6,575 research outputs found
Wavelet treatment of the intra-chain correlation functions of homopolymers in dilute solutions
Discrete wavelets are applied to parametrization of the intra-chain two-point
correlation functions of homopolymers in dilute solutions obtained from Monte
Carlo simulation. Several orthogonal and biorthogonal basis sets have been
investigated for use in the truncated wavelet approximation. Quality of the
approximation has been assessed by calculation of the scaling exponents
obtained from des Cloizeaux ansatz for the correlation functions of
homopolymers with different connectivities in a good solvent. The resulting
exponents are in a better agreement with those from the recent renormalisation
group calculations as compared to the data without the wavelet denoising. We
also discuss how the wavelet treatment improves the quality of data for
correlation functions from simulations of homopolymers at varied solvent
conditions and of heteropolymers.Comment: RevTeX, 19 pages, 7 PS figures. Accepted for publication in PR
Multiscale 3D Shape Analysis using Spherical Wavelets
©2005 Springer. The original publication is available at www.springerlink.com:
http://dx.doi.org/10.1007/11566489_57DOI: 10.1007/11566489_57Shape priors attempt to represent biological variations within a population. When variations are global, Principal Component Analysis (PCA) can be used to learn major modes of variation, even from a limited training set. However, when significant local variations exist, PCA typically cannot represent such variations from a small training set. To address this issue, we present a novel algorithm that learns shape variations from data at multiple scales and locations using spherical wavelets and spectral graph partitioning. Our results show that when the training set is small, our algorithm significantly improves the approximation of shapes in a testing set over PCA, which tends to oversmooth data
Multilinear Wavelets: A Statistical Shape Space for Human Faces
We present a statistical model for D human faces in varying expression,
which decomposes the surface of the face using a wavelet transform, and learns
many localized, decorrelated multilinear models on the resulting coefficients.
Using this model we are able to reconstruct faces from noisy and occluded D
face scans, and facial motion sequences. Accurate reconstruction of face shape
is important for applications such as tele-presence and gaming. The localized
and multi-scale nature of our model allows for recovery of fine-scale detail
while retaining robustness to severe noise and occlusion, and is
computationally efficient and scalable. We validate these properties
experimentally on challenging data in the form of static scans and motion
sequences. We show that in comparison to a global multilinear model, our model
better preserves fine detail and is computationally faster, while in comparison
to a localized PCA model, our model better handles variation in expression, is
faster, and allows us to fix identity parameters for a given subject.Comment: 10 pages, 7 figures; accepted to ECCV 201
Multi-scale analysis of the roughness effect on lubricated rough contact
Determining friction is as equally essential as determining the film thickness in the lubricated contact, and is an important research subject. Indeed, reduction of friction in the automotive industry is important for both the minimization of fuel consumption as well as the decrease in the emissions of greenhouse gases. However, the progress in friction reduction has been limited by the difficulty in understanding the mechanism of roughness effects on friction. It was observed that micro-surface geometry or roughness was one of the major factors that affected the friction coefficient. In the present study, a new methodology coupling the multi-scale decomposition of the surface and the prediction of the friction coefficient by numerical simulation was developed to understand the influence of the scale of roughness in the friction coefficient. In particular, the real surface decomposed in different roughness scale by multi-scale decomposition, based on ridgelets transform was used as input into the model. This model predicts the effect of scale on mixed elastohydroynamic point contact. The results indicate a good influence of the fine scale of surface roughness on the friction coefficient for full-film lubrication as well as a beginning of improvement for mixed lubrication
Besov regularity for operator equations on patchwise smooth manifolds
We study regularity properties of solutions to operator equations on
patchwise smooth manifolds such as, e.g., boundaries of
polyhedral domains . Using suitable biorthogonal
wavelet bases , we introduce a new class of Besov-type spaces
of functions
. Special attention is paid on the
rate of convergence for best -term wavelet approximation to functions in
these scales since this determines the performance of adaptive numerical
schemes. We show embeddings of (weighted) Sobolev spaces on
into , ,
which lead us to regularity assertions for the equations under consideration.
Finally, we apply our results to a boundary integral equation of the second
kind which arises from the double layer ansatz for Dirichlet problems for
Laplace's equation in .Comment: 42 pages, 3 figures, updated after peer review. Preprint: Bericht
Mathematik Nr. 2013-03 des Fachbereichs Mathematik und Informatik,
Universit\"at Marburg. To appear in J. Found. Comput. Mat
A Multiscale Guide to Brownian Motion
We revise the Levy's construction of Brownian motion as a simple though still
rigorous approach to operate with various Gaussian processes. A Brownian path
is explicitly constructed as a linear combination of wavelet-based "geometrical
features" at multiple length scales with random weights. Such a wavelet
representation gives a closed formula mapping of the unit interval onto the
functional space of Brownian paths. This formula elucidates many classical
results about Brownian motion (e.g., non-differentiability of its path),
providing intuitive feeling for non-mathematicians. The illustrative character
of the wavelet representation, along with the simple structure of the
underlying probability space, is different from the usual presentation of most
classical textbooks. Similar concepts are discussed for fractional Brownian
motion, Ornstein-Uhlenbeck process, Gaussian free field, and fractional
Gaussian fields. Wavelet representations and dyadic decompositions form the
basis of many highly efficient numerical methods to simulate Gaussian processes
and fields, including Brownian motion and other diffusive processes in
confining domains
On the non-local geometry of turbulence
A multi-scale methodology for the study of the non-local geometry of eddy structures in turbulence is developed. Starting from a given three-dimensional field, this consists of three main steps: extraction, characterization and classification of structures. The extraction step is done in two stages. First, a multi-scale decomposition based on the curvelet transform is applied to the full three-dimensional field, resulting in a finite set of component three-dimensional fields, one per scale. Second, by iso-contouring each component field at one or more iso-contour levels, a set of closed iso-surfaces is obtained that represents the structures at that scale. The characterization stage is based on the joint probability density function (p.d.f.), in terms of area coverage on each individual iso-surface, of two differential-geometry properties, the shape index and curvedness, plus the stretching parameter, a dimensionless global invariant of the surface. Taken together, this defines the geometrical signature of the iso-surface. The classification step is based on the construction of a finite set of parameters, obtained from algebraic functions of moments of the joint p.d.f. of each structure, that specify its location as a point in a multi-dimensional ‘feature space’. At each scale the set of points in feature space represents all structures at that scale, for the specified iso-contour value. This then allows the application, to the set, of clustering techniques that search for groups of structures with a common geometry. Results are presented of a first application of this technique to a passive scalar field obtained from 5123 direct numerical simulation of scalar mixing by forced, isotropic turbulence (Reλ = 265). These show transition, with decreasing scale, from blob-like structures in the larger scales to blob- and tube-like structures with small or moderate stretching in the inertial range of scales, and then toward tube and, predominantly, sheet-like structures with high level of stretching in the dissipation range of scales. Implications of these results for the dynamical behaviour of passive scalar stirring and mixing by turbulence are discussed
An Optimization Based Empirical Mode Decomposition Scheme for Images
Bidimensional empirical mode decompositions (BEMD) have been developed to decompose any bivariate function or image
additively into multiscale components, so-called intrinsic mode functions (IMFs), which are approximately orthogonal to each other with respect to the inner product. In this paper, a novel optimization problem is designed to achieve this decomposition which takes into account important features desired of the BEMD. Specifically, we propose a data-adapted iterative method which we call Opt-BEMD which minimizes in each iteration a smoothness functional subject to inequality constraints involving the strictly local extrema of the image. In this way, the method constructs a sparse data-adapted basis for the input function as well as an envelope in a mathematically stringent sense. Moreover, we propose an ensemble version of Opt-BEMD to strengthen its performance when applied to noise-contaminated images or images with only few extrema
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