In this paper, meshless methods and partition of unity based finite element methods are reviewed. In meshless methods, the approximation is built without the explicit connectivity information between the nodes; moving-least squares approximants and natural neighbor-based interpolants are discussed. The enrichment of the finite element approximation through the partition of unity framework is de...

Based on noise intensity, in this paper, we propose a feature-preserving smoothing algorithm for point-sampled geometry (PSG). The noise intensity of each sample point on PSG is first measured by using a combined criterion. Based on mean shift clustering, the PSG is then clustered in terms of the local geometry-features similarity. According to the cluster to which a sample point belongs, a mov...

In this paper a stochastic resonance (SR)-based method for recovering weak impulsive signals is developed for quantitative diagnosis of faults in rotating machinery. It was shown in theory that weak impulsive signals follow the mechanism of SR, but the SR produces a nonlinear distortion of the shape of the impulsive signal. To eliminate the distortion a moving least squares fitting method is in...

A local symmetric weak form (LSWF) for linear potential problems is developed, and a truly meshless method, based on the LSWF and the moving least squares approximation, is presented for solving potential problems with high accuracy. The essential boundary conditions in the present formulation are imposed by a penalty method. The present method does not need a ``®nite element mesh'', either for...

(2001) A Meshless Local Petrov-Galerkin (MLPG) method for free and forced vibration analyses for solids. Abstract The Meshless Local Petrov-Galerkin (MLPG) method is an effective truly meshless method for solving partial differential equations using Moving Least Squares (MLS) interpolants and local weak forms. In this paper, a MLPG formulation is proposed for free and forced vibration analyses....

Image registration is a method of determining a mapping or a transformation that relates positions in one image, to the corresponding positions in the other images under considerations. The process of registration depends on the homologous control points that are selected from the source and the target images. This paper focuses on the use of the structural information of an image, for selectin...

In time series analysis, fitting the Moving Average (MA) model is more complicated than Autoregressive (AR) models because the error terms are not observable. This means that iterative nonlinear fitting procedures need to be used in place of linear least squares. In this paper, Time-Varying Moving Average (TVMA) models are proposed for an autocovariance nonstationary time series. Through statis...

Various MLPG methods, with the MLS approximation for the trial function, in the solution of a 4th order ordinary differential equation are illustrated. Both the primal MLPG methods and the mixed MLPG methods are used. All the possible local weak forms for a 4th order ordinary differential equation are presented. In the first kind of mixed MLPG methods, both the displacement and its second deriv...

In this paper, we propose a new automatically generation system of caricature which emphasizes the unique characteristics of the input images. This system can create the cartoon character similar to user’s features by using set rules adopted a particular artist's technique. Input image is transformed by using MLS(Moving Least Squares) approximation[1] based on a predefined cartoon character’s i...

This part of the course notes describes some of the fundamental techniques that are used to define more sophisticated processing algorithms for point-based surfaces. In particular, efficient methods for estimating local surface properties, such as normal vector and curvature, are described. These computations are based on local neighborhoods of point samples, which are defined as subsets of a g...