Nonlinear Spectral Geometry Processing via the TV Transform

We introduce a novel computational framework for digital geometry processing, based upon the derivation of a nonlinear operator associated to the total variation functional. Such operator admits a generalized notion of spectral decomposition, yielding a sparse multiscale representation akin to Laplacian-based methods, while at the same time avoiding undesirable over-smoothing effects typical of such techniques. Our approach entails accurate, detail-preserving decomposition and manipulation of 3D shape geometry while taking an especially intuitive form: non-local semantic details are well separated into different bands, which can then be filtered and re-synthesized with a straightforward linear step. Our computational framework is flexible, can be applied to a variety of signals, and is easily adapted to different geometry representations, including triangle meshes and point clouds. We showcase our method throughout multiple applications in graphics, ranging from surface and signal denoising to detail transfer and cubic stylization.Comment: 16 pages, 20 figure

Signal Processing on Textured Meshes

In this thesis we extend signal processing techniques originally formulated in the context of image processing to techniques that can be applied to signals on arbitrary triangles meshes. We develop methods for the two most common representations of signals on triangle meshes: signals sampled at the vertices of a finely tessellated mesh, and signals mapped to a coarsely tessellated mesh through texture maps. Our first contribution is the combination of Lagrangian Integration and the Finite Elements Method in the formulation of two signal processing tasks: Shock Filters for texture and geometry sharpening, and Optical Flow for texture registration. Our second contribution is the formulation of Gradient-Domain processing within the texture atlas. We define a function space that handles chart discontinuities, and linear operators that capture the metric distortion introduced by the parameterization. Our third contribution is the construction of a spatiotemporal atlas parameterization for evolving meshes. Our method introduces localized remeshing operations and a compact parameterization that improves geometry and texture video compression. We show temporally coherent signal processing using partial correspondences

Anisotropic Diffusion Partial Differential Equations in Multi-Channel Image Processing : Framework and Applications

We review recent methods based on diffusion PDE's (Partial Differential Equations) for the purpose of multi-channel image regularization. Such methods have the ability to smooth multi-channel images anisotropically and can preserve then image contours while removing noise or other undesired local artifacts. We point out the pros and cons of the existing equations, providing at each time a local geometric interpretation of the corresponding processes. We focus then on an alternate and generic tensor-driven formulation, able to regularize images while specifically taking the curvatures of local image structures into account. This particular diffusion PDE variant is actually well suited for the preservation of thin structures and gives regularization results where important image features can be particularly well preserved compared to its competitors. A direct link between this curvature-preserving equation and a continuous formulation of the Line Integral Convolution technique (Cabral and Leedom, 1993) is demonstrated. It allows the design of a very fast and stable numerical scheme which implements the multi-valued regularization method by successive integrations of the pixel values along curved integral lines. Besides, the proposed implementation, based on a fourth-order Runge Kutta numerical integration, can be applied with a subpixel accuracy and preserves then thin image structures much better than classical finite-differences discretizations, usually chosen to implement PDE-based diffusions. We finally illustrate the efficiency of this diffusion PDE's for multi-channel image regularization - in terms of speed and visual quality - with various applications and results on color images, including image denoising, inpainting and edge-preserving interpolation

Numerical methods for large-scale, time-dependent partial differential equations

A survey of numerical methods for time dependent partial differential equations is presented. The emphasis is on practical applications to large scale problems. A discussion of new developments in high order methods and moving grids is given. The importance of boundary conditions is stressed for both internal and external flows. A description of implicit methods is presented including generalizations to multidimensions. Shocks, aerodynamics, meteorology, plasma physics and combustion applications are also briefly described

1st year EFAST annual report

The present report provides information about the activities conducted during the 1st year of the EFAST project. The first chapter is dedicated to describe the inquiries conducted at the beginning of the project and to briefly summarise the main results. The second chapter is dedicated to the first EFAST workshop where some of the leading scientists in the field of earthquake engineering have met to discuss about the need and the technologies related to earthquake engineering. The third chapter contains a state of the art and future direction in seismic testing and simulation. The final chapter is dedicated to describe the preliminary design of the web portal of the future testing facility.JRC.DG.G.5-European laboratory for structural assessmen

Magnetohydrodynamic Modelling of Supersonic Jets and Colliding Blast Waves for Laboratory Astrophysics Investigation

The thesis is related to laboratory astrophysics, and investigates with this technique, the launching mechanism for young stellar object jets and the interaction of two supernovae remnant in the Sedov-Taylor regime. Recent experiments performed at Imperial College on the pulsed-power magpie facility have successfully shown the formation of magnetically driven radiatively cooled plasmas jets formed from radial wire arrays, which are relevant to studying the launching mechanisms of astrophysical jets [A. Ciardi, et al. Phys. Plasmas 14, p056501 (2007)]. The experiments have been now extended to study episodic mass ejection ( 25 ns [F. A. Suzuki-Vidal, et al. 49th Annual Meeting of the Division of Plasma Physics, UO4.00007 (2007)]) and the interaction of jets and magnetic bubbles with an ambient gas. The dynamics of the interaction is investigated through three-dimensional resistive magneto-hydrodynamic simulations using the code gorgon [A. Ciardi, et al. Phys. Plasmas 14, p056501 (2007) – J.P. Chittenden, et al. Plasma Phys. Control. Fusion 46 B457 (2004)]. In particular ablation of the cathode is investigated numerically to explain the periodicity and subsequent formation of multiple bubbles. Comparison with experiments is offered to validate the results. The complex structure of the magnetic field is investigated, the conservation of the magnetic flux is explained and the consequent confinement offered to the central jet. Furthermore the interaction of the plasma outflows with an ambient gas is investigated. The formation of shocks in the ambient gas, as well as the formation of three-dimensional Mach stems is analyzed. In addition, recent experiment at Imperial College performed by the QOLS group, by laser-heating a medium of atomic clusters [R. A. Smith, et al. 2007 Plasma Phys. Control. Fusion 49 B117-B124 (2007)], shows the capability to create plasmas with sufficiently high energy densities to launch strong shocks. Interactions between high-Mach number shock waves are believed to be responsible for many of the complex, turbulent structures seen in astrophysical objects including supernova remnants. The experiment of two colliding Sedov-Taylor regime blast-waves is modelled. Detailed 3D numerical modeling is performed in order to study the importance of thermal conduction, rarefaction waves, refractive shock waves and complex three-dimensional mach stem formation. The simulated data are benchmark against a three-dimensional tomography image (newly developed experimental technique). The collision of two blast-waves should reproduce the non uniform interstellar medium where supernovas normally expand

Turbulence: Numerical Analysis, Modelling and Simulation

The problem of accurate and reliable simulation of turbulent flows is a central and intractable challenge that crosses disciplinary boundaries. As the needs for accuracy increase and the applications expand beyond flows where extensive data is available for calibration, the importance of a sound mathematical foundation that addresses the needs of practical computing increases. This Special Issue is directed at this crossroads of rigorous numerical analysis, the physics of turbulence and the practical needs of turbulent flow simulations. It seeks papers providing a broad understanding of the status of the problem considered and open problems that comprise further steps