moving least squares particle hydrodynamics i consistency and stability the smooth particle hydrodynamics sph method is derived in a novel manner by means of a galerkin approximation applied to the lagrangian equations of continuum mechanics as in the finite element method this derivation is modified to replace the sph interpolant with the moving least squares mls interpolant of lancaster and saulkaskas and define a new particle volume which ensures thermodynamic compatibility a variable rank modification of the mls interpolants which retains their desirable summation properties is introduced to remove the singularities that occur when divergent flow reduces the number of neighbours of a particle to less than the minimum required a surprise benefit of the galerkin sph derivation is a theoretical justification of a common ad hoc technique for variable h sph the new mlsph method is conservative if an anti symmetric quadrature rule for the stiffness matrix elements can be supplied in this paper a simple one point collocation rule is used to retain similarity with sph leading to a non conservative method several examples document how mlsph renders dramatic improvements due to the linear consistency of its gradients on three canonical difficulties of the sph method spurious boundary effects erroneous rates of strain and rotation and tension instability two of these examples are non linear lagrangian patch tests with analytic solutions with which mlsph agrees almost exactly the examples also show that mlsph is not absolutely stable if the problems are run to very long times a linear stability analysis explains both why it is more stable than sph and not yet absolutely stable and an argument is made that for realistic dynamic problems mlsph is stable enough the notion of coherent particles for which the numerical stability is identical to the physical stability is introduced the new method is easily retrofitted into a generic sph code and some observations on performance are made copyright 1999 john wiley sons ltd

variational and momentum preservation aspects of smooth particle hydrodynamic formulations this paper presents a new variational framework for various existing smooth particle hydrodynamic sph techniques and presents a new corrected sph formulation the linear and angular momentum preserving properties of sph formulations are also discussed the paper will show that in general in order to preserve angular momentum the sph equations must correctly evaluate the gradient of a linear velocity field a corrected algorithm that combines kernel correction with gradient correction is presented the paper will illustrate the theory presented with several examples relating to simple free surface flows

sph simulations of time dependent poiseuille flow at low reynolds numbers a working smoothed particle hydrodynamics sph formalism for solving the equations of motion of a viscous fluid is presented the method is based on a standard symmetrized sph expression for the viscous forces which involves only first order derivatives of the kernel through a direct evaluation of the viscous stress tensor therefore the interpolation can be performed using low order kernels of compact support without compromising the accuracy and stability of the results in principle the scheme is suitable for treating compressible fluids with arbitrary shear and bulk viscosities here we demonstrate that when it is combined with the pressure gradient correction proposed by morris et al the method is also suitable for solving the navier stokes equations for incompressible flows without any further assumptions simulations using the method show close agreement with the analytic series solutions for plane poiseuille and hagen poiseuille flows at very low reynolds numbers at least for these specific tests the results obtained are essentially independent of employing either a cubic or a quintic spline kernel

efficient graph based image segmentation this paper addresses the problem of segmenting an image into regions we define a predicate for measuring the evidence for a boundary between two regions using a graph based representation of the image we then develop an efficient segmentation algorithm based on this predicate and show that although this algorithm makes greedy decisions it produces segmentations that satisfy global properties we apply the algorithm to image segmentation using two different kinds of local neighborhoods in constructing the graph and illustrate the results with both real and synthetic images the algorithm runs in time nearly linear in the number of graph edges and is also fast in practice an important characteristic of the method is its ability to preserve detail in low variability image regions while ignoring detail in high variability regions

fixed order robust h sub spl infin filter design for markovian jump systems with uncertain switching probabilities this paper discusses the fixed order robust h sub spl infin filtering problem for a class of markovian jump linear systems with uncertain switching probabilities the uncertainties under consideration are assumed to be norm bounded in the system matrices and to be elementwise bounded in the mode transition rate matrix respectively first a criterion based on linear matrix inequalities is provided for testing the h sub spl infin filtering level of a filter over all the admissible uncertainties then a sufficient condition for the existence of the fixed order robust h sub spl infin filters is established in terms of the solvability of a set of linear matrix inequalities with equality constraints to determine the filter a globally convergent algorithm involving convex optimization is suggested finally a numerical example is used to illustrate that the developed theory is more effective than the existing results

development of a finite volume particle method for 3 d fluid flow simulations the finite volume particle method fvpm is a meshless method for simulating fluid flows which includes many of the desirable features of mesh based finite volume methods fvpm benefits from particle interaction vectors to weight conservative fluxes exchanged between particles these vectors are equivalent to the intercell area vectors in mesh based finite volume methods to compute the interaction vectors either numerical or exact integration has been used numerical integration based on quadrature rules is approximate and costly whereas the exact method employing a top hat kernel is precise and fast to date quadrature integration has not been used in 3 d due to its excessive cost and the exact method has been developed only for 2 d computations in this study we develop a new 3 d fvpm formulation which features a rectangular top hat kernel to compute interaction vectors exactly and efficiently we also introduce a new boundary condition enforcement technique based on a single layer of boundary particles in this technique no slip wall boundary conditions with complex geometries are precisely enforced by overlaying a layer of particles on wall surfaces employing ausm for inviscid fluxes weakly compressible fluid flow is studied with the proposed method to achieve more accurate results the solution can be refined near the wall boundary by splitting the fluid particles this formulation is validated for lid driven cavity flow a moving square and jet impingement test cases

an extended validation of the last generation of particle finite element method for free surface flows in this paper a new generation of the particle method known as particle finite element method pfem which combines convective particle movement and a fixed mesh resolution is applied to free surface flows this interesting variant previously described in the literature as pfem 2 is able to use larger time steps when compared to other similar numerical tools which implies shorter computational times while maintaining the accuracy of the computation pfem 2 has already been extended to free surface problems being the main topic of this paper a deep validation of this methodology for a wider range of flows to accomplish this task different improved versions of discontinuous and continuous enriched basis functions for the pressure field have been developed to capture the free surface dynamics without artificial diffusion or undesired numerical effects when different density ratios are involved a collection of problems has been carefully selected such that a wide variety of froude numbers density ratios and dominant dissipative cases are reported with the intention of presenting a general methodology not restricted to a particular range of parameters and capable of using large time steps the results of the different free surface problems solved which include rayleigh taylor instability sloshing problems viscous standing waves and the dam break problem are compared to well validated numerical alternatives or experimental measurements obtaining accurate approximations for such complex flows

high re solutions for incompressible flow using the navier stokes equations and a multigrid method the vorticity stream function formulation of the two dimensional incompressible navierstokes equations is used to study the effectiveness of the coupled strongly implicit multigrid csi mg method in the determination of high re fine mesh flow solutions the driven flow in a square cavity is used as the model problem solutions are obtained for configurations with reynolds number as high as 10 000 and meshes consisting of as many as 257 x 257 points for re 1000 the 129 x 129 grid solution required 1 5 minutes of cpu time on the amdahl 470 v 6 computer because of the appearance of one or more secondary vortices in the flow field uniform mesh refinement was preferred to the use of one dimensional gridclustering coordinate transformations the past decade has witnessed a great deal of progress in the area of computational fluid dynamics developments in computer technology hardware as well as in advanced numerical algorithms have enabled attempts to be made towards analysis and numerical solution of highly complex flow problems for some of these applications the use of simple iterative techniques to solve the navier stokes equations leads to a rather slow convergence rate for the solutions the solution convergence rate can be seriously affected if the coupling among the various governing differential equations is not properly honored either in the interior of the solution domain or at its boundaries the rate of convergence is also generally strongly dependent on such problem parameters as the reynolds number the mesh size and the total number of computational points this has led several researchers to examine carefully the recently emerging multigrid mg technique as a useful means for enhancing the convergence rate of iterative numerical methods for solving discretized equations at a number of computational grid points so large as to be considered impractical previously

slic superpixels compared to state of the art superpixel methods computer vision applications have come to rely increasingly on superpixels in recent years but it is not always clear what constitutes a good superpixel algorithm in an effort to understand the benefits and drawbacks of existing methods we empirically compare five state of the art superpixel algorithms for their ability to adhere to image boundaries speed memory efficiency and their impact on segmentation performance we then introduce a new superpixel algorithm simple linear iterative clustering slic which adapts a k means clustering approach to efficiently generate superpixels despite its simplicity slic adheres to boundaries as well as or better than previous methods at the same time it is faster and more memory efficient improves segmentation performance and is straightforward to extend to supervoxel generation

simulating free surface flows with sph the sph smoothed particle hydrodynamics method is extended to deal with free surface incompressible flows the method is easy to use and examples will be given of its application to a breaking dam a bore the simulation of a wave maker and the propagation of waves towards a beach arbitrary moving boundaries can be included by modelling the boundaries by particles which repel the fluid particles the method is explicit and the time steps are therefore much shorter than required by other less flexible methods but it is robust and easy to program

image signature highlighting sparse salient regions we introduce a simple image descriptor referred to as the image signature we show within the theoretical framework of sparse signal mixing that this quantity spatially approximates the foreground of an image we experimentally investigate whether this approximate foreground overlaps with visually conspicuous image locations by developing a saliency algorithm based on the image signature this saliency algorithm predicts human fixation points best among competitors on the bruce and tsotsos 1 benchmark data set and does so in much shorter running time in a related experiment we demonstrate with a change blindness data set that the distance between images induced by the image signature is closer to human perceptual distance than can be achieved using other saliency algorithms pixel wise or gist 2 descriptor methods

robust recovery of subspace structures by low rank representation in this paper we address the subspace clustering problem given a set of data samples vectors approximately drawn from a union of multiple subspaces our goal is to cluster the samples into their respective subspaces and remove possible outliers as well to this end we propose a novel objective function named low rank representation lrr which seeks the lowest rank representation among all the candidates that can represent the data samples as linear combinations of the bases in a given dictionary it is shown that the convex program associated with lrr solves the subspace clustering problem in the following sense when the data is clean we prove that lrr exactly recovers the true subspace structures when the data are contaminated by outliers we prove that under certain conditions lrr can exactly recover the row space of the original data and detect the outlier as well for data corrupted by arbitrary sparse errors lrr can also approximately recover the row space with theoretical guarantees since the subspace membership is provably determined by the row space these further imply that lrr can perform robust subspace clustering and error correction in an efficient and effective way

extension of the finite volume particle method to viscous flow the finite volume particle method fvpm is a mesh free method for fluid dynamics which allows simple and accurate implementation of boundary conditions and retains the conservation and consistency properties of classical finite volume methods in this article the fvpm is extended to viscous flows using a consistency corrected smoothed particle hydrodynamics sph approximation to evaluate velocity gradients the accuracy of the viscous fvpm is improved by a higher order discretisation of the inviscid flux combined with a second order temporal discretisation the higher order inviscid fvpm is validated for a 1 d shock tube problem in which it demonstrates an enhanced shock capturing ability for two dimensional simulations a small arbitrary lagrange euler correction to fully lagrangian particle motion is beneficial in maintaining a favourable particle distribution over long simulation times the viscous fvpm is validated for two dimensional poiseuille taylor green and lid driven cavity flows and good agreement is achieved with analytic or reference numerical solutions these results establish the viability of fvpm as a tool for mesh free simulation of viscous flows in engineering

graph regularized nonnegative matrix factorization for data representation matrix factorization techniques have been frequently applied in information retrieval computer vision and pattern recognition among them nonnegative matrix factorization nmf has received considerable attention due to its psychological and physiological interpretation of naturally occurring data whose representation may be parts based in the human brain on the other hand from the geometric perspective the data is usually sampled from a low dimensional manifold embedded in a high dimensional ambient space one then hopes to find a compact representation which uncovers the hidden semantics and simultaneously respects the intrinsic geometric structure in this paper we propose a novel algorithm called graph regularized nonnegative matrix factorization gnmf for this purpose in gnmf an affinity graph is constructed to encode the geometrical information and we seek a matrix factorization which respects the graph structure our empirical study shows encouraging results of the proposed algorithm in comparison to the state of the art algorithms on real world problems

an analysis of 1 d smoothed particle hydrodynamics kernels in this paper the smoothed particle hydrodynamics sph kernel is analyzed resulting in measures of merit for one dimensional sph various methods of obtaining an objective measure of the quality and accuracy of the sph kernel are addressed since the kernel is the key element in the sph methodology this should be of primary concern to any user of sph the results of this work are two measures of merit one for smooth data and one near shocks the measure of merit for smooth data is shown to be quite accurate and a useful delineator of better and poorer kernels the measure of merit for non smooth data is not quite as accurate but results indicate the kernel is much less important for these types of problems in addition to the theory 20 kernels are analyzed using the measure of merit demonstrating the general usefulness of the measure of merit and the individual kernels in general it was decided that bell shaped kernels perform better than other shapes

visual saliency based on scale space analysis in the frequency domain we address the issue of visual saliency from three perspectives first we consider saliency detection as a frequency domain analysis problem second we achieve this by employing the concept of nonsaliency third we simultaneously consider the detection of salient regions of different size the paper proposes a new bottom up paradigm for detecting visual saliency characterized by a scale space analysis of the amplitude spectrum of natural images we show that the convolution of the image amplitude spectrum with a low pass gaussian kernel of an appropriate scale is equivalent to an image saliency detector the saliency map is obtained by reconstructing the 2d signal using the original phase and the amplitude spectrum filtered at a scale selected by minimizing saliency map entropy a hypercomplex fourier transform performs the analysis in the frequency domain using available databases we demonstrate experimentally that the proposed model can predict human fixation data we also introduce a new image database and use it to show that the saliency detector can highlight both small and large salient regions as well as inhibit repeated distractors in cluttered images in addition we show that it is able to predict salient regions on which people focus their attention

incompressible moving boundary flows with the finite volume particle method abstract mesh free methods offer the potential for greatly simplified modeling of flow with moving walls and phase interfaces the finite volume particle method fvpm is a mesh free technique based on interparticle fluxes which are exactly analogous to intercell fluxes in the mesh based finite volume method consequently the method inherits many of the desirable properties of the classical finite volume method including implicit conservation and a natural introduction of boundary conditions via appropriate flux terms in this paper we describe the extension of fvpm to incompressible viscous flow with moving boundaries an arbitrary lagrangian eulerian approach is used in conjunction with the mesh free discretisation to facilitate a straightforward treatment of moving bodies non uniform particle distribution is used to concentrate computational effort in regions of high gradients the underlying method for viscous incompressible flow is validated for a lid driven cavity problem at reynolds numbers of 100 and 1000 to validate the simulation of moving boundaries flow around a translating cylinder at reynolds numbers of 20 40 and 100 is modeled results for pressure distribution surface forces and vortex shedding frequency are in good agreement with reference data from the literature and with fvpm results for an equivalent flow around a stationary cylinder these results establish the capability of fvpm to simulate large wall motions accurately in an entirely mesh free framework

exact finite volume particle method with spherical support kernels abstract the finite volume particle method fvpm is a meshless method for simulating fluid flows which includes many of the desirable features of mesh based finite volume methods in this paper we develop a new 3 d fvpm formulation that features spherical kernel supports the formulation is based on exact integration of interaction vectors constructed from top hat kernels the exact integration is obtained by an innovative surface partitioning algorithm as well as precise area computation of the sphere subsurfaces spherical support fvpm improves the recently developed cubic support version in two main aspects spherical kernels have no directionality and result in smooth interactions between particles leading to an improved method we present three test cases that illustrate the improved accuracy and robustness brought by the spherical kernel although computations are 1 5 times slower on spherical support than cubic support the cost is more than compensated by lower error with a higher convergence rate

salient object detection via structured matrix decomposition low rank recovery models have shown potential for salient object detection where a matrix is decomposed into a low rank matrix representing image background and a sparse matrix identifying salient objects two deficiencies however still exist first previous work typically assumes the elements in the sparse matrix are mutually independent ignoring the spatial and pattern relations of image regions second when the low rank and sparse matrices are relatively coherent e g when there are similarities between the salient objects and background or when the background is complicated it is difficult for previous models to disentangle them to address these problems we propose a novel structured matrix decomposition model with two structural regularizations 1 a tree structured sparsity inducing regularization that captures the image structure and enforces patches from the same object to have similar saliency values and 2 a laplacian regularization that enlarges the gaps between salient objects and the background in feature space furthermore high level priors are integrated to guide the matrix decomposition and boost the detection we evaluate our model for salient object detection on five challenging datasets including single object multiple objects and complex scene images and show competitive results as compared with 24 state of the art methods in terms of seven performance metrics

saliency detection by multitask sparsity pursuit this paper addresses the problem of detecting salient areas within natural images we shall mainly study the problem under unsupervised setting i e saliency detection without learning from labeled images a solution of multitask sparsity pursuit is proposed to integrate multiple types of features for detecting saliency collaboratively given an image described by multiple features its saliency map is inferred by seeking the consistently sparse elements from the joint decompositions of multiple feature matrices into pairs of low rank and sparse matrices the inference process is formulated as a constrained nuclear norm and as an l2 1 norm minimization problem which is convex and can be solved efficiently with an augmented lagrange multiplier method compared with previous methods which usually make use of multiple features by combining the saliency maps obtained from individual features the proposed method seamlessly integrates multiple features to produce jointly the saliency map with a single inference step and thus produces more accurate and reliable results in addition to the unsupervised setting the proposed method can be also generalized to incorporate the top down priors obtained from supervised environment extensive experiments well validate its superiority over other state of the art methods

a hybridized discontinuous galerkin framework for high order particle mesh operator splitting of the incompressible navier stokes equations abstract a generic particle mesh method using a hybridized discontinuous galerkin hdg framework is presented and validated for the solution of the incompressible navier stokes equations building upon particle in cell concepts the method is formulated in terms of an operator splitting technique in which lagrangian particles are used to discretize an advection operator and an eulerian mesh based hdg method is employed for the constitutive modeling to account for the inter particle interactions key to the method is the variational framework provided by the hdg method this allows to formulate the projections between the lagrangian particle space and the eulerian finite element space in terms of local i e cellwise l 2 projections efficiently furthermore exploiting the hdg framework for solving the constitutive equations results in velocity fields which excellently approach the incompressibility constraint in a local sense by advecting the particles through these velocity fields the particle distribution remains uniform over time obviating the need for additional quality control the presented methodology allows for a straightforward extension to arbitrary order spatial accuracy on general meshes a range of numerical examples shows that optimal convergence rates are obtained in space and given the particular time stepping strategy second order accuracy is obtained in time the model capabilities are further demonstrated by presenting results for the flow over a backward facing step and for the flow around a cylinder

modeling low reynolds number incompressible flows using sph the method of smoothed particle hydrodynamics sph is extended to model incompressible flows of low reynolds number for such flows modification of the standard sph formalism is required to minimize errors associated with the use of a quasi incompressible equation of state treatment of viscosity state equation kernel interpolation and boundary conditions are described simulations using the method show close agreement with series solutions for couette and poiseuille flows furthermore comparison with finite element solutions for flow past a regular lattice of cylinders shows close agreement for the velocity and pressure fields the sph results exhibit small pressure fluctuations near curved boundaries further improvements to the boundary conditions may be possible which will reduce these errors a similar method to that used here may permit the simulation of other flows at low reynolds numbers using sph further development will be needed for cases involving free surfaces or substantially different equations of state