a multi level fast multipole bem for 3 d elastodynamics in the frequency domain to reduce computational complexity and memory requirement for 3 d elastodynamics using the boundary element method bem a multi level fast multipole bem fm bem is proposed the diagonal form for the expansion of the elastodynamic fundamental solution is used with a truncation parameter adjusted to the subdivision level a feature necessary for achieving optimal computational efficiency both the single level and mul ti level forms of the elastodynamic fm bem are considered with emphasis on the latter crucial implementation issues including the truncation of the multipole expansion the optimal number of levels the direct and inverse extrapolation steps are examined in detail with the backing of numerical experiments a complexity analysis for both the single level and multi level versions is conducted the correctness and computational performances of the proposed elastodynamic fmm are demonstrated on numerical examples featuring up to o 10 6 dofs run on a single processor pc and including the diffraction of an incident p plane wave by a semi spherical or semi ellipsoidal canyon representative of topographic site effects

boundary integral equation methods for the elastic and thermoelastic waves in three dimensions in this paper we consider the boundary integral equation bie methods for solving the exterior neumann boundary value problems of elastic and thermoelastic waves in three dimensions based on the fredholm integral equations of the first kind the innovative contribution of this work lies in the proposal of the new regularized formulations for the hyper singular boundary integral operators bio associated with the time harmonic elastic and thermoelastic wave equations with the help of the new regularized formulations we only need to compute the integrals with weak singularities at most in the corresponding variational forms of the boundary integral equations the accuracy of the regularized formulations is demonstrated through numerical examples using the galerkin boundary element method bem

subpixel edge localization and the interpolation of still images in this paper we present a nonlinear interpolation scheme for still image resolution enhancement the algorithm is based on a source model emphasizing the visual integrity of detected edges and incorporates a novel edge fitting operator that has been developed for this application a small neighborhood about each pixel in the low resolution image is first mapped to a best fit continuous space step edge the bilevel approximation serves as a local template on which the higher resolution sampling grid can then be superimposed where disputed values in regions of local window overlap are averaged to smooth errors the result is an image of increased resolution with noticeably sharper edges and in all tried cases lower mean squared reconstruction error than that produced by linear techniques

single image super resolution using local geometric duality and non local similarity super resolution sr from a single image plays an important role in many computer vision applications it aims to estimate a high resolution hr image from an input low resolution lr image to ensure a reliable and robust estimation of the hr image we propose a novel single image sr method that exploits both the local geometric duality gd and the non local similarity of images the main principle is to formulate these two typically existing features of images as effective priors to constrain the super resolved results in consideration of this principle the robust soft decision interpolation method is generalized as an outstanding adaptive gd agd based local prior to adaptively design weights for the agd prior a local non smoothness detection method and a directional standard deviation based weights selection method are proposed after that the agd prior is combined with a variational framework based non local prior furthermore the proposed algorithm is speeded up by a fast gd matrices construction method which primarily relies on the selective pixel processing the extensive experimental results verify the effectiveness of the proposed method compared with several state of the art sr algorithms

annihilating filter based low rank hankel matrix approach for image inpainting in this paper we propose a patch based image inpainting method using a low rank hankel structured matrix completion approach the proposed method exploits the annihilation property between a shift invariant filter and image data observed in many existing inpainting algorithms in particular by exploiting the commutative property of the convolution the annihilation property results in a low rank block hankel structure data matrix and the image inpainting problem becomes a low rank structured matrix completion problem the block hankel structured matrices are obtained patch by patch to adapt to the local changes in the image statistics to solve the structured low rank matrix completion problem we employ an alternating direction method of multipliers with factorization matrix initialization using the low rank matrix fitting algorithm as a side product of the matrix factorization locally adaptive dictionaries can be also easily constructed despite the simplicity of the algorithm the experimental results using irregularly subsampled images as well as various images with globally missing patterns showed that the proposed method outperforms existing state of the art image inpainting methods

fast image upsampling via the displacement field in this paper we present a fast image upsampling method within a two scale framework to ensure the sharp construction of upsampled image for both large scale edges and small scale structures in our approach the low frequency image is recovered via a novel sharpness preserving interpolation technique based on a well constructed displacement field which is estimated by a cross resolution sharpness preserving model within this model the distances of pixels on edges are preserved which enables the recovery of sharp edges in the high resolution result likewise local high frequency structures are reconstructed via a sharpness preserving reconstruction algorithm extensive experiments show that our method outperforms current state of the art approaches based on quantitative and qualitative evaluations as well as perceptual evaluation by a user study moreover our approach is very fast so as to be practical for real applications

q lorentz group and braided coaddition on q minkowski space we present a new version ofq minkowski space which has both a coaddition law and anslq 2 decomposition the additive structure forms a braided group rather than a quantum one in the process we obtain aq lorentz group which coacts covariantly on thisq minkowski space

a fast and high order method for the three dimensional elastic wave scattering problem in this paper we present a fast and high order boundary integral equation method for the elastic scattering by three dimensional large penetrable obstacles the algorithm extends the method introduced in 5 for the acoustic surface scattering to the fully elastic case in our algorithm high order accuracy is achieved through the use of the partition of unity and a semi classical treatment of relevant singular integrals the computational efficiency associated with the nonsingular integrals is attained by the method of equivalent source representations on a cartesian grid and fast fourier transform fft the resulting algorithm computes one matrix vector product associated with the discretization of the integral equation with o n 4 3 log n operations and it shows algebraic convergence several numerical experiments are provided to demonstrate the efficiency of the method

stochastic relaxation gibbs distributions and the bayesian restoration of images we make an analogy between images and statistical mechanics systems pixel gray levels and the presence and orientation of edges are viewed as states of atoms or molecules in a lattice like physical system the assignment of an energy function in the physical system determines its gibbs distribution because of the gibbs distribution markov random field mrf equivalence this assignment also determines an mrf image model the energy function is a more convenient and natural mechanism for embodying picture attributes than are the local characteristics of the mrf for a range of degradation mechanisms including blurring nonlinear deformations and multiplicative or additive noise the posterior distribution is an mrf with a structure akin to the image model by the analogy the posterior distribution defines another imaginary physical system gradual temperature reduction in the physical system isolates low energy states annealing or what is the same thing the most probable states under the gibbs distribution the analogous operation under the posterior distribution yields the maximum a posteriori map estimate of the image given the degraded observations the result is a highly parallel relaxation algorithm for map estimation we establish convergence properties of the algorithm and we experiment with some simple pictures for which good restorations are obtained at low signal to noise ratios

on discontinuity adaptive smoothness priors in computer vision a variety of analytic and probabilistic models in connection with markov random fields mrfs have been proposed in the last decade for solving low level vision problems involving discontinuities this paper presents a systematic study of these models and defines a general discontinuity adaptive da mrf model by analyzing the euler equation associated with the energy minimization it shows that the fundamental difference between different models lies in the behavior of interaction between neighboring points which is determined by the a priori smoothness constraint encoded into the energy function an important necessary condition is derived for the interaction to be adaptive to discontinuities to avoid oversmoothing this forms the basis on which a class of adaptive interaction functions aifs is defined the da model is defined in terms of the euler equation constrained by this class of aifs its solution is c sup 1 continuous and allows arbitrarily large but bounded slopes in dealing with discontinuities because of the continuous nature it is stable to changes in parameters and data a good property for regularizing ill posed problems experimental results are shown

adaptive image resizing based on continuous domain stochastic modeling we introduce an adaptive continuous domain modeling approach to texture and natural images the continuous domain image is assumed to be a smooth function and we embed it in a parameterized sobolev space we point out a link between sobolev spaces and stochastic auto regressive models and exploit it for optimally choosing sobolev parameters from available pixel values to this aim we use exact continuous to discrete mapping of the auto regressive model that is based on symmetric exponential splines the mapping is computationally efficient and we exploit it for maximizing an approximated gaussian likelihood function we account for non gaussian levy type processes by deriving a more robust estimator that is based on the sample auto correlation sequence both estimators use multiple initialization values for overcoming the local minima structure of the fitting criteria experimental image resizing results indicate that the auto correlation criterion can cope better with non gaussian processes and model mismatch our work demonstrates the importance of the auto correlation function in adaptive image interpolation and image modeling tasks and we believe it is instrumental in other image processing tasks as well

nystrom method for elastic wave scattering by three dimensional obstacles nystrom method is developed to solve for boundary integral equations bie s for elastic wave scattering by three dimensional obstacles to generate the matrix equation from a bie nystrom method applies a quadrature rule to the integrations of smooth integrands over a discretized element directly and chooses the values of the unknown function at quadrature points as the system s unknowns to be solved this leads to a simple procedure to form the off diagonal entries of matrix by simply evaluating the integrands without numerical integrations for the diagonal or near diagonal entries corresponding to the integrals over a singular or near singular element where the kernels are singular or near singular we develop a systematic singularity treatment technique known as the local correction scheme based on the linear approximation of elements the scheme differs from the singularity regularization or subtraction technique used in the boundary element method bem it applies the series expansion of scalar green s function to the kernels and derives analytical solutions for the strongly singular integrals under the cauchy principal value like cpv like sense since the approach avoids the need for reformulating the bie for singularity removal in bem and solves for the somigliana s equation directly it is easy to implement and efficient in calculation numerical examples are used to demonstrate its robustness

boundary element methods in three dimensional thermoelasticity abstract a boundary element method is developed for the solution of time dependent problems in three dimensional thermoelasticity the time domain boundary only formulation represents the first of its kind for quasistatic analysis which by definition considers transient heat conduction but ignores the effects of inertia by eliminating the need for volume discretization the method becomes an attractive alternative to finite element analysis for this class of problems additionally because an exact green s function is used in the interior steep thermal gradients can be captured much more readily than with standard domain based methods the presentation includes details of the fundamental solution a derivation of the boundary integral equations and an overview of a general purpose numerical implementation this implementation permits the solution of large multiregion problems with arbitrary geometry and boundary conditions several examples are included to validate the proposed method as well as to highlight its usefulness

nonlinear image upsampling method based on radial basis function interpolation in this paper we present a novel edge directed upsampling method based on radial basis function rbf interpolation in order to remove artifacts such as blurred edges or blocking effects we suggest a nonlinear method capable of taking edge information into account the resampling evaluation is determined according to the edge orientation the proposed scheme is as simple to implement as linear methods but it demonstrates improved visual quality by preserving the edge features better than the classical linear interpolation methods the algorithm is compared with some well known linear schemes as well as recently developed nonlinear schemes the resulting images demonstrate the new algorithm s ability to magnify an image while preserving the edge features

markov random field model based edge directed image interpolation this paper presents an edge directed image interpolation algorithm in the proposed algorithm the edge directions are implicitly estimated with a statistical based approach in opposite to explicit edge directions the local edge directions are indicated by length 16 weighting vectors implicitly the weighting vectors are used to formulate geometric regularity gr constraint smoothness along edges and sharpness across edges and the gr constraint is imposed on the interpolated image through the markov random field mrf model furthermore under the maximum a posteriori mrf framework the desired interpolated image corresponds to the minimal energy state of a 2 d random field given the low resolution image simulated annealing methods are used to search for the minimal energy state from the state space to lower the computational complexity of mrf a single pass implementation is designed which performs nearly as well as the iterative optimization simulation results show that the proposed mrf model based edge directed interpolation method produces edges with strong geometric regularity compared to traditional methods and other edge directed interpolation methods the proposed method improves the subjective quality of the interpolated edges while maintaining a high psnr level

a high order spectral algorithm for elastic obstacle scattering in three dimensions in this paper we describe a high order spectral algorithm for solving the time harmonic navier equations in the exterior of a bounded obstacle in three space dimensions with dirichlet or neumann boundary conditions our approach is based on combined field boundary integral equation cfie reformulations of the navier equations we extend the spectral method developed by ganesh and hawkins 20 for solving second kind boundary integral equations in electromagnetism to linear elasticity for solving cfies that commonly involve integral operators with a strongly singular or hypersingular kernel the numerical scheme applies to boundaries which are globally parametrised by spherical coordinates the algorithm has the interesting feature that it leads to solve linear systems with substantially fewer unknowns than with other existing fast methods the computational performances of the proposed spectral algorithm are demonstrated using numerical examples for a variety of three dimensional convex and non convex smooth obstacles

the boundary integro differential equations of three dimensional neumann problem in linear elasticity in this paper we mainly consider the three dimensional neumann problem in linear elasticity which is reduced to a system of integro differential equations on the boundary based on a new representation of the derivatives of the double layer potential furthermore a new boundary finite element method for this neumann problem is presented

selective data pruning based compression using high order edge directed interpolation this paper proposes a selective data pruning based compression scheme to improve the rate distortion relation of compressed images and video sequences the original frames are pruned to a smaller size before compression after decoding they are interpolated back to their original size by an edge directed interpolation method the data pruning phase is optimized to obtain the minimal distortion in the interpolation phase furthermore a novel high order interpolation is proposed to adapt the interpolation to several edge directions in the current frame this high order filtering uses more surrounding pixels in the frame than the fourth order edge directed method and it is more robust the algorithm is also considered for multiframe based interpolation by using spatio temporally surrounding pixels coming from the previous frame simulation results are shown for both image interpolation and coding applications to validate the effectiveness of the proposed methods

hypersingular boundary integral equations for radiation and scattering of elastic waves in three dimensions abstract a weakly singular form of the hypersingular boundary integral equation bie traction equation for 3 d elastic wave problems is developed in this paper all integrals involved are at most weakly singular and except for a stronger smoothness requirement on boundary elements regular quadrature and collocation procedures used for conventional bies are sufficient for the discretization of the original hypersingular bie this weakly singular form of the hypersingular bie is applied to the composite bie formulation which uses a linear combination of the conventional bie and the hypersingular bie to remove the fictitious eigenfrequencies existing in the conventional bie formulation for elastic wave problems numerical examples employing different types of boundary elements clearly demonstrate the effectiveness and efficiency of the developed formulation

multilevel fast multipole algorithm for elastic wave scattering by large three dimensional objects multilevel fast multipole algorithm mlfma is developed for solving elastic wave scattering by large three dimensional 3d objects since the governing set of boundary integral equations bie for the problem includes both compressional and shear waves with different wave numbers in one medium the double tree structure for each medium is used in the mlfma implementation when both the object and surrounding media are elastic four wave numbers in total and thus four fma trees are involved we employ nystrom method to discretize the bie and generate the corresponding matrix equation the mlfma is used to accelerate the solution process by reducing the complexity of matrix vector product from o n 2 to o nlogn in iterative solvers the multiple tree structure differs from the single tree frame in electromagnetics em and acoustics and greatly complicates the mlfma implementation due to the different definitions for well separated groups in different fma trees our nystrom method has made use of the cancellation of leading terms in the series expansion of integral kernels to handle hyper singularities in near terms this feature is kept in the mlfma by seeking the common near patches in different fma trees and treating the involved near terms synergistically due to the high cost of the multiple tree structure our numerical examples show that we can only solve the elastic wave scattering problems with 0 3 0 4 millions of unknowns on our dell precision 690 workstation using one core