a remark on computing distance functions we propose a new method for the reconstruction of the signed distance function in the context of level set methods the new method is a modification of the algorithm which makes use of the pde equation for the distance function introduced by m sussman p smereka and s osher 1994 j comput phys 119 146 it is based mainly on the use of a truly upwind discretization near the interface comparison with the previous algorithm shows a definite improvement when used with a first order upwind scheme the method provides first order accuracy for the signed distance function in the whole computational domain and second order accuracy in the location of the interface a second order version of the method is also presented

a fast level set method for propagating interfaces a method is introduced to decrease the computational labor of the standard level set method for propagating interfaces the fast approach uses only points close to the curve at every time step we describe this new algorithm and compare its efficiency and accuracy with the standard level set approach

a gradient augmented level set method for unstructured grids we present and test a gradient augmented level set method for unstructured grids which has been designed to allow for easy integration in parallel flow solvers the means to this end is a hermite formulation where the gradient is stored and advected as an independent variable along with the level set function the method uses narrow band storage in conjunction with a fast marching method which is also designed to take advantage of the gradient augmentation we demonstrate through standard passive advection test cases that the proposed method is able to compute interface motion with performance comparable to popular high performing methods on structured grids

reflection coefficients counterpart of cardan viete formulas polynomials can be represented by their coefficients or by their zeros the link between these two representations is the cardan viete formulas that let us express the coefficients as elementary symmetric functions in the zeros in this paper as a consequence of levinson recursion we present a counterpart to the cardan viete formulas that expresses the polynomial coefficients or the regression vector of an autoregressive filter when a lattice representation is considered in terms of its reflection coefficients

computing interface motion in compressible gas dynamics a hamilton jacobi level set formulation of the equations of motion for propagating interfaces has been introduced recently by osher and sethian this formulation allows fronts to self intersect develop singularities and change topology the numerical algorithms based on this approach handle topological merging and breaking naturally work in any number of space dimensions and do not require that the moving front be written as a function instead the moving front is embedded as a particular level set in a fixed domain partial differential equation numerical techniques borrowed from hyperbolic conservation laws are then used to accurately capture the complicated surface motion that satisfies the global entropy condition for propagating fronts given by sethian in this paper we analyze the coupling of this level set formulation to a system of conservation laws for compressible gas dynamics we study both conservative and non conservative differencing of the level set function and compare the two approaches to illustrate the capability of the method we study the compressible rayleigh taylor and kelvin helmholtz instabilities for air air and air helium boundaries we perform numerical convergence studies of the method over a range of parameters and analyze the accuracy of this approach applied to these problems

hamilton jacobi equations on a manifold and applications to grid generation or refinement in this paper we consider hamilton jacobi equations on a manifold typically on the graph of some previously computed function z x y and we show how the corresponding level set method allows us to generate and or to refine a mesh in regions where this function z has large derivatives such as it is the method needs to be strongly improved and accelerated but the principle is awfully natural and in principle the method is fully automatic similar ideas are also useful in image processing in particular for the active contours method

error sources and error propagation in the levinson durbin algorithm it is proved that there are two types of numerical error due to finite precision in the levinson durbin algorithms an erratic and a systematic one the erratic one depends on the value the input autocorrelation accidentally takes at an iteration and essentially it affects only the results obtained at this particular recursion on the contrary the systematic numerical error increases with the information the system carries and propagates essentially throughout the algorithm it is shown that for both types of error as well as the overall one there are specific intermediate quantities calculated in the evolution of the algorithm which may serve as precise indicators of the exact number of erroneous digits with which the various quantities are computed including the parcor coefficients and the filter coefficients therefore the generated numerical error can be accurately traced

a hybrid ψ v hoc approach for surface tension driven flows in level set framework abstract in this study a higher order compact hoc finite difference scheme is proposed for the simulation of multiphase flows with surface tension effects by coupling the pure streamfunction formulation of navier stokes n s equations with the level set method unlike most of the existing methods for multiphase flows that solve the incompressible navier stokes equations in the velocity pressure form or the stream function vorticity form we recast the governing equations into the biharmonic form of the n s equations which carries stream function as the only variable to be computed the coupling of this formulation with level set ls enables the simulation of two phase flows by the core computation of only the single variable free from discontinuities in the whole physical domain in the process we also propose a novel hybrid hoc algorithm for post processing the pressure on either side of the interface including the jump across it the robustness of this method is established through a series of benchmark problems such as dispersion of capillary waves static bubble and oscillating bubble at equilibrium in a fluid at rest and deforming circular drops in shear flows we compare our numerical results with available benchmark results and excellent match is obtained in all the cases along with accurate representation of overall trends our approach is proved to be very efficient in terms of its easy implementation relatively low computational time and high order of accuracy

a simple level set method for solving stefan problems a simple level set method for solving stefan problems is presented this method can be applied to problems involving dendritic solidification our method consists of an implicit finite difference scheme for solving the heat equation and a level set approach for capturing the front between solid and liquid phases of a pure substance our method is accurate with respect to some exact solutions of the stefan problem results indicate that this method can handle topology changes and complicated interfacial shapes and that it can numerically simulate many of the physical features of dendritic solidification

a level set approach for computing solutions to incompressible two phase flow a level set approach for computing solutions to incompressible two phase flow is presented the interface between the two fluids is considered to be sharp and is described as the zero level set of a smooth function a new treatment of the level set method allows us to efficiently maintain the level set function as the signed distance from the interface we never have to explicitly reconstruct or find the zero level set consequently we are able to handle arbitrarily complex topologies large density and viscosity ratios and surface tension on relatively coarse grids we use a second order projection method along with a second order upwinded procedure for advecting the momentum and level set equations we consider the motion of air bubbles and water drops we also compute flows with multiple fluids such as air oil and water

alternating direction ghost fluid methods for solving the heat equation with interfaces abstract this work presents two new alternating direction implicit adi schemes for solving parabolic interface problems in two and three dimensions first the ghost fluid method gfm is adopted for the first time in the literature to treat interface jumps in the adi framework which results in symmetric and tridiagonal finite difference matrices in each adi step the proposed gfm adi scheme achieves a first order of accuracy in both space and time as confirmed by numerical experiments involving complex interface shapes and spatial temporal dependent jumps the gfm adi scheme also maintains the adi efficiency the computational complexity for each time step scales as o n for a total degree of freedom n in higher dimensions second a new matched interface and boundary mib scheme is constructed which downgrades the quadratic polynomial bases in the existing second order mib to linear ones interestingly the resulting mib adi or madi scheme produces the same finite difference matrices as the gfm adi scheme in all dimensions hence the madi scheme can be regarded as an improvement of the gfm because it calculates tangential jumps which are omitted in the gfm consequently the present madi scheme is constantly more accurate than the gfm adi in all numerical examples while keeping the same computational efficiency nevertheless the madi scheme is semi implicit due to tangential jump approximations while the gfm adi scheme is fully implicit without tangential corrections thus the gfm adi scheme could be more stable than the madi scheme when a huge contrast is presented in diffusion coefficients

binary level set shape optimization model and algorithm for volumetric modulated arc therapy in radiotherapy treatment we introduce in this paper a variational framework for the construction of improved treatment plans in volumetric modulated arc therapy for cancer treatment this framework consists of a shape optimization component from the molding of beam shapes as well as strong constraints from the equipment involved on both beam shapes and intensities we apply the binary level set method to handle complex shape topologies and the fast sweeping method to handle beam intensity constraints the result is a fast flow based algorithm in a simplified setting that guarantees energy decrease we include numerical simulations of clinical cases to demonstrate the efficacy of the approach

a balanced force refined level set grid method for two phase flows on unstructured flow solver grids a balanced force refined level set grid method for two phase flows on structured and unstructured flow solver grids is presented to accurately track the phase interface location an auxiliary high resolution equidistant cartesian grid is introduced in conjunction with a dual layer narrow band approach this refined level set grid method allows for parallel efficient grid convergence and error estimation studies of the interface tracking method the navier stokes equations are solved on an unstructured flow solver grid with a novel balanced force algorithm for level set methods based on the recently proposed method by francois et al m m francois s j cummins e d dendy d b kothe j m sicilian m w williams a balanced force algorithm for continuous and sharp interfacial surface tension models within a volume tracking framework j comput phys 213 2006 141 173 for volume of fluid methods on structured grids to minimize spurious currents a second order converging curvature evaluation technique for level set methods is presented the results of several different test cases demonstrate the effectiveness of the proposed method showing good mass conservation properties and second order converging spurious current magnitudes

discretization of dirac delta functions in level set methods discretization of singular functions is an important component in many problems to which level set methods have been applied we present two methods for constructing consistent approximations to dirac delta measures concentrated on piecewise smooth curves or surfaces both methods are designed to be convenient for level set simulations and are introduced to replace the commonly used but inconsistent regularization technique that is solely based on a regularization parameter proportional to the mesh size the first algorithm is based on a tensor product of regularized one dimensional delta functions it is independent of the irregularity relative to the grid in the second method the regularization is constructed from a one dimensional regularization that is extended to multi dimensions with a variable support depending on the orientation of the singularity relative to the computational grid convergence analysis and numerical results are given

regular article a pde based fast local level set method we develop a fast method to localize the level set method of osher and sethian 1988 j comput phys 79 12 and address two important issues that are intrinsic to the level set method a how to extend a quantity that is given only on the interface to a neighborhood of the interface b how to reset the level set function to be a signed distance function to the interface efficiently without appreciably moving the interface this fast local level set method reduces the computational effort by one order of magnitude works in as much generality as the original one and is conceptually simple and easy to implement our approach differs from previous related works in that we extract all the information needed from the level set function or functions in multiphase flow and do not need to find explicitly the location of the interface in the space domain the complexity of our method to do tasks such as extension and distance reinitialization is o n where n is the number of points in space not o n log n as in works by sethian 1996 proc nat acad sci 93 1591 and helmsen and co workers 1996 spie microlithography ix p 253 this complexity estimation is also valid for quite general geometrically based front motion for our localized method

convergence of the ghost fluid method for elliptic equations with interfaces this paper proves the convergence of the ghost fluid method for second order elliptic partial differential equations with interfacial jumps a weak formulation of the problem is first presented which then yields the existence and uniqueness of a solution to the problem by classical methods it is shown that the application of the ghost fluid method by fedkiw kang and liu to this problem can be obtained in a natural way through discretization of the weak formulation an abstract framework is given for proving the convergence of finite difference methods derived from a weak problem and as a consequence the ghost fluid method is proved to be convergent

some properties of lattice autoregressive filters an autoregressive filter is defined either by the components of the regression vector or by the reflection coefficients appearing in its lattice representation the mathematical expression of the regression vector in terms of the reflection coefficients is very complex but many structural properties can be obtained without this exact expression in this paper we present some examples of such structural properties and we apply these results to prove some extremal properties of stable filters such as the maximum value of the components of the regression vector or the maximum value of its norm moreover some properties of the boundary of the stability domain are discussed

stochastic differential equations and geometric flows in previous years curve evolution applied to a single contour or to the level sets of an image via partial differential equations has emerged as an important tool in image processing and computer vision curve evolution techniques have been utilized in problems such as image smoothing segmentation and shape analysis we give a local stochastic interpretation of the basic curve smoothing equation the so called geometric heat equation and show that this evolution amounts to a tangential diffusion movement of the particles along the contour moreover assuming that a priori information about the shapes of objects in an image is known we present modifications of the geometric heat equation designed to preserve certain features in these shapes while removing noise we also show how these new flows may be applied to smooth noisy curves without destroying their larger scale features in contrast to the original geometric heat flow which tends to circularize any closed curve

level set jet schemes for stiff advection equations the semijet method abstract many interfacial phenomena in physical and biological systems are dominated by high order geometric quantities such as curvature here a semi implicit method is combined with a level set jet scheme to handle stiff nonlinear advection problems the new method offers an improvement over the semi implicit gradient augmented level set method previously introduced by requiring only one smoothing step when updating the level set jet function while still preserving the underlying methods higher accuracy sample results demonstrate that accuracy is not sacrificed while strict time step restrictions can be avoided

an efficient interface preserving level set redistancing algorithm and its application to interfacial incompressible fluid flow in sussman smereka and osher j comp phys 94 1994 pp 146 159 a numerical scheme was presented for computing incompressible air water flows using the level set method crucial to the above method was a new iteration method for maintaining the level set function as the signed distance from the zero level set in this paper we implement a constraint along with higher order difference schemes in order to make the iteration method more accurate and efficient accuracy is measured in terms of the new computed signed distance function and the original level set function having the same zero level set we apply our redistancing scheme to incompressible flows with noticeably better resolved results at reduced cost we validate our results with experiment and theory we show that our distance level set scheme with the added constraint competes well with available interface tracking schemes for basic advection of an interface we perform basic accuracy checks and more stringent tests involving complicated interfacial structures as with all level set schemes our method is easy to implement

an efficient mass preserving interface correction level set ghost fluid method for droplet suspensions under depletion forces abstract aiming for the simulation of colloidal droplets in microfluidic devices we present here a numerical method for two fluid systems subject to surface tension and depletion forces among the suspended droplets the algorithm is based on an efficient solver for the incompressible two phase navier stokes equations and uses a mass conserving level set method to capture the fluid interface the four novel ingredients proposed here are firstly an interface correction level set icls method global mass conservation is achieved by performing an additional advection near the interface with a correction velocity obtained by locally solving an algebraic equation which is easy to implement in both 2d and 3d secondly we report a second order accurate geometric estimation of the curvature at the interface and thirdly the combination of the ghost fluid method with the fast pressure correction approach enabling an accurate and fast computation even for large density contrasts finally we derive a hydrodynamic model for the interaction forces induced by depletion of surfactant micelles and combine it with a multiple level set approach to study short range interactions among droplets in the presence of attracting forces

a balanced force algorithm for continuous and sharp interfacial surface tension models within a volume tracking framework a new balanced force algorithm is presented for modeling interfacial flow with surface tension the algorithm is characterized by a pressure correction method with the interfaces represented by volume fractions within this flow algorithm we devise a continuous e g continuum surface tension model and a sharp e g a ghost fluid method interface representation of the surface tension induced interfacial pressure jump condition the sharp interface representation is achieved by temporarily reconstructing distance functions from volume fractions we demonstrate that a flow algorithm designed to legislate force balance retains an exact balance between surface tension forces and the resulting pressure gradients this balance holds for both continuous and sharp representations of interfacial surface tension the algorithm design eliminates one of the elusive impediments to more accurate models of surface tension driven flow the remaining of which is accurate curvature estimation to validate our formulation we present results for an equilibrium static drop in two and three dimensions having an arbitrary density jump across the interface we find that the sharp surface tension method yields an abrupt pressure jump across the interface whereas the continuous surface tension method results in a smoother transition both methods however yield spurious velocities of the same order the origin of which is due solely to errors in curvature dynamic results are also presented to illustrate the versatility of the method

a coupled level set and volume of fluid method for computing 3d and axisymmetric incompressible two phase flows we present a coupled level set volume of fluid clsvof method for computing 3d and axisymmetric incompressible two phase flows this method combines some of the advantages of the volume of fluid method with the level set method to obtain a method which is generally superior to either method alone we present direct comparisons between computations made with the clsvof method and computations made with the level set method the volume of fluid method and the boundary integral method we also compare our computations to the exact solution for an oscillating ellipse due to lamb and experimental results obtained for a rising gas bubble in liquid obtained by hnat and buckmaster our computational examples focus on flows in which surface tension forces and changes in topology are dominant features of the flow

a variational approach for the segmentation of the left ventricle in cardiac image analysis in this paper we propose a level set method to segment mr cardiac images our approach is based on a coupled propagation of two cardiac contours and integrates visual information with anatomical constraints the visual information is expressed through a gradient vector flow based boundary component and a region term that aims at best separating the cardiac contours regions according to their global intensity properties in order to deal with misleading visual support an anatomical constraint is considered that couples the propagation of the cardiac contours according to their relative distance the resulting motion equations are implemented using a level set approach and a fast and stable numerical approximation scheme the additive operator splitting encouraging experimental results are provided using real data

a hybrid particle level set method for improved interface capturing in this paper we propose a new numerical method for improving the mass conservation properties of the level set method when the interface is passively advected in a flow field our method uses lagrangian marker particles to rebuild the level set in regions which are underresolved this is often the case for flows undergoing stretching and tearing the overall method maintains a smooth geometrical description of the interface and the implementation simplicity characteristic of the level set method our method compares favorably with volume of fluid methods in the conservation of mass and purely lagrangian schemes for interface resolution the method is presented in three spatial dimensions

modeling multistage cutting stock problems abstract in multistage cutting stock problems csp the cutting process is distributed over several successive stages every stage except the last one produces intermediate products the list of intermediate products may be given or arbitrary the goal is to minimize the total amount of material taken out of stock to cut finished products sufficient to meet customer demands if the intermediate sizes are given the column generation technique can be applied to multistage cutting problems if the intermediate sizes are not given then another dimension is added to the problem complexity we propose a special procedure for this case that dynamically generates both rows intermediate sizes and columns patterns we refer to this method as row and column generation the method uses an auxiliary problem embedded into the frame of the revised simplex algorithm it is a non linear knapsack problem that can be solved efficiently in contrast to the column generation method the developed technique cannot guarantee the optimal solution however the results of computational experiments are very promising and prove that the method is a valuable addition to the set of tools for modeling and solving multistage csps

an immersed boundary method with direct forcing for the simulation of particulate flows we present an improved method for computing incompressible viscous flow around suspended rigid particles using a fixed and uniform computational grid the main idea is to incorporate peskin s regularized delta function approach acta numerica 11 2002 1 into a direct formulation of the fluid solid interaction force in order to allow for a smooth transfer between eulerian and lagrangian representations while at the same time avoiding strong restrictions of the time step this technique was implemented in a finite difference and fractional step context a variety of two and three dimensional simulations are presented ranging from the flow around a single cylinder to the sedimentation of 1000 spherical particles the accuracy and efficiency of the current method are clearly demonstrated

dti segmentation using an information theoretic tensor dissimilarity measure in recent years diffusion tensor imaging dti has become a popular in vivo diagnostic imaging technique in radiological sciences in order for this imaging technique to be more effective proper image analysis techniques suited for analyzing these high dimensional data need to be developed in this paper we present a novel definition of tensor distance grounded in concepts from information theory and incorporate it in the segmentation of dti in a dti the symmetric positive definite spd diffusion tensor at each voxel can be interpreted as the covariance matrix of a local gaussian distribution thus a natural measure of dissimilarity between spd tensors would be the kullback leibler kl divergence or its relative we propose the square root of the j divergence symmetrized kl between two gaussian distributions corresponding to the diffusion tensors being compared and this leads to a novel closed form expression for the distance as well as the mean value of a dti unlike the traditional frobenius norm based tensor distance our distance is affine invariant a desirable property in segmentation and many other applications we then incorporate this new tensor distance in a region based active contour model for dti segmentation synthetic and real data experiments are shown to depict the performance of the proposed model

fast fourier transforms for direct solution of poisson s equation with staggered boundary conditions abstract this paper describes pre and postprocessing algorithms used to incorporate the fast fourier transform fft into the solution of finite difference approximations to multi dimensional poisson s equation on a staggered grid where the boundary is located midway between two grid points all frequently occurring boundary conditions neumann dirichlet or cyclic are considered including the combination of staggered neumann boundary condition on one side with nonstaggered dirichlet boundary condition on the other side experiences from implementing these algorithms in vectorized coding in fortran subroutines are reported

accelerated boundary integral method for multiphase flow in non periodic geometries an accelerated boundary integral method for stokes flow of a suspension of deformable particles is presented for an arbitrary domain and implemented for the important case of a planar slit geometry the computational complexity of the algorithm scales as o n or o n log n where n is proportional to the product of number of particles and the number of elements employed to discretize the particle this technique is enabled by the use of an alternative boundary integral formulation in which the velocity field is expressed in terms of a single layer integral alone even in problems with non matched viscosities the density of the single layer integral is obtained from a fredholm integral equation of the second kind involving the double layer integral acceleration in this implementation is provided by the use of general geometry ewald like method ggem for computing the velocity and stress fields driven by a set of point forces in the geometry of interest for the particular case of the slit geometry a fourier chebyshev spectral discretization of ggem is developed efficient implementations employing the ggem methodology are presented for the resulting single and the double layer integrals the implementation is validated with test problems on the velocity of rigid particles and drops between parallel walls in pressure driven flow the taylor deformation parameter of capsules in simple shear flow and the particle trajectories in pair collisions of capsules in simple shear flow the computational complexity of the algorithm is verified with results from several large scale multiparticle simulations

constrained wiener filtering corresp as is well known the introduction of causality conditions in wiener filtering problems completely changes their solution a constraint such as causality can be presented as a particular reduction of the observation space and the constrained filter can always be obtained by projection onto this space however it is sometimes simpler to use an indirect method which gives the impulse response of the constrained filter by an appropriate modification of the unconstrained response this method is presented and applied to many examples in particular the structure of constrained prediction filters is analyzed and it is shown that the constrained innovation can be expressed in terms of the unconstrained one by an appropriate filter

crystal growth and dendritic solidification we present a numerical method which computes the motion of complex solid liquid boundaries in crystal growth the model we solve includes physical effects such as crystalline anisotropy surface tension molecular kinetics and undercooling the method is based on two ideas first the equations of motion are recast as a single history dependent boundary integral equation on the solid liquid boundary a fast algorithm is used to solve the integral equation efficiently second the boundary is moved by solving a hamiltonjacobi type equation on a fixed domain formulated by osher and sethian for a function in which the boundary is a particular level set this equation is solved by finite difference schemes borrowed from the technology of hyperbolic conservation laws the two ideas are combined by constructing a smooth extension of the normal velocity off the moving boundary in a way suggested by the physics of the problem our numerical experiments show the evolution of complex crystalline shapes development of large spikes and corners dendrite formation and side branching and pieces of solid merging and breaking off freely

finite difference methods for approximating heaviside functions we present a finite difference method for discretizing a heaviside function h u x where u is a level set function u r email protected r that is positive on a bounded region email protected r n there are two variants of our algorithm both of which are adapted from finite difference methods that we proposed for discretizing delta functions in j d towers two methods for discretizing a delta function supported on a level set j comput phys 220 2007 915 931 j d towers discretizing delta functions via finite differences and gradient normalization preprint at http www miracosta edu home jtowers j d towers a convergence rate theorem for finite difference approximations to delta functions j comput phys 227 2008 6591 6597 we consider our approximate heaviside functions as they are used to approximate integrals over w we prove that our first approximate heaviside function leads to second order accurate quadrature algorithms numerical experiments verify this second order accuracy for our second algorithm numerical experiments indicate at least third order accuracy if the integrand f and email protected are sufficiently smooth numerical experiments also indicate that our approximations are effective when used to discretize certain singular source terms in partial differential equations we mostly focus on smooth f and u by this we mean that f is smooth in a neighborhood of w u is smooth in a neighborhood of email protected and the level set u x 0 is a manifold of codimension one however our algorithms still give reasonable results if either f or u has jumps in its derivatives numerical experiments indicate approximately second order accuracy for both algorithms if the regularity of the data is reduced in this way assuming that the level set u x 0 is a manifold numerical experiments indicate that dependence on the placement of w with respect to the grid is quite small for our algorithms specifically a grid shift results in an o h p change in the computed solution where p is the observed rate of convergence

evolution implementation and application of level set and fast marching methods for advancing fronts abstract a variety of numerical techniques are available for tracking moving interfaces in this review we concentrate on techniques that result from the link between the partial differential equations that describe moving interfaces and numerical schemes designed for approximating the solutions to hyperbolic conservation laws this link gives rise to computational techniques for tracking moving interfaces in two and three space dimensions under complex speed laws we discuss the evolution of these techniques the fundamental numerical approximations involved implementation details and applications in particular we review some work on three aspects of materials sciences semiconductor process simulations seismic processing and optimal structural topology design

a conservative level set method for two phase flow ii in this paper we continue to develop and study the conservative level set method for incompressible two phase flow with surface tension introduced in j comput phys 210 2005 225 246 we formulate a modification of the reinitialization and present a theoretical study of what kind of conservation we can expect of the method a finite element discretization is presented as well as an adaptive mesh control procedure numerical experiments relevant for problems in petroleum engineering and material science are presented for these problems the surface tension is strong and conservation of mass is important problems in both two and three dimensions with uniform as well as non uniform grids are studied from these calculations convergence and conservation is studied good conservation and convergence are observed

local or global minima flexible dual front active contours most variational active contour models are designed to find local minima of data dependent energy functionals with the hope that reasonable initial placement of the active contour will drive it toward a desirable local minimum as opposed to an undesirable configuration due to noise or complex image structure as such there has been much research into the design of complex region based energy functionals that are less likely to yield undesirable local minima when compared to simpler edge based energy functionals whose sensitivity to noise and texture is significantly worse unfortunately most of these more robust region based energy functionals are applicable to a much narrower class of imagery compared to typical edge based energies due to stronger global assumptions about the underlying image data devising new implementation algorithms for active contours that attempt to capture more global minimizers of already proposed image based energies would allow us to choose an energy that makes sense for a particular class of energy without concern over its sensitivity to local minima such implementations have been proposed for capturing global minima however sometimes the completely global minimum is just as undesirable as a minimum that is too local in this paper we propose a novel fast and flexible dual front implementation of active contours motivated by minimal path techniques and utilizing fast sweeping algorithms which is easily manipulated to yield minima with variable degrees of localness and globalness by simply adjusting the size of active regions the ability to gracefully move from capturing minima that are more local according to the initial placement of the active contour surface to minima that are more global allows this model to more easily obtain desirable minimizers which often are neither the most local nor the most global experiments on various 2d and 3d images and comparisons with some active contour models and region growing methods are also given to illustrate the properties of this model and its performance in a variety of segmentation applications

a stabilized finite element method using a discontinuous level set approach for the computation of bubble dynamics a novel numerical method for solving three dimensional two phase flow problems is presented this method combines a quadrature free discontinuous galerkin method for the level set equation with a pressure stabilized finite element method for the navier stokes equations the main challenge in the computation of such flows is the accurate evaluation of surface tension forces this involves the computation of the curvature of the fluid interface in the context of the discontinuous galerkin method we show that the use of a curvature computed by means of a direct derivation of the level set function leads to inaccurate and oscillatory results a more robust second order least squares computation of the curvature that filters out the high frequencies and produces converged results is presented this whole numerical technology allows to simulate a wide range of flow regimes with large density ratios to accurately capture the shape of the deforming interface of the bubble and to maintain good mass conservation

reflection coefficients of polynomials and stable polytopes the geometry of stable discrete polynomials using their coefficients and reflection coefficients is investigated two linear schur invariant transformations with a free parameter in the polynomial coefficient space are introduced the first transformation rfrn times rfrrarrrfrn maps an arbitrary stable polytope into another stable polytope the second transformation rfrn times rfrrarrrfrn maps a stable tilted n dimensional hyperrectangle defined by the discrete kharitonov theorem into a stable n 1 dimensional polytope

a geometric description of stable linear predictive coding digital filters corresp if the linear predictive coding filter coefficients are imagined as specifying a point in an n dimensional space then the set of all stable filters fills up a certain region in this space the shape of this region is determined for low order filters and general properties are deduced for higher order filters

an lp based approach to a two stage cutting stock problem this paper describes a linear programming model for a two stage cutting stock problem that arises in a make to order steel company for technological reasons there are two different cutting operations between the cutting operations the intermediate rolls are processed to obtain the required characteristics the minimization of the trim loss and the reduction of the number of set ups are primary concerns in cutting stock problems in this case it is also important to minimize the number of intermediate rolls in order to reduce the processing work these objectives may be conflicting and a balance may be necessary we present a simplified lp model which is solved by a column generation technique the subproblems are relatively large knapsack problems computational results for a microcomputer are presented

global minimum for active contour models a minimal path approach a new boundary detection approach for shape modeling is presented it detects the global minimum of an active contour model s energy between two end points initialization is made easier and the curve is not trapped at a local minimum by spurious edges we modify the snake energy by including the internal regularization term in the external potential term our method is based on finding a path of minimal length in a riemannian metric we then make use of a new efficient numerical method to find this shortest path it is shown that the proposed energy though based only on a potential integrated along the curve imposes a regularization effect like snakes we explore the relation between the maximum curvature along the resulting contour and the potential generated from the image the method is capable to close contours given only one point on the objects boundary by using a topology based saddle search routine we show examples of our method applied to real aerial and medical images

an accurate adaptive solver for surface tension driven interfacial flows a method combining an adaptive quad octree spatial discretisation geometrical volume of fluid interface representation balanced force continuum surface force surface tension formulation and height function curvature estimation is presented the extension of these methods to the quad octree discretisation allows adaptive variable resolution along the interface and is described in detail the method is shown to recover exact equilibrium to machine accuracy between surface tension and pressure gradient in the case of a stationary droplet irrespective of viscosity and spatial resolution accurate solutions are obtained for the classical test case of capillary wave oscillations an application to the capillary breakup of a jet of water in air further illustrates the accuracy and efficiency of the method the source code of the implementation is freely available as part of the gerris flow solver

simultaneous column and row generation for large scale linear programs with column dependent rows in this paper we develop a simultaneous column and row generation algorithm that could be applied to a general class of large scale linear programming problems these problems typically arise in the context of linear programming formulations with exponentially many variables the defining property for these formulations is a set of linking constraints which are either too many to be included in the formulation directly or the full set of linking constraints can only be identified if all variables are generated explicitly due to this dependence between columns and rows we refer to this class of linear programs as problems with column dependent rows to solve these problems we need to be able to generate both columns and rows on the fly within an efficient solution approach we emphasize that the generated rows are structural constraints and distinguish our work from the branch and cut and price framework we first characterize the underlying assumptions for the proposed column and row generation algorithm these assumptions are general enough and cover all problems with column dependent rows studied in the literature up until now to the best of our knowledge we then introduce in detail a set of pricing subproblems which are used within the proposed column and row generation algorithm this is followed by a formal discussion on the optimality of the algorithm to illustrate our approach the paper is concluded by applying the proposed framework to the multi stage cutting stock and the quadratic set covering problems

sobolev active contours all previous geometric active contour models that have been formulated as gradient flows of various energies use the same l 2 type inner product to define the notion of gradient recent work has shown that this inner product induces a pathological riemannian metric on the space of smooth curves however there are also undesirable features associated with the gradient flows that this inner product induces in this paper we reformulate the generic geometric active contour model by redefining the notion of gradient in accordance with sobolev type inner products we call the resulting flows sobolev active contours sobolev metrics induce favorable regularity properties in their gradient flows in addition sobolev active contours favor global translations but are not restricted to such motions they are also less susceptible to certain types of local minima in contrast to traditional active contours these properties are particularly useful in tracking applications we demonstrate the general methodology by reformulating some standard edge based and region based active contour models as sobolev active contours and show the substantial improvements gained in segmentation

solving partial differential equations on irregular domains with moving interfaces with applications to superconformal electrodeposition in semiconductor manufacturing we present a numerical algorithm for solving partial differential equations on irregular domains with moving interfaces instead of the typical approach of solving in a larger rectangular domain our approach performs most calculations only in the desired domain to do so efficiently we have developed a one sided multigrid method to solve the corresponding large sparse linear systems our focus is on the simulation of the electrodeposition process in semiconductor manufacturing in both two and three dimensions our goal is to track the position of the interface between the metal and the electrolyte as the features are filled and to determine which initial configurations and physical parameters lead to superfilling we begin by motivating the set of equations which model the electrodeposition process building on existing models for superconformal electrodeposition we develop a model which naturally arises from a conservation law form of surface additive evolution we then introduce several numerical algorithms including a conservative material transport level set method and our multigrid method for one sided diffusion equations we then analyze the accuracy of our numerical methods finally we compare our result with experiment over a wide range of physical parameters

numerical conditioning problems and solutions for nonparametric i i d statistical active contours in this paper we propose an active contour model based on nonparametric independent and identically distributed i i d statistics of the image that can segment an image without any a priori information about the intensity distributions of the region of interest or the background this is not however the first active contour model proposed to solve the segmentation problem under these same assumptions in contrast to prior active contour models based on nonparametric i i d statistics we do not formulate our optimization criterion according to any distance measure between estimated probability densities inside and outside the active contour instead treating the segmentation problem as a pixel wise classification problem we formulate an active contour to minimize the unbiased pixel wise average misclassification probability amp this not only simplifies the problem by avoiding the need to arbitrarily select among many sensible distance measures to measure the difference between the probability densities estimated inside and outside the active contour but it also solves a numerical conditioning problem that arises with such prior active contour models as a result the amp model exhibits faster convergence with higher accuracy and robustness when compared to active contour models previously formulated to solve the same nonparametric i i d statistical segmentation problem via probability distances to discuss this improved numerical behavior more precisely we introduce the notion of x201c conditioning ratio x201d and demonstrate that the proposed amp active contour is numerically better conditioned i e exhibits a much smaller conditioning ratio than prior probability distance based active contours

best stable and invertible approximations for arma systems a method is proposed for finding the best stable and invertible approximations for an autoregressive moving average arma system relative to a general quadratic metric in the coefficient space mathematically the problem is equivalent to projecting the regression and moving average vectors of the system onto the set s of coefficients of monic schur polynomials the geometry of s is too complex to allow the problem to be approached directly in the arma coefficient space a solution is obtained by constrained steepest descent in the hypercube of reflection coefficients which is homomorphic to s

some improvements of the fast marching method the fast marching method published by sethian proc natl acad sci usa 93 1996 pp 1591 1595 is an optimally efficient algorithm for solving problems of front evolution where the front speed is monotonic it has been used in a wide variety of applications such as robotic path planning r kimmel and j sethian fast marching methods for computing distance maps and shortest paths tech report 669 cpam university of california berkeley 1996 crack propagation m stolarska et al modelling crack growth by level sets in the extended finite element method comput methods appl mech engrg to appear internat j numer methods engrg 51 2001 pp 943 960 n sukumar d l chopp and b moran extended finite element method and fast marching method for three dimensional fatigue crack propagation j comput phys submitted seismology j sethian and a popovici geophysics 64 1999 pp 516 523 photolithography j sethian fast marching level set methods for three dimensional photolithography development in proceedings of the spie 1996 international symposium on microlithography santa clara ca 1996 and medical imaging r malladi and j sethian proc natl acad sci usa 93 1996 pp 9389 9392 it has also been a valuable tool for the implementation of modern level set methods where it is used to efficiently compute the distance to the front and or an extended velocity function in this paper we improve upon the second order fast marching method of sethian siam rev 41 1999 pp 199 235 by constructing a second order approximation of the interface generated from local data on the mesh the data is interpolated on a single box of the mesh using a bicubic approximation the distance to the front is then calculated by using a variant of newton s method to solve both the level curve equation and the orthogonality condition for the nearest point to a given node the result is a second order approximation of the distance to the interface which can then be used to produce second order accurate initial conditions for the fast marching method and a third order fast marching method

semi lagrangian methods for level set equations a new numerical method for solving geometric moving interface problems is presented the method combines a level set approach and a semi lagrangian time stepping scheme which is explicit yet unconditionally stable the combination decouples each mesh point from the others and the time step from the cfl stability condition permitting the construction of methods which are efficient adaptive and modular analysis of a linear one dimensional model problem suggests a surprising convergence criterion which is supported by heuristic arguments and confirmed by an extensive collection of two dimensional numerical results the new method computes correct viscosity solutions to problems involving geometry anisotropy curvature and complex topological events

minimal surfaces based object segmentation a geometric approach for 3d object segmentation and representation is presented the segmentation is obtained by deformable surfaces moving towards the objects to be detected in the 3d image the model is based on curvature motion and the computation of surfaces with minimal areas better known as minimal surfaces the space where the surfaces are computed is induced from the 3d image volumetric data in which the objects are to be detected the model links between classical deformable surfaces obtained via energy minimization and intrinsic ones derived from curvature based flows the new approach is stable robust and automatically handles changes in the surface topology during the deformation

numerical time step restrictions as a result of capillary waves the propagation of capillary waves on material interfaces between two fluids imposes a strict constraint on the numerical time step applied to solve the equations governing this problem and is directly associated with the stability of interfacial flow simulations the explicit implementation of surface tension is the generally accepted reason for the restrictions on the temporal resolution caused by capillary waves in this article a fully coupled numerical framework with an implicit treatment of surface tension is proposed and applied demonstrating that the capillary time step constraint is in fact a constraint imposed by the temporal sampling of capillary waves irrespective of the type of implementation the presented results show that the capillary time step constraint can be exceeded by several orders of magnitude with the explicit as well as the implicit treatment of surface tension if capillary waves are absent furthermore a revised capillary time step constraint is derived by studying the temporal resolution of capillary waves based on numerical stability and signal processing theory including the doppler shift caused by an underlying fluid motion the revised capillary time step constraint assures a robust aliasing free result as demonstrated by representative numerical experiments and is in the static case less restrictive than previously proposed time step limits associated with capillary waves

a time stepping scheme involving constant coefficient matrices for phase field simulations of two phase incompressible flows with large density ratios we present an efficient time stepping scheme for simulations of the coupled navier stokes cahn hilliard equations for the phase field approach the scheme has several attractive characteristics i it is suitable for large density ratios and numerical experiments with density ratios up to 1000 have been presented ii it involves only constant time independent coefficient matrices for all flow variables which can be pre computed during pre processing so it effectively overcomes the performance bottleneck induced by variable coefficient matrices associated with the variable density and variable viscosity iii it completely de couples the computations of the velocity pressure and the phase field function strategy for spectral element type spatial discretizations to overcome the difficulty associated with the large spatial order of the cahn hilliard equation is also discussed ample numerical simulations demonstrate that the current algorithm together with the navier stokes cahn hilliard phase field approach is an efficient and effective method for studying two phase flows involving large density ratios moving contact lines and interfacial topology changes

a second order accurate immersed boundary method for fully resolved simulations of particle laden flows an immersed boundary method ibm with second order spatial accuracy is presented for fully resolved simulations of incompressible viscous flows laden with rigid particles the method is based on the computationally efficient direct forcing method of uhlmann m uhlmann an immersed boundary method with direct forcing for simulation of particulate flows j comput phys 209 2005 448 476 that is embedded in a finite volume pressure correction method the ibm consists of two grids a fixed uniform eulerian grid for the fluid phase and a uniform lagrangian grid attached to and moving with the particles a regularized delta function is used to communicate between the two grids and proved to be effective in suppressing grid locking without significant loss of efficiency the original method is improved by 1 a better approximation of the no slip no penetration ns np condition on the surface of the particles by a multidirect forcing scheme 2 a correction for the excess in the effective particle diameter by a slight retraction of the lagrangian grid from the surface towards the interior of the particles with a fraction of the eulerian grid spacing and 3 an enhancement of the numerical stability for particle fluid mass density ratios near unity by a direct account of the inertia of the fluid contained within the particles the new ibm contains two new parameters the number of iterations n s of the multidirect forcing scheme and the retraction distance r d the effect of n s and r d on the accuracy is investigated for five different flows the results show that r d has a strong influence on the effective particle diameter and little influence on the error in the ns np condition while exactly the opposite holds for n s a novel finding of this study is the demonstration that r d has a strong influence on the order of grid convergence it is found that for spheres the choice of r d 0 3 dx yields second order accuracy compared to first order accuracy of the original method that corresponds to r d 0 finally n s 2 appears optimal for reducing the error in the ns np condition and maintaining the computational efficiency of the method

comparing ls fir filtering and l step ahead linear prediction this comparative study of the l step ahead linear prediction and least squares finite impulse response ls fir filtering problems emphasizes the numerical behavior of the resulting toeplitz systems it is shown that although these systems are similar the restraints on the autocorrelation coefficients fundamentally differentiate them in the process of doing so a new algorithmic scheme for the computation of the lagged lattice coefficients is developed which exhibits fundamentally improved numerical behavior moreover explicit formulas for the supremums of the absolute values of both the lagged lattice and filter coefficients are found theoretically and are experimentally confirmed by using the proposed algorithm finally the bounds of the ls fir filter coefficients are treated in comparison with the supremums of the lagged quantities

voronoi regions of lattices second moments of polytopes and quantization if a point is picked at random inside a regular simplex octahedron 600 cell or other polytope what is its average squared distance from the centroid in n dimensional space what is the average squared distance of a random point from the closest point of the lattice a n or d n e n a n ast or d n ast the answers are given here together with a description of the voronoi or nearest neighbor regions of these lattices the results have applications to quantization and to the design of signals for the gaussian channel for example a quantizer based on the eight dimensional lattice e8 has a mean squared error per symbol of 0 0717 cdots when applied to uniformly distributed data compared with 0 08333 cdots for the best one dimensional quantizer

ordered upwind methods for static hamilton jacobi equations theory and algorithms we develop a family of fast methods for approximating the solutions to a wide class of static hamilton jacobi pdes these fast methods include both semi lagrangian and fully eulerian versions numerical solutions to these problems are typically obtained by solving large systems of coupled nonlinear discretized equations our techniques which we refer to as ordered upwind methods oums use partial information about the characteristic directions to decouple these nonlinear systems greatly reducing the computational labor our techniques are considered in the context of control theoretic and front propagation problems we begin by discussing existing oums focusing on those designed for isotropic problems we then introduce a new class of oums which decouple systems for general anisotropic problems we prove convergence of one such scheme to the viscosity solution of the corresponding hamilton jacobi pde next we introduce a set of finite differences methods based on an analysis of the role played by anisotropy in the context of front propagation and optimal trajectory problems the performance of the methods is analyzed and computational experiments are performed using test problems from computational geometry and seismology

on the structure of vector quantizers vector quantization is intrinsically superior to predictive coding transform coding and other suboptimal and em ad hoc procedures since it achieves optimal rate distortion performance subject only to a constraint on memory or block length of the observable signal segment being encoded the key limitation of existing techniques is the very large randomly generated code books which must be stored and the computational complexity of the associated encoding procedures the quantization operation is decomposed into its rudimentary structural components this leads to a simple and elegant approach to derive analytical properties of optimal quantizers some useful properties of quantizers and algorithmic approaches are given which are relevant to the complexity of both storage and processing in the encoding operation highly disordered quantizers which have been designed using a clustering algorithm are considered finally lattice quantizers are examined which circumvent the need for a code book by using a highly structured code based on lattices the code vectors are algorithmically generated in a simple manner rather than stored in a code book and fast algorithms perform the encoding algorithm with negligible complexity

a fast pressure correction method for incompressible two fluid flows we have developed a new pressure correction method for simulating incompressible two fluid flows with large density and viscosity ratios the method s main advantage is that the variable coefficient poisson equation that arises in solving the incompressible navier stokes equations for two fluid flows is reduced to a constant coefficient equation which can be solved with an fft based fast poisson solver this reduction is achieved by splitting the variable density pressure gradient term in the governing equations the validity of this splitting is demonstrated from our numerical tests and it is explained from a physical viewpoint in this paper the new pressure correction method is coupled with a mass conserving volume of fluid method to capture the motion of the interface between the two fluids but in general it could be coupled with other interface advection methods such as level set phase field or front tracking first we verified the new pressure correction method using the capillary wave test case up to density and viscosity ratios of 10 000 then we validated the method by simulating the motion of a falling water droplet in air and comparing the droplet terminal velocity with an experimental value next the method is shown to be second order accurate in space and time independent of the vof method and it conserves mass momentum and kinetic energy in the inviscid limit also we show that for solving the two fluid navier stokes equations the method is 10 40 times faster than the standard pressure correction method which uses multigrid to solve the variable coefficient poisson equation finally we show that the method is capable of performing fully resolved direct numerical simulation dns of droplet laden isotropic turbulence with thousands of droplets using a computational mesh of 1024 3 points

level set methods an overview and some recent results the level set method was devised by s osher and j a sethian 1988 j comput phys 79 12 49 as a simple and versatile method for computing and analyzing the motion of an interface in two or three dimensions bounds a possibly multiply connected region the goal is to compute and analyze the subsequent motion of under a velocity field v this velocity can depend on position time the geometry of the interface and the external physics the interface is captured for later time as the zero level set of a smooth at least lipschitz continuous function x t i e t x x t 0 is positive inside negative outside and is zero on t topological merging and breaking are well defined and easily performed in this review article we discuss recent variants and extensions including the motion of curves in three dimensions the dynamic surface extension method fast methods for steady state problems diffusion generated motion and the variational level set approach we also give a user s guide to the level set dictionary and technology and couple the method to a wide variety of problems involving external physics such as compressible and incompressible possibly reacting flow stefan problems kinetic crystal growth epitaxial growth of thin films vortex dominated flows and extensions to multiphase motion we conclude with a discussion of applications to computer vision and image processing

a boundary condition capturing method for poisson s equation on irregular domains interfaces have a variety of boundary conditions or jump conditions that need to be enforced the ghost fluid method gfm was developed to capture the boundary conditions at a contact discontinuity in the inviscid euler equations and has been extended to treat more general discontinuities such as shocks detonations and deflagrations and compressible viscous flows in this paper a similar boundary condition capturing approach is used to develop a new numerical method for the variable coefficient poisson equation in the presence of interfaces where both the variable coefficients and the solution itself may be discontinuous this new method is robust and easy to implement even in three spatial dimensions furthermore the coefficient matrix of the associated linear system is the standard symmetric matrix for the variable coefficient poisson equation in the absence of interfaces allowing for straightforward application of standard black box solvers

a continuum method for modeling surface tension abstract a new method for modeling surface tension effects on fluid motion has been developed interfaces between fluids of different properties or colors are represented as transition regions of finite thickness across which the color variable varies continuously at each point in the transition region a force density is defined which is proportional to the curvature of the surface of constant color at that point it is normalized so that the conventional description of surface tension on an interface is recovered when the ratio of local transition region thickness to local radius of curvature approaches zero the continuum method eliminates the need for interface reconstruction simplifies the calculation of surface tension enables accurate modeling of two and three dimensional fluid flows driven by surface forces and does not impose any modeling restrictions on the number complexity or dynamic evolution of fluid interfaces having surface tension computational results for two dimensional flows are given to illustrate the properties of the method

nonconvexity of the stability domain of digital filters the stability of a causal digital filter with a rational transfer function h z is completely specified by the location of its poles with respect to the unit circle uc the set of points a corresponding to stable filters i e to polynomials p with roots inside the uc is called the stability domain sigma of digital filters results are established that concern the convexity of sigma the denominator of a rational digital filter of nth order is a polynomial represented by a point a of the n dimensional space of its coefficients it is shown that for n or 3 sigma is not convex and especially if point a belongs to sigma and a satisfies 0

computing minimal surfaces via level set curvature flow given a fixed closed curve or curves in r sp3 there is an associated problem of finding a surface with mean curvature zero which has that curve or curves as its boundary in this paper a new approach to numerically solving the minimal surface problem is introduced the surface is represented as a level set of a global function phi r sp3 to r the family of surfaces evolve in time according to mean curvature flow a solution is found when a steady state condition is achieved a new system of interpolatory boundary conditions are used to maintain the connection between the surface and the fixed boundary contour several computer surfaces are shown including examples of topological changes

robust pole assignment via reflection coefficients of polynomials a robust version of the output controller design for discrete time systems is introduced instead of a single stable point a stable polytope or simplex is preselected in the closed loop characteristic polynomial coefficients space a constructive procedure for generating stable polytopes is given starting from the unit hypercube of reflection coefficients of monic polynomials this procedure is quite straightforward because for a special family of polynomials the linear cover of so called reflection vectors is stable the roots placement of reflection vectors is studied if a stable target simplex is preselected then the robust output controller design task is solved by quadratic programming approach

dynamic mesh adaptation for front evolution using discontinuous galerkin based weighted condition number relaxation a new mesh smoothing method designed to cluster cells near a dynamically evolving interface is presented the method is based on weighted condition number mesh relaxation with the weight function computed from a level set representation of the interface the weight function is expressed as a taylor series based discontinuous galerkin projection which makes the computation of the derivatives of the weight function needed during the condition number optimization process a trivial matter for cases when a level set is not available a fast method for generating a low order level set from discrete cell centered fields such as a volume fraction or index function is provided results show that the low order level set works equally well as the actual level set for mesh smoothing meshes generated for a number of interface geometries are presented including cases with multiple level sets dynamic cases with moving interfaces show the new method is capable of maintaining a desired resolution near the interface with an acceptable number of relaxation iterations per time step which demonstrates the method s potential to be used as a mesh relaxer for arbitrary lagrangian eulerian ale methods

a fast approximation of the bilateral filter using a signal processing approach the bilateral filter is a nonlinear filter that smoothes a signal while preserving strong edges it has demonstrated great effectiveness for a variety of problems in computer vision and computer graphics and fast versions have been proposed unfortunately little is known about the accuracy of such accelerations in this paper we propose a new signal processing analysis of the bilateral filter which complements the recent studies that analyzed it as a pde or as a robust statistical estimator the key to our analysis is to express the filter in a higher dimensional space where the signal intensity is added to the original domain dimensions importantly this signal processing perspective allows us to develop a novel bilateral filtering acceleration using downsampling in space and intensity this affords a principled expression of accuracy in terms of bandwidth and sampling the bilateral filter can be expressed as linear convolutions in this augmented space followed by two simple nonlinearities this allows us to derive criteria for downsampling the key operations and achieving important acceleration of the bilateral filter we show that for the same running time our method is more accurate than previous acceleration techniques typically we are able to process a 2 megapixel image using our acceleration technique in less than a second and have the result be visually similar to the exact computation that takes several tens of minutes the acceleration is most effective with large spatial kernels furthermore this approach extends naturally to color images and cross bilateral filtering

maximum entropy and spectral estimation a review the method of maximum entropy is reviewed with emphasis on its relationship to entropy rate wiener filters autoregressive processes extrapolation the levinson algorithm lattice all pole and all pass filters and stability

tree methods for moving interfaces fast adaptive numerical methods for solving moving interface problems are presented the methods combine a level set approach with frequent redistancing and semi lagrangian time stepping schemes which are explicit yet unconditionally stable a quadtree mesh is used to concentrate computational effort on the interface so the methods move an interface withndegrees of freedom ino nlogn work per time step efficiency is increased by taking large time steps even for parabolic curvature flows the methods compute accurate viscosity solutions to a wide variety of difficult moving interface problems involving merging anisotropy faceting and curvature

motion of multiple junctions a level set approach abstract a coupled level set method for the motion of multiple junctions is proposed the new method extends the hamilton jacobi level set formulation of osher and sethian it retains the feature of tracking fronts by following level sets and allows the specification of arbitrary velocities on each front the diffusion equation is shown to generate curvature dependent motion and this is used to develop an algorithm to move multiple junctions with curvature dependent speed systems of reaction diffusion equations are shown to possess inherent properties which prohibit efficient numerical solutions when applied to curvature dependent motion

a note on a lp based heuristic for a time constrained routing problem in their paper avella et al 2006 investigate a time constrained routing problem the core of the proposed solution approach is a large scale linear program that grows both row and column wise when new variables are introduced thus a column and row generation algorithm is proposed to solve this linear program optimally and an optimality condition is presented to terminate the column and row generation algorithm we demonstrate by using lagrangian duality that this optimality condition is incorrect and may lead to a suboptimal solution at termination

numerical simulation of drop impact on a liquid liquid interface with a multiple marker front capturing method the gravity driven motion of a droplet impacting on a liquid liquid interface is studied the full navier stokes equations are solved on a fixed uniform grid using a finite difference front capturing method for the representation of fluid fluid interfaces a coupled level set volume of fluid method m sussman e g puckett a coupled level set and volume of fluid method for computing 3d and axisymmetric incompressible two phase flows j comp phys 162 2000 301 337 is used in which we introduce the novel approach of describing separate interfaces with different marker functions as a consequence we prevent numerical coalescence of the droplet and the liquid liquid interface without excessive local grid refinement to validate our method numerical simulations of the drop impact event are compared with experiments z mohamed kassim e k longmire drop impact on a liquid liquid interface phys fluids 15 2003 3263 3273 furthermore a comparison is made with the numerical results of a esmaeeli g tryggvason direct numerical simulations of bubbly flows part 2 moderate reynolds number arrays j fluid mech 385 1999 325 358 for an array of rising bubbles the investigation shows that the multiple marker approach successfully prevents numerical coalescence of interfaces and adequately captures the effect of surface tension

some properties of prediction and interpolation errors linear prediction and interpolation are widely used in signal processing usually they are obtained by linear filters of finite memory and the prediction and interpolation errors decrease when this memory increases if the asymptotic values of these errors are null the signal is singular some theoretical aspects of finite and infinite prediction and interpolation are discussed and a numerical method to compute the prediction and interpolation errors for signals with a given power spectrum is presented a large number of results obtained with this method are discussed especially the difference between regular and singular signals this method also allows the behavior of prediction and interpolation errors when the memory of the filter increases to be studied

dynamic active contours for visual tracking visual tracking using active contours is usually set in a static framework the active contour tracks the object of interest in a given frame of an image sequence a subsequent prediction step ensures good initial placement for the next frame this approach is unnatural the curve evolution gets decoupled from the actual dynamics of the objects to be tracked true dynamical approaches exist all being marker particle based and thus prone to the shortcomings of such particle based implementations in particular topological changes are not handled naturally in this framework the now classical level set approach is tailored for evolutions of manifolds of codimension one however dynamic curve evolution is at least a codimension two problem we propose an efficient level set based approach for dynamic curve evolution which addresses the artificial separation of segmentation and prediction while retaining all the desirable properties of the level set formulation it is based on a new energy minimization functional which for the first time puts dynamics into the geodesic active contour framework

benders decomposition and column and row generation for solving large scale linear programs with column dependent rows in a recent work muter birbil and bulbul 2013a identified and characterized a general class of linear programming lp problems known as problems with column dependent rows cdr problems these lps feature two sets of constraints with mutually exclusive groups of variables in addition to a set of structural linking constraints in which variables from both groups appear together in a typical cdr problem the number of linking constraints grows very quickly with the number of variables which motivates generating both columns and their associated linking constraints simultaneously on the fly in this paper we expose the decomposable structure of cdr problems via benders decomposition however this approach brings on its own theoretical challenges one group of variables is generated in the benders master problem while the generation of the linking constraints is relegated to the benders subproblem along with the second group of variables a fallout of this separation is that only a partial description of the dual of the benders subproblem is available over the course of the algorithm we demonstrate how the pricing subproblem for the column generation applied to the benders master problem does also update the dual polyhedron and the existing benders cuts in the master problem to ensure convergence ultimately a novel integration of benders cut generation and the simultaneous generation of columns and constraints yields a brand new algorithm for solving large scale cdr problems we illustrate the application of the proposed method on a time constrained routing problem our numerical experiments confirm the outstanding performance of the new decomposition method

the constrained compartmentalized knapsack problem mathematical models and solution methods the constrained compartmentalized knapsack problem can be seen as an extension of the constrained knapsack problem however the items are grouped into different classes so that the overall knapsack has to be divided into compartments and each compartment is loaded with items from the same class moreover building a compartment incurs a fixed cost and a fixed loss of the capacity in the original knapsack and the compartments are lower and upper bounded the objective is to maximize the total value of the items loaded in the overall knapsack minus the cost of the compartments this problem has been formulated as an integer non linear program and in this paper we reformulate the non linear model as an integer linear master problem with a large number of variables some heuristics based on the solution of the restricted master problem are investigated a new and more compact integer linear model is also presented which can be solved by a branch and bound commercial solver that found most of the optimal solutions for the constrained compartmentalized knapsack problem on the other hand heuristics provide good solutions with low computational effort

multidimensional spherical coordinates quantization several investigators have considered polar coordinates quantization of a circularly symmetric source in particular the independent bivariate gaussian source their schemes quantize the polar coordinates independently in an attempt to reduce the mean square error below that of an analogous rectangular coordinates quantizer yet retain an implementation simpler than that of the optimal bivariate quantizer the design of a spherical coordinates quantizer in k dimensions with k 2 k 2 matches published results is considered examples are presented along with comparisons to the rectangular one dimensional and optimal schemes

extensions of the stability criterion for arma filters using the lattice representation of an arma filter it is well known that the necessary and sufficient condition so that the poles are inside the unit circle is k i where the k i s are the reflection coefficients the filter is said to be wide sense stable if no pole is located outside the unit circle and it is interesting to characterize this stability by an appropriate necessary and sufficient condition to establish this condition the concept of canonical reflection coefficient is introduced which eliminates the problems appearing when the levinson recursion is not inversible some examples are discussed and a simple and practical test for wide sense stability is given

structural stability of least squares prediction methods a structural stability condition is sought for least squares linear prediction methods in the given data case save the toeplitz case the structure of the normal equation matrix yields no acknowledged guarantee of stability here a new sufficient condition is provided and several least squares prediction methods are shown to be structurally stable