Wavelet Basis (wavelet + basis)

Distribution by Scientific Domains


Selected Abstracts


Space-Time Hierarchical Radiosity with Clustering and Higher-Order Wavelets

COMPUTER GRAPHICS FORUM, Issue 2 2004
Cyrille Damez
Abstract We address in this paper the issue of computing diffuse global illumination solutions for animation sequences. The principal difficulties lie in the computational complexity of global illumination, emphasized by the movement of objects and the large number of frames to compute, as well as the potential for creating temporal discontinuities in the illumination, a particularly noticeable artifact. We demonstrate how space-time hierarchical radiosity, i.e. the application to the time dimension of a hierarchical decomposition algorithm, can be effectively used to obtain smooth animations: first by proposing the integration of spatial clustering in a space-time hierarchy; second, by using a higher-order wavelet basis adapted for the temporal dimension. The resulting algorithm is capable of creating time-dependent radiosity solutions efficiently. [source]


Surface wavelets: a multiresolution signal processing tool for 3D computational modelling

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 3 2001
Kevin Amaratunga
Abstract In this paper, we provide an introduction to wavelet representations for complex surfaces (surface wavelets), with the goal of demonstrating their potential for 3D scientific and engineering computing applications. Surface wavelets were originally developed for representing geometric objects in a multiresolution format in computer graphics. These wavelets share all of the major advantages of conventional wavelets, in that they provide an analysis tool for studying data, functions and operators at different scales. However, unlike conventional wavelets, which are restricted to uniform grids, surface wavelets have the power to perform signal processing operations on complex meshes, such as those encountered in finite element modelling. This motivates the study of surface wavelets as an efficient representation for the modelling and simulation of physical processes. We show how surface wavelets can be applied to partial differential equations, stated either in integral form or in differential form. We analyse and implement the wavelet approach for a model 3D potential problem using a surface wavelet basis with linear interpolating properties. We show both theoretically and experimentally that an O(h) convergence rate, hn being the mesh size, can be obtained by retaining only O((logN) 7/2N) entries in the discrete operator matrix, where N is the number of unknowns. The principles described here may also be extended to volumetric discretizations. Copyright © 2001 John Wiley & Sons, Ltd. [source]


On a quadrature algorithm for the piecewise linear wavelet collocation applied to boundary integral equations

MATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 11 2003
Andreas Rathsfeld
Abstract In this paper, we consider a piecewise linear collocation method for the solution of a pseudo-differential equation of order r=0, ,1 over a closed and smooth boundary manifold. The trial space is the space of all continuous and piecewise linear functions defined over a uniform triangular grid and the collocation points are the grid points. For the wavelet basis in the trial space we choose the three-point hierarchical basis together with a slight modification near the boundary points of the global patches of parametrization. We choose linear combinations of Dirac delta functionals as wavelet basis in the space of test functionals. For the corresponding wavelet algorithm, we show that the parametrization can be approximated by low-order piecewise polynomial interpolation and that the integrals in the stiffness matrix can be computed by quadrature, where the quadrature rules are composite rules of simple low-order quadratures. The whole algorithm for the assembling of the matrix requires no more than O(N [logN]3) arithmetic operations, and the error of the collocation approximation, including the compression, the approximative parametrization, and the quadratures, is less than O(N,(2,r)/2). Note that, in contrast to well-known algorithms by Petersdorff, Schwab, and Schneider, only a finite degree of smoothness is required. In contrast to an algorithm of Ehrich and Rathsfeld, no multiplicative splitting of the kernel function is required. Beside the usual mapping properties of the integral operator in low order Sobolev spaces, estimates of Calderón,Zygmund type are the only assumptions on the kernel function. Copyright © 2003 John Wiley & Sons, Ltd. [source]


Use of wavelet transform to the method-of-moments matrix arising from electromagnetic scattering problems of 2D objects due to oblique plane-wave incidence

MICROWAVE AND OPTICAL TECHNOLOGY LETTERS, Issue 2 2002
Jin Yu
Abstract An efficient method is presented for transforming the matrix of the method of moments obtained by the expansion of the unknown surface currents with pulse basis function and the use of point match testing to a matrix with wavelet basis and testing functions. When the electromagnetic scattering object is a dielectric or object under oblique plane-wave incidence, more than one equivalent surface current component exists at the object surface. When these currents are connected into one current vector in the method of moments, there must be some discontinuities between the current components. These discontinuities make the direct wavelet transform to the whole MoM matrix inefficient and not equivalent to the use of the wavelet functions in the expansion of the unknown currents and the testing. Therefore, the wavelet transform must be constructed in a different way to avoid these discontinuities. Here, the proper wavelet transform that is equivalent to the use of the wavelet functions in the MoM, which avoids such discontinuities, is presented. This transform is referred to as wavelet subtransform. © 2002 Wiley Periodicals, Inc. Microwave Opt Technol Lett 34: 130,134, 2002; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.10394 [source]


Do wavelets really detect non-Gaussianity in the 4-year COBE data?

MONTHLY NOTICES OF THE ROYAL ASTRONOMICAL SOCIETY, Issue 4 2000
P. Mukherjee
We investigate the detection of non-Gaussianity in the 4-year COBE data reported by Pando, Valls-Gabaud & Fang, using a technique based on the discrete wavelet transform. Their analysis was performed on the two DMR faces centred on the North and South Galactic poles, respectively, using the Daubechies 4 wavelet basis. We show that these results depend critically on the orientation of the data, and so should be treated with caution. For two distinct orientations of the data, we calculate estimates of the skewness, kurtosis and scale,scale correlation of the corresponding wavelet coefficients in all of the available scale domains of the transform. We obtain several detections of non-Gaussianity in the DMR-DSMB map at greater than the 99 per cent confidence level, but most of these occur on pixel,pixel scales and are therefore not cosmological in origin. Indeed, after removing all multipoles beyond ,=40 from the COBE maps, only one robust detection remains. Moreover, using Monte Carlo simulations, we find that the probability of obtaining such a detection by chance is 0.59. We repeat the analysis for the 53+90 GHz coadded COBE map. In this case, after removing ,>40 multipoles, two non-Gaussian detections at the 99 per cent level remain. Nevertheless, again using Monte Carlo simulations, we find that the probability of obtaining two such detections by chance is 0.28. Thus, we conclude the wavelet technique does not yield strong evidence for non-Gaussianity of cosmological origin in the 4-year COBE data. [source]


An adaptive wavelet viscosity method for hyperbolic conservation laws

NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS, Issue 6 2008
Daniel Castaño Díez
Abstract We extend the multiscale finite element viscosity method for hyperbolic conservation laws developed in terms of hierarchical finite element bases to a (pre-orthogonal spline-)wavelet basis. Depending on an appropriate error criterion, the multiscale framework allows for a controlled adaptive resolution of discontinuities of the solution. The nonlinearity in the weak form is treated by solving a least-squares data fitting problem. © 2008 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 2008 [source]