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Smoothing Approach (smoothing + approach)
Selected AbstractsLocal volume-conserving free surface smoothingINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 2 2007F. S. Sousa Abstract Removing high-frequency undulations in surfaces is a problem that appears in different fields, such as computer graphics and computational fluid mechanics. This problem is typically handled by surface smoothing techniques, such as Laplacian filters, that eliminate high-frequency undulations but degrade the volume encompassed by the surface. The need for conserving volume (or mass) rules out the use of such techniques in several application, as for example incompressible flows. In this work we present a smoothing technique that suppresses undulations while conserving local volumes, ensuring that the global mass is conserved. The effectiveness of the proposed technique is illustrated in synthetic datasets as well as in free surface flows simulation. Comparisons between our smoothing approach and the well-known Laplacian filter are also presented. Copyright © 2006 John Wiley & Sons, Ltd. [source] Parameter estimation for differential equations: a generalized smoothing approachJOURNAL OF THE ROYAL STATISTICAL SOCIETY: SERIES B (STATISTICAL METHODOLOGY), Issue 5 2007J. O. Ramsay Summary., We propose a new method for estimating parameters in models that are defined by a system of non-linear differential equations. Such equations represent changes in system outputs by linking the behaviour of derivatives of a process to the behaviour of the process itself. Current methods for estimating parameters in differential equations from noisy data are computationally intensive and often poorly suited to the realization of statistical objectives such as inference and interval estimation. The paper describes a new method that uses noisy measurements on a subset of variables to estimate the parameters defining a system of non-linear differential equations. The approach is based on a modification of data smoothing methods along with a generalization of profiled estimation. We derive estimates and confidence intervals, and show that these have low bias and good coverage properties respectively for data that are simulated from models in chemical engineering and neurobiology. The performance of the method is demonstrated by using real world data from chemistry and from the progress of the autoimmune disease lupus. [source] Penalized spline models for functional principal component analysisJOURNAL OF THE ROYAL STATISTICAL SOCIETY: SERIES B (STATISTICAL METHODOLOGY), Issue 1 2006Fang Yao Summary., We propose an iterative estimation procedure for performing functional principal component analysis. The procedure aims at functional or longitudinal data where the repeated measurements from the same subject are correlated. An increasingly popular smoothing approach, penalized spline regression, is used to represent the mean function. This allows straightforward incorporation of covariates and simple implementation of approximate inference procedures for coefficients. For the handling of the within-subject correlation, we develop an iterative procedure which reduces the dependence between the repeated measurements that are made for the same subject. The resulting data after iteration are theoretically shown to be asymptotically equivalent (in probability) to a set of independent data. This suggests that the general theory of penalized spline regression that has been developed for independent data can also be applied to functional data. The effectiveness of the proposed procedure is demonstrated via a simulation study and an application to yeast cell cycle gene expression data. [source] Smoothing that does not blur: Effects of the anisotropic approach for evaluating diffusion tensor imaging data in the clinicJOURNAL OF MAGNETIC RESONANCE IMAGING, Issue 3 2010Marta Moraschi MS Abstract Purpose: To compare the effects of anisotropic and Gaussian smoothing on the outcomes of diffusion tensor imaging (DTI) voxel-based (VB) analyses in the clinic, in terms of signal-to-noise ratio (SNR) enhancement and directional information and boundary structures preservation. Materials and Methods: DTI data of 30 Alzheimer's disease (AD) patients and 30 matched control subjects were obtained at 3T. Fractional anisotropy (FA) maps with variable degrees and quality (Gaussian and anisotropic) of smoothing were created and compared with an unsmoothed dataset. The two smoothing approaches were evaluated in terms of SNR improvements, capability to separate differential effects between patients and controls by a standard VB analysis, and level of artifacts introduced by the preprocessing. Results: Gaussian smoothing regionally biased the FA values and introduced a high variability of results in clinical analysis, greatly dependent on the kernel size. On the contrary, anisotropic smoothing proved itself capable of enhancing the SNR of images and maintaining boundary structures, with only moderate dependence of results on smoothing parameters. Conclusion: Our study suggests that anisotropic smoothing is more suitable in DTI studies; however, regardless of technique, a moderate level of smoothing seems to be preferable considering the artifacts introduced by this manipulation. J. Magn. Reson. Imaging 2010;31:690,697. © 2010 Wiley-Liss, Inc. [source] A systematic comparison of coupled and distributive smoothing in multigrid for the poroelasticity systemNUMERICAL LINEAR ALGEBRA WITH APPLICATIONS, Issue 2-3 2004F. J. Gaspar Abstract In this paper, we present efficient multigrid methods for the system of poroelasticity equations discretized on a staggered grid. In particular, we compare two different smoothing approaches with respect to efficiency and robustness. One approach is based on the coupled relaxation philosophy. We introduce ,cell-wise' and ,line-wise' versions of the coupled smoothers. They are compared with a distributive relaxation, that gives us a decoupled system of equations. It can be smoothed equation-wise with basic iterative methods. All smoothing methods are evaluated for the same poroelasticity test problems in which parameters, like the time step, or the Lamé coefficients are varied. Some highly efficient methods result, as is confirmed by the numerical experiments. Copyright © 2004 John Wiley & Sons, Ltd. [source] | ||||||||||