providing a globally smooth surface parametrizat...

Many functions can map images to the sphere for use as environment maps or spherical panoramas. We develop a new metric that asymptotically measures how well these maps use a given number of samples to provide the greatest worst-case frequency content of the image everywhere over the sphere. Since this metric assumes perfect reconstruction filtering even with highly anisotropic maps, we define ...

Pose uncertainty estimation of calibrated cameras is a common task in the field of computer vision and uses location uncertainties of image features. For spherical cameras, those uncertainties cannot be optimally described using conventional latitude-longitude representation. Increasing distortions close to the poles of the spherical coordinate system prevent a suitable description through Gaus...

A full view spherical camera exploits its extended field of view to map the complete environment onto a 2D image plane. Thus, with a single shot, it delivers a lot more information about the surroundings than one can gather with a normal perspective or plenoptic camera, which are commonly used in light field imaging. However, in contrast to a light field camera, a spherical camera does not capt...

Convolutional Neural Networks (CNNs) have become the method of choice for learning problems involving 2D planar images. However, a number of problems of recent interest have created a demand for models that can analyze spherical images. Examples include omnidirectional vision for drones, robots, and autonomous cars, molecular regression problems, and global weather and climate modelling. A naiv...