from geometric quantization to moyal quantization it is shown how the moyal product of phase space functions and the weyl correspondence between symbols and operator kernels may be obtained directly using the procedures of geometric quantization applied to the symplectic groupoid constructed by doubling the phase space

robust noise region based active contour model via local similarity factor for image segmentation abstract image segmentation using a region based active contour model could present difficulties when its noise distribution is unknown to overcome this problem this paper proposes a novel region based model for the segmentation of objects or structures in images by introducing a local similarity factor which relies on the local spatial distance within a local window and local intensity difference to improve the segmentation results by using this local similarity factor the proposed method can accurately extract the object boundary while guaranteeing certain noise robustness furthermore the proposed algorithm completely avoids the pre processing steps typical of region based contour model segmentation resulting in a higher preservation of image details experiments performed on synthetic images and real word images demonstrate that the proposed algorithm as compared with the state of art algorithms is more efficient and robust to higher noise level manifestations in the images

black box multigrid one major problem with the multigrid method has been that each new grid configuration has required a major programming effort to develop a code that specifically handles that grid configuration such a penalty is not required for methods like sor iccg etc in these methods one need only specify the matrix problem no matter what the grid configuration in this paper we investigate such a situation for the multigrid method the end result is code boxmg in which one need only specify the logically rectangular positive definite matrix problem boxmg does everything else necessary to set up the auxilliary coarser problems to achieve a multigrid solution

multi reference shape priors for active contours in this paper we present a new way of constraining the evolution of an active contour with respect to a set of fixed reference shapes this approach is based on a description of shapes by the legendre moments computed from their characteristic function this provides a region based representation that can handle arbitrary shape topologies moreover exploiting the properties of moments it is possible to include intrinsic affine invariance in the descriptor which solves the issue of shape alignment without increasing the number of d o f of the initial problem and allows introducing geometric shape variabilities our new shape prior is based on a distance in terms of descriptors between the evolving curve and the reference shapes minimizing the corresponding shape energy leads to a geometric flow that does not rely on any particular representation of the contour and can be implemented with any contour evolution algorithm we introduce our prior into a two class segmentation functional showing its benefits on segmentation results in presence of severe occlusions and clutter examples illustrate the ability of the model to deal with large affine deformation and to take into account a set of reference shapes of different topologies

an active contour model and its algorithms with local and global gaussian distribution fitting energies in this paper we propose an active contour model and its corresponding algorithms with detailed implementation for image segmentation in the proposed model the local and global region fitting energies are described by the combination of the local and global gaussian distributions with different means and variances respectively in this combination we increase a weighting coefficient by which we can adjust the ratio between the local and global region fitting energies then we present an algorithm for implementing the proposed model directly considering that in practice the selection of the weighting coefficient is troublesome we present a modified algorithm in order to overcome this problem and increase the flexibility by adaptively updating the weighting coefficient and the time step with the contour evolution this algorithm is less sensitive to the initialization of the contour and can speed up the convergence rate besides it is robust to the noise and can be used to extract the desired objects experiment results demonstrate that the proposed model and its algorithms are effective with application to both the synthetic and real world images

active contours driven by local image fitting energy a new region based active contour model that embeds the image local information is proposed in this paper by introducing the local image fitting lif energy to extract the local image information our model is able to segment images with intensity inhomogeneities moreover a novel method based on gaussian filtering for variational level set is proposed to regularize the level set function it can not only ensure the smoothness of the level set function but also eliminate the requirement of re initialization which is very computationally expensive experiments show that the proposed method achieves similar results to the lbf local binary fitting energy model but it is much more computationally efficient in addition our approach maintains the sub pixel accuracy and boundary regularization properties

matrix dependent multigrid homogenization for diffusion problems for problems with strongly varying or discontinuous diffusion coefficients we present a method to compute coarse scale operators and to approximately determine the effective diffusion tensor on the coarse scale level the approach is based on techniques that are used in multigrid such as matrix dependent prolongations and the construction of coarse grid operators by means of the galerkin approximation in numerical experiments we compare our multigrid homogenization method with continuous homogenization renormalization and simple averaging approaches

elimination of adaptive grid interface errors in the discrete cell centered pressure equation classical cell centered discretization of the reservoir simulation pressure equation on anh adaptive grid results in ano 1 h leading truncation error at the grid interface a new flux continuous finite volume correction is presented together with an improved version of a previously proposed correction while both corrections eliminate the leading error the new correction exhibits the best convergence rates and has the following properties the resulting matrix is in general symmetric positive definite diagonally dominant for locally isotropic spatially varying coefficients convergence too h is demonstrated and support of the standard approximation is retained ensuring a fully implicit implementation results computed by the uncorrected classical scheme and both correction schemes are compared for two phase flow simulations with multilevel dynamic local grid refinement

fast finite volume simulation of 3d electromagnetic problems with highly discontinuous coefficients we consider solving three dimensional electromagnetic problems in parameter regimes where the quasi static approximation applies and the permeability permittivity and conductivity may vary significantly the difficulties encountered include handling solution discontinuities across interfaces and accelerating convergence of traditional iterative methods for the solution of the linear systems of algebraic equations that arise when discretizing maxwell s equations in the frequency domain the present article extends methods we proposed earlier for constant permeability e haber u ascher d aruliah and d oldenburg j comput phys 163 2000 pp 150 171 d aruliah u ascher e haber and d oldenburg math models methods appl sci to appear to handle also problems in which the permeability is variable and may contain significant jump discontinuities in order to address the problem of slow convergence we reformulate maxwell s equations in terms of potentials applying a helmholtz decomposition to either the electric field or the magnetic field the null space of the curl operators can then be annihilated by adding a stabilizing term using a gauge condition and thus obtaining a strongly elliptic differential operator a staggered grid finite volume discretization is subsequently applied to the reformulated pde system this scheme works well for sources of various types even in the presence of strong material discontinuities in both conductivity and permeability the resulting discrete system is amenable to fast convergence of ilu preconditioned krylov methods we test our method using several numerical examples and demonstrate its robust efficiency we also compare it to the classical yee method using similar iterative techniques for the resulting algebraic system and we show that our method is significantly faster especially for electric sources

fast simulation of 3d electromagnetic problems using potentials we consider solving three dimensional electromagnetic problems in parameter regimes where the quasi static approximation applies the permeability is constant the conductivity may vary significantly and the range of frequencies is moderate the difficulties encountered include handling solution discontinuities across interfaces and accelerating convergence of traditional iterative methods for the solution of the linear systems of algebraic equations that arise when discretizing maxwell s equations in the frequency domain we use a potential current formulation a with a coulomb gauge the potentials a and decompose the electric field e into components in the active and null spaces of the operator we develop a finite volume discretization on a staggered grid that naturally employs harmonic averages for the conductivity at cell faces after discretization we eliminate the current and the resulting large sparse linear system of equations has a block structure that is diagonally dominant allowing an efficient solution with preconditioned krylov space methods a particularly efficient algorithm results from the combination of bicgstab and an incomplete lu decomposition we demonstrate the efficacy of our method in several numerical experiments

weighted level set evolution based on local edge features for medical image segmentation level set methods have been widely used to implement active contours for image segmentation applications due to their good boundary detection accuracy in the context of medical image segmentation weak edges and inhomogeneities remain important issues that may hinder the accuracy of any segmentation method based on active contours implemented using level set methods this paper proposes a method based on active contours implemented using level set methods for segmentation of such medical images the proposed method uses a level set evolution that is based on the minimization of an objective energy functional whose energy terms are weighted according to their relative importance in detecting boundaries this relative importance is computed based on local edge features collected from the adjacent region located inside and outside of the evolving contour the local edge features employed are the edge intensity and the degree of alignment between the image s gradient vector flow field and the evolving contour s normal we evaluate the proposed method for segmentation of various regions in real mri and ct slices x ray images and ultra sound images evaluation results confirm the advantage of weighting energy forces using local edge features to reduce leakage these results also show that the proposed method leads to more accurate boundary detection results than the state of the art edge based level set segmentation methods particularly around weak edges

active contours driven by global and local weighted signed pressure force for image segmentation abstract this paper proposes a new global and local weighted signed pressure force spf based active contour model acm to segment various types of images first by introducing the normalized global minimum absolute differences as the coefficients of global inner and outer region fitting centers a new global weighted spf gwspf is defined which makes the best of the difference information of inner and outer regions and improves segmentation performance second by introducing the normalized local minimum absolute differences as the coefficients of local inner and outer region fitting centers similarly a new local weighted spf lwspf is defined and added to the above global weighted spf third the global and local within class variances of the image are used to weight the gwspf and the lwspf which can automatically adjust the effect degrees of the gwspf and the lwspf experiments on many kinds of real world images have validated that the proposed model is superior to popular acms in segmentation accuracy in addition it is robust to the initial curve

active contours driven by local likelihood image fitting energy for image segmentation accurate image segmentation is an essential step in image analysis and understanding where active contour models play an important part due to the noise low contrast and intensity inhomogeneity in images many segmentation algorithms suffer from limited accuracy this paper presents a novel region based active contour model for image segmentation by using the variational level set formulation in this model we construct the local likelihood image fitting llif energy functional by describing the neighboring intensities with local gaussian distributions the means and variances of local intensities in the llif energy functional are spatially varying functions which can be iteratively estimated during an energy minimization process to guide the contour evolving toward object boundaries to address diverse image segmentation needs we also expand this model to the multiphase level set multi scale gaussian kernels and narrowband formulations the proposed model has been compared with several state of the art active contour models on images with different modalities our results indicate that the proposed llif model achieves superior performance in image segmentation

nonparametric joint shape and feature priors for image segmentation in many image segmentation problems involving limited and low quality data employing statistical prior information about the shapes of the objects to be segmented can significantly improve the segmentation result however defining probability densities in the space of shapes is an open and challenging problem especially if the object to be segmented comes from a shape density involving multiple modes classes existing techniques in the literature estimate the underlying shape distribution by extending parzen density estimator to the space of shapes in these methods the evolving curve may converge to a shape from a wrong mode of the posterior density when the observed intensities provide very little information about the object boundaries in such scenarios employing both shape and class dependent discriminative feature priors can aid the segmentation process such features may involve e g intensity based textural or geometric information about the objects to be segmented in this paper we propose a segmentation algorithm that uses nonparametric joint shape and feature priors constructed by parzen density estimation we incorporate the learned joint shape and feature prior distribution into a maximum a posteriori estimation framework for segmentation the resulting optimization problem is solved using active contours we present experimental results on a variety of synthetic and real data sets from several fields involving multimodal shape densities experimental results demonstrate the potential of the proposed method

multigrid preconditioning for krylov methods for time harmonic maxwell s equations in three dimensions we consider the rapid simulation of three dimensional electromagnetic problems in geophysical parameter regimes where the conductivity may vary significantly and the range of frequencies is moderate toward developing a multigrid preconditioner we present a fourier analysis based on a finite volume discretization of a vector potential formulation of time harmonic maxwell s equations on a staggered grid in three dimensions we prove grid independent bounds on the eigenvalue and singular value ranges of the system obtained using a preconditioner based on exact inversion of the dominant diagonal blocks of the non hermitian coefficient matrix this result implies that a preconditioner that uses single multigrid cycles to effect inversion of the diagonal blocks also yields a preconditioned system with an ell 2 condition number bounded independent of the grid size we then present numerical examples for more realistic situations involving large variations in conductivity i e jump discontinuities block preconditioning with one multigrid cycle using dendy s boxmg solver is found to yield convergence in very few iterations apparently independent of the grid size the experiments show that the somewhat restrictive assumptions of the fourier analysis do not prohibit it from describing the essential local behavior of the preconditioned operator under consideration a very efficient practical solver is obtained

mimetic discretizations for maxwell s equations we have constructed reliable finite difference methods for approximating the solution to maxwell s equations using accurate discrete analogs of differential operators that satisfy the identities and theorems of vector and tensor calculus in discrete form the numerical approximation does not have spurious modes and mimics many fundamental properties of the underlying physical problem including conservation laws symmetries in the solution and the nondivergence of particular vector fields numerical examples demonstrate the high quality of the method when the medium is strongly discontinuous and for nonorthogonal nonsmooth computational grids

an octree multigrid method for quasi static maxwell s equations with highly discontinuous coefficients in this paper we develop an octree discretization for maxwell s equations in the quasi static regime we then use this discretization in order to develop a multigrid method for maxwell s equations with highly discontinuous coefficients we test our algorithms and compare it to other multilevel algorithms

toward an h independent algebraic multigrid method for maxwell s equations we propose a new algebraic multigrid amg method for solving the eddy current approximations to maxwell s equations this amg method has its roots in an algorithm proposed by reitzinger and schoberl the main focus in the reitzinger and schoberl method is to maintain null space properties of the weak nabla times nabla times operator on coarse grids while these null space properties are critical they are not enough to guarantee h independent convergence rates of the overall multigrid scheme we present a new strategy for choosing intergrid transfers that not only maintains the important null space properties on coarse grids but also yields significantly improved multigrid convergence rates this improvement is related to those we explored in a previous paper but is fundamentally simpler easier to compute and performs better with respect to both multigrid operator complexity and convergence rates the new strategy builds on ideas in smoothed aggregation to improve the approximation property of an existing interpolation operator by carefully choosing the smoothing operators we show how it is sometimes possible to achieve h independent convergence rates with a modest increase in multigrid operator complexity though this ideal case is not always possible the overall algorithm performs significantly better than the original scheme in both iterations and run time finally the reitzinger and schoberl method as well as our previous smoothed method are shown to be special cases of this new algorithm

a second order discretization of maxwell s equations in the quasi static regime on octree grids in this study we consider adaptive mesh refinement for the solution of maxwell s equations in the quasi static or diffusion regime we propose a new finite volume octree discretization for the problem and show how to construct second order stencils on yee grids extending the known first order discretization stencils we then develop an effective preconditioner to the problem we show that our preconditioner performs well for discontinuous conductivities as well as for a wide range of frequencies

a novel active contour model for image segmentation using distance regularization term abstract in this paper a novel active contour model r drlse model based on level set method is proposed for image segmentation the r drlse model is a variational level set approach that utilizes the region information to find image contours by minimizing the presented energy functional to avoid the time consuming re initialization step the distance regularization term is used to penalize the deviation of the level set function from a signed distance function the numerical implementation scheme of the model can significantly reduce the iteration number and computation time the results of experiments performed on some synthetic and real images show that the r drlse model is effective and efficient in particular our method has been applied to mr kidney image segmentation with desirable results

mimetic finite difference methods for diffusion equations on non orthogonal non conformal meshes mimetic discretizations based on the support operators methodology are derived for non orthogonal locally refined quadrilateral meshes the second order convergence rate on non smooth meshes is verified with numerical examples

distance regularized level set evolution and its application to image segmentation level set methods have been widely used in image processing and computer vision in conventional level set formulations the level set function typically develops irregularities during its evolution which may cause numerical errors and eventually destroy the stability of the evolution therefore a numerical remedy called reinitialization is typically applied to periodically replace the degraded level set function with a signed distance function however the practice of reinitialization not only raises serious problems as when and how it should be performed but also affects numerical accuracy in an undesirable way this paper proposes a new variational level set formulation in which the regularity of the level set function is intrinsically maintained during the level set evolution the level set evolution is derived as the gradient flow that minimizes an energy functional with a distance regularization term and an external energy that drives the motion of the zero level set toward desired locations the distance regularization term is defined with a potential function such that the derived level set evolution has a unique forward and backward fab diffusion effect which is able to maintain a desired shape of the level set function particularly a signed distance profile near the zero level set this yields a new type of level set evolution called distance regularized level set evolution drlse the distance regularization effect eliminates the need for reinitialization and thereby avoids its induced numerical errors in contrast to complicated implementations of conventional level set formulations a simpler and more efficient finite difference scheme can be used to implement the drlse formulation drlse also allows the use of more general and efficient initialization of the level set function in its numerical implementation relatively large time steps can be used in the finite difference scheme to reduce the number of iterations while ensuring sufficient numerical accuracy to demonstrate the effectiveness of the drlse formulation we apply it to an edge based active contour model for image segmentation and provide a simple narrowband implementation to greatly reduce computational cost

kernel density estimation and intrinsic alignment for shape priors in level set segmentation in this paper we make two contributions to the field of level set based image segmentation firstly we propose shape dissimilarity measures on the space of level set functions which are analytically invariant under the action of certain transformation groups the invariance is obtained by an intrinsic registration of the evolving level set function in contrast to existing approaches to invariance in the level set framework this closed form solution removes the need to iteratively optimize explicit pose parameters the resulting shape gradient is more accurate in that it takes into account the effect of boundary variation on the object s pose secondly based on these invariant shape dissimilarity measures we propose a statistical shape prior which allows to accurately encode multiple fairly distinct training shapes this prior constitutes an extension of kernel density estimators to the level set domain in contrast to the commonly employed gaussian distribution such nonparametric density estimators are suited to model aribtrary distributions we demonstrate the advantages of this multi modal shape prior applied to the segmentation and tracking of a partially occluded walking person in a video sequence and on the segmentation of the left ventricle in cardiac ultrasound images we give quantitative results on segmentation accuracy and on the dependency of segmentation results on the number of training shapes