automatic ventricular cavity boundary detection from sequential ultrasound images using simulated annealing an automatic algorithm has been developed for high speed detection of cavity boundaries in sequential 2 d echocardiograms using an optimization algorithm called simulated annealing sa the algorithm has three stages 1 a predetermined window of size n m is decimated to size n m after low pass filtering 2 an iterative radial gradient algorithm is employed to determine the center of gravity cg of the cavity 3 64 radii which originate from the cg defined in stage 2 are bounded by the high probability region each bounded radius is defined as a link in a 1 d 64 member cyclic markov random field this algorithm is unique in that it compounds spatial and temporal information along with a physical model in its decision rule whereas most other algorithms base their decisions on spatial data alone this is the first implementation of a relaxation algorithm for edge detection in echocardiograms results attained using this algorithm on real data have been highly encouraging

adaptive noise smoothing filter for images with signal dependent noise in this paper we consider the restoration of images with signal dependent noise the filter is noise smoothing and adapts to local changes in image statistics based on a nonstationary mean nonstationary variance nmnv image model for images degraded by a class of uncorrelated signal dependent noise without blur the adaptive noise smoothing filter becomes a point processor and is similar to lee s local statistics algorithm 16 the filter is able to adapt itself to the nonstationary local image statistics in the presence of different types of signal dependent noise for multiplicative noise the adaptive noise smoothing filter is a systematic derivation of lee s algorithm with some extensions that allow different estimators for the local image variance the advantage of the derivation is its easy extension to deal with various types of signal dependent noise film grain and poisson signal dependent restoration problems are also considered as examples all the nonstationary image statistical parameters needed for the filter can be estimated from the noisy image and no a priori information about the original image is required

estimating normal means with a dirichlet process prior abstract in this article the dirichlet process prior is used to provide a nonparametric bayesian estimate of a vector of normal means in the past there have been computational difficulties with this model this article solves the computational difficulties by developing a gibbs sampler algorithm the estimator developed in this article is then compared to parametric empirical bayes estimators peb and nonparametric empirical bayes estimators npeb in a monte carlo study the monte carlo study demonstrates that in some conditions the peb is better than the npeb and in other conditions the npeb is better than the peb the monte carlo study also shows that the estimator developed in this article produces estimates that are about as good as the peb when the peb is better and produces estimates that are as good as the npeb estimator when that method is better

a finite dimensional approach to light rays in general relativity abstract we propose a finite dimensional setup for the study of lightlike geodesics starting orthogonally to a spacelike n 2 submanifold and arriving orthogonally to the time slices of an n 1 dimensional timelike submanifold of a n dimensional spacetime under a transversality and a nonfocality assumption we prove a finite dimensional reduction of a general relativistic fermat principle and we give a formula for the morse index we present some applications to bifurcation theory and we conclude the paper with the discussion of some examples that illustrate our results

the method of space time conservation element and solution element a new approach for solving the navier stokes and euler equations a new numerical framework for solving conservation laws is being developed this new framework differs substantially in both concept and methodology from the well established methods i e finite difference finite volume finite element and spectral methods it is conceptually simple and designed to overcome several key limitations of the above traditional methods a two level scheme for solving the convection diffusion equation u t a u x 2u x2 0 0 is constructed and used to illuminate major differences between the present method and those mentioned above this explicit scheme referred to as the a scheme has two independent marching variables unj and ux nj which are the numerical analogues of u and u x at j n respectively the a scheme has the unusual property that its stability is limited only by the cfl condition i e it is independent of also it can be shown that the amplification factors of the a scheme are identical to those of the leapfrog scheme if o and to those of the dufort frankel scheme if a o these coincidences are unexpected because the a scheme and the above classical schemes are derived from completely different perspectives and the a scheme does not reduce to the above classical schemes in the limiting cases the a scheme is extended to solve the 1d time dependent navier stokes equations of a perfect gas stability of this explicit solver also is limited only by the cfl condition in spite of the fact that it does not use i any techniques related to the high resolution upwind methods and ii any ad hoc parameter the current navier stokes solver is capable of generating highly accurate shock tube solutions particularly for high reynolds number flows shock discontinuities can be resolved within one mesh interval the inviscid 0 a scheme is reversible in time it also is neutrally stable i e free from numerical dissipation such a scheme generally cannot be extended to solve the euler equations thus the inviscid version is modified stability of this modified scheme referred to as the a scheme is limited by the cfl condition and 0 1 where is a special parameter that controls numerical dissipation moreover if 0 the amplification factors of the a scheme are identical to those of the leapfrog scheme which has no numerical dissipation on the other hand if 1 the two amplification factors of the a scheme become the same function of the courant number and the phase angle unexpectedly this function also is the amplification factor of the highly diffusive lax scheme note that because the lax scheme is very diffusive and it uses a mesh that is staggered in time a two level scheme using such a mesh is often associated with a highly diffusive scheme the a scheme which also uses a mesh staggering in time demonstrates that it can also be a scheme with no numerical dissipation the euler extension of the a scheme has stability conditions similar to those of the a epsiv scheme itself it has the unusual property that numerical dissipation at all mesh points can be controlled by a set of local parameters moreover it is capable of generating accurate shock tube solutions with the cfl number ranging from close to 1 to 0 022

scale space and edge detection using anisotropic diffusion a new definition of scale space is suggested and a class of algorithms used to realize a diffusion process is introduced the diffusion coefficient is chosen to vary spatially in such a way as to encourage intraregion smoothing rather than interregion smoothing it is shown that the no new maxima should be generated at coarse scales property of conventional scale space is preserved as the region boundaries in the approach remain sharp a high quality edge detector which successfully exploits global information is obtained experimental results are shown on a number of images parallel hardware implementations are made feasible because the algorithm involves elementary local operations replicated over the image

comparing images using the hausdorff distance the hausdorff distance measures the extent to which each point of a model set lies near some point of an image set and vice versa thus this distance can be used to determine the degree of resemblance between two objects that are superimposed on one another efficient algorithms for computing the hausdorff distance between all possible relative positions of a binary image and a model are presented the focus is primarily on the case in which the model is only allowed to translate with respect to the image the techniques are extended to rigid motion the hausdorff distance computation differs from many other shape comparison methods in that no correspondence between the model and the image is derived the method is quite tolerant of small position errors such as those that occur with edge detectors and other feature extraction methods it is shown that the method extends naturally to the problem of comparing a portion of a model against an image

an index theorem for non periodic solutions of hamiltonian systems we consider a hamiltonian setup m h l p where m is a symplectic manifold l is a distribution of lagrangian subspaces in m p a lagrangian submanifold of m h is a smooth time dependent hamiltonian function on m and a b m is an integral curve of the hamiltonian flow h starting at p we do not require any convexity property of the hamiltonian function h under the assump tion that b is not p focal it is introduced the maslov index imaslov of given in terms of the first relative homology group of the lagrangian g rassmannian under generic circumstances imaslov is computed as a sort of algebraic count of the p focal points along we prove the following version of the index theorem under suitable hypothe ses the morse index of the lagrangian action functional restricted to suitable variations of is equal to the sum of imaslov and a convexity term of the hamiltonian h rela tive to the submanifold p when the result is applied to the case of the cotangent bundle m t mof a semi riemannian manifold m g and to the geodesic hamiltonian h q p 1 g 1 p p we obtain a semi riemannian version of the celebrated morse index theorem for geodesics with variable endpoints in riemannian geometry

a stochastic method for bayesian estimation of hidden markov random field models with application to a color model we propose a new stochastic algorithm for computing useful bayesian estimators of hidden markov random field hmrf models that we call exploration selection estimation ese procedure the algorithm is based on an optimization algorithm of o francois called the exploration selection e s algorithm the novelty consists of using the a posteriori distribution of the hmrf as exploration distribution in the e s algorithm the ese procedure computes the estimation of the likelihood parameters and the optimal number of region classes according to global constraints as well as the segmentation of the image in our formulation the total number of region classes is fixed but classes are allowed or disallowed dynamically this framework replaces the mechanism of the split and merge of regions that can be used in the context of image segmentation the procedure is applied to the estimation of a hmrf color model for images whose likelihood is based on multivariate distributions with each component following a beta distribution meanwhile a method for computing the maximum likelihood estimators of beta distributions is presented experimental results performed on 100 natural images are reported we also include a proof of convergence of the e s algorithm in the case of nonsymmetric exploration graphs

regular article the space time conservation element and solution element method a new high resolution and genuinely multidimensional paradigm for solving conservation laws a new high resolution and genuinely multidimensional numerical method for solving conservation laws is being developed it was designed to avoid the limitations of the traditional methods and was built from ground zero with extensive physics considerations nevertheless its foundation is mathematically simple enough that one can build from it a coherent robust efficient and accurate numerical framework two basic beliefs that set the new method apart from the established methods are at the core of its development the first belief is that in order to capture physics more efficiently and realistically the modeling focus should be placed on the original integral form of the physical conservation laws rather than the differential form the latter form follows from the integral form under the additional assumption that the physical solution is smooth an assumption that is difficult to realize numerically in a region of rapid change such as a boundary layer or a shock the second belief is that with proper modeling of the integral and differential forms themselves the resulting numerical solution should automatically be consistent with the properties derived from the integral and differential forms e g the jump conditions across a shock and the properties of characteristics therefore a much simpler and more robust method can be developed by avoiding the explicit use of the above derived properties specifically to capture physics as fully as possible the method requires that i space and time be unified and treated as a single entity ii both local and global flux conservation in space and time be enforced and iii a multidimensional scheme be constructed without using the dimensional splitting approach such that multidimensional effects and source terms which are scalars can be modeled more realistically to simplify mathematics and broaden its applicability as much as possible the method attempts to use the simplest logical structures and approximation techniques specifically i it uses a staggered space time mesh such that flux at any interface separating two conservation elements can be evaluated internally in a simpler and more consistent manner without using a separate flux model ii it avoids the use of many well established techniques such as riemann solvers flux splittings and monotonicity constraints such that the complications and possibly even the limitations associated with them may be avoided and iii it avoids the use of special techniques that are not applicable to more general problems furthermore triangles in 2d space and tetrahedrons in 3d space are used as the basic building blocks of the spatial meshes such that the method i can be used to construct 2d and 3d nondissipative schemes in a natural manner and ii is compatible with the simplest unstructured meshes note that while numerical dissipation is required for shock capturing it may also result in annihilation of small disturbances such as sound waves and in the case of flow with a large reynolds number may overwhelm physical dissipation to overcome this difficulty two different and mutually complementary types of adjustable numerical dissipation are introduced in the present development

partial discreteness a novel prior for magnetic resonance image reconstruction an important factor influencing the quality of magnetic resonance mr images is the reconstruction method that is employed and specifically the type of prior knowledge that is exploited during reconstruction in this work we introduce a new type of prior knowledge partial discreteness pd where a small number of regions in the image are assumed to be homogeneous and can be well represented by a constant magnitude in particular we mathematically formalize the partial discreteness property based on a gaussian mixture model gmm and derive a partial discreteness image representation that characterizes the salient features of partially discrete images a constant intensity in homogeneous areas and texture in heterogeneous areas the partial discreteness representation is then used to construct a novel prior dedicated to the reconstruction of partially discrete mr images the strength of the proposed prior is demonstrated on various simulated and real k space data based experiments with partially discrete images results demonstrate that the pd algorithm performs competitively with state of the art reconstruction methods being flexible and easy to implement

speckle reducing anisotropic diffusion this paper provides the derivation of speckle reducing anisotropic diffusion srad a diffusion method tailored to ultrasonic and radar imaging applications srad is the edge sensitive diffusion for speckled images in the same way that conventional anisotropic diffusion is the edge sensitive diffusion for images corrupted with additive noise we first show that the lee and frost filters can be cast as partial differential equations and then we derive srad by allowing edge sensitive anisotropic diffusion within this context just as the lee 1980 1981 1986 and frost 1982 filters utilize the coefficient of variation in adaptive filtering srad exploits the instantaneous coefficient of variation which is shown to be a function of the local gradient magnitude and laplacian operators we validate the new algorithm using both synthetic and real linear scan ultrasonic imagery of the carotid artery we also demonstrate the algorithm performance with real sar data the performance measures obtained by means of computer simulation of carotid artery images are compared with three existing speckle reduction schemes in the presence of speckle noise speckle reducing anisotropic diffusion excels over the traditional speckle removal filters and over the conventional anisotropic diffusion method in terms of mean preservation variance reduction and edge localization

evaluation of four probability distribution models for speckle in clinical cardiac ultrasound images segmenting cardiac ultrasound images requires a model for the statistics of speckle in the images although the statistics of speckle are well understood for the raw transducer signal the statistics of speckle in the image are not this paper evaluates simple empirical models for first order statistics for the distribution of gray levels in speckle the models are created by analyzing over 100 images obtained from commercial ultrasound machines in clinical settings the data in the images suggests a unimodal scalable family of distributions as a plausible model four families of distributions gamma weibull normal and log normal are compared with the data using goodness of fit and misclassification tests attention is devoted to the analysis of artifacts in images and to the choice of goodness of fit and misclassification tests the distribution of parameters of one of the models is investigated and priors for the distribution are suggested

nonlinear multiscale analysis of three dimensional echocardiographic sequences introduces a new model for multiscale analysis of space time echocardiographic sequences the proposed nonlinear partial differential equation representing the multiscale analysis filters the sequence while keeping the space time coherent structures it combines the ideas of regularized perona malik anisotropic diffusion and the galilean invariant movie multiscale analysis of alvarez et al arch rat mech anal vol 123 p 200 57 1993 a numerical method for solving the proposed partial differential equation is suggested and its stability is shown computational results on synthesized and real sequences are provided a qualitative and quantitative evaluation of the accuracy of the method is presented

segmentation in ultrasonic b mode images of healthy carotid arteries using mixtures of nakagami distributions and stochastic optimization the goal of this work is to perform a segmentation of the intimamedia thickness imt of carotid arteries in view of computing various dynamical properties of that tissue such as the elasticity distribution elastogram the echogenicity of a region of interest comprising the intima media layers the lumen and the adventitia in an ultrasonic b mode image is modeled by a mixture of three nakagami distributions in a first step we compute the maximum a posteriori estimator of the proposed model using the expectation maximization em algorithm we then compute the optimal segmentation based on the estimated distributions as well as a statistical prior for disease free imt using a variant of the exploration selection es algorithm convergence of the es algorithm to the optimal solution is assured asymptotically and is independent of the initial solution in particular our method is well suited to a semi automatic context that requires minimal manual initialization tests of the proposed method on 30 sequences of ultrasonic b mode images of presumably disease free control subjects are reported they suggest that the semi automatic segmentations obtained by the proposed method are within the variability of the manual segmentations of two experts

application of space time ce se method to shallow water magnetohydrodynamic equations in this article we apply a space time conservation element and solution element ce se method for the approximate solution of shallow water magnetohydrodynamic smhd equations in one and two space dimensions these equations model the dynamics of nearly incompressible conducting fluids for which the evolution is nearly two dimensional with magnetic equilibrium in the third direction in this article we are using a variant of the ce se method developed by zhang et al a space time conservation element and solution element method for solving the two dimensional unsteady euler equations using quadrilateral and hexahedral meshes j comput phys 175 2002 168 199 this method uses structured and unstructured quadrilateral and hexahedral meshes in two and three space dimensions respectively in this method a single conservation element at each grid point is employed for solving conservation laws no matter in one two and three space dimensions the present scheme use the conservation element to calculate flow variables only while the gradients of flow variables are calculated by central differencing reconstruction procedure we give both one and two dimensional test computations a qualitative comparison reveals an excellent agreement with previous published results of wave propagation method and evolution galerkin schemes the one and two dimensional computations reported in this paper demonstrate the remarkable versatility of the present ce se scheme

fusion of hidden markov random field models and its bayesian estimation in this paper we present a hidden markov random field hmrf data fusion model the proposed model is applied to the segmentation of natural images based on the fusion of colors and textons into julesz ensembles the corresponding exploration selection estimation ese procedure for the estimation of the parameters is presented this method achieves the estimation of the parameters of the gaussian kernels the mixture proportions the region labels the number of regions and the markov hyper parameter meanwhile we present a new proof of the asymptotic convergence of the ese procedure based on original finite time bounds for the rate of convergence

the morse index theorem where the ends are submanifolds in this paper the morse index theorem is proven in the case where submanifolds p and q are at the endpoints of a geodesic y at y the index of the hessian of the energy function defined on paths joining p and q is computed using p focal points and a calculation at the endpoint of y involving the second fundamental form of q

a volterra type model for image processing we present a class of time delay anisotropic diffusion models for image restoration these models lead to asymptotic states that are selected on the basis of a contrast parameter and bear some analogy with neural networks with hebbian dynamical learning rules numerical examples show that these models are efficient in removing even high levels of noise while allowing an accurate tracking of the edges

a note on the morse index theorem for geodesics between submanifolds in semi riemannian geometry the computation of the index of the hessian of the action functional in semi riemannian geometry at geodesics with two variable endpoints is reduced to the case of a fixed final endpoint using this observation we give an elementary proof of the morse index theorem for riemannian geodesics with two variable endpoints in the spirit of the original morse proof this approach reduces substantially the effort required in the proofs of the theorem given previously ann math 73 1 49 86 1961 j diff geom 12 567 581 1977 trans am math soc 308 1 341 348 1988 exactly the same argument works also in the case of timelike geodesics between two submanifolds of a lorentzian manifold for the extension to the lightlike lorentzian case just minor changes are required and one obtains easily a proof of the focal index theorem previously presented j geom phys 6 4 657 670 1989

a space time conservation element and solution element method for solving the two and three dimensional unsteady euler equations using quadrilateral and hexahedral meshes in this paper we report a version of the space time conservation element and solution element ce se method in which the 2d and 3d unsteady euler equations are simulated using structured or unstructured quadrilateral and hexahedral meshes respectively in the present method mesh values of flow variables and their spatial derivatives are treated as independent unknowns to be solved for at each mesh point the value of a flow variable is obtained by imposing a flux conservation condition on the other hand the spatial derivatives are evaluated using a finite difference weighted average procedure note that the present extension retains many key advantages of the original ce se method which uses triangular and tetrahedral meshes respectively for its 2d and 3d applications these advantages include efficient parallel computing ease of implementing nonreflecting boundary conditions high fidelity resolution of shocks and waves and a genuinely multidimensional formulation without the need to use a dimensional splitting approach in particular because riemann solvers the cornerstones of the godunov type upwind schemes are not needed to capture shocks the computational logic of the present method is considerably simpler to demonstrate the capability of the present method numerical results are presented for several benchmark problems including oblique shock reflection supersonic flow over a wedge and a 3d detonation flow

functions on the sphere with critical points in pairs and orthogonal geodesic chords abstract using an estimate on the number of critical points for a morse even function on the sphere s m m 1 we prove a multiplicity result for orthogonal geodesic chords in riemannian manifolds with boundary that are diffeomorphic to euclidean balls this yields also a multiplicity result for brake orbits in a potential well

a well balanced scheme for the numerical processing of source terms in hyperbolic equations in a variety of physical problems one encounters source terms that are balanced by internal forces and this balance supports multiple steady state solutions that are stable typical of these are gravity driven flows such as those described by the shallow water equations over a nonuniform ocean bottom 1 10 qquad h t hu x 0 text and hu t left hu 2 frac gh 2 2 right x ga x x h 0 many classic numerical schemes cannot maintain these steady solutions or achieve them in the long time limit with an acceptable level of accuracy because they do not preserve the proper balance between the source terms and internal forces we propose here a numerical scheme adapted to a scalar conservation law that preserves this balance and that can it is hoped be extended to more general hyperbolic systems the proof of convergence of this scheme toward the entropy solution is given and some numerical tests are reported

on the statistical analysis of dirty pictures may 7th 1986 professor a f m smith in the chair summary a continuous two dimensional region is partitioned into a fine rectangular array of sites or pixels each pixel having a particular colour belonging to a prescribed finite set the true colouring of the region is unknown but associated with each pixel there is a possibly multivariate record which conveys imperfect information about its colour according to a known statistical model the aim is to reconstruct the true scene with the additional knowledge that pixels close together tend to have the same or similar colours in this paper it is assumed that the local characteristics of the true scene can be represented by a nondegenerate markov random field such information can be combined with the records by bayes theorem and the true scene can be estimated according to standard criteria however the computational burden is enormous and the reconstruction may reflect undesirable largescale properties of the random field thus a simple iterative method of reconstruction is proposed which does not depend on these large scale characteristics the method is illustrated by computer simulations in which the original scene is not directly related to the assumed random field some complications including parameter estimation are discussed potential applications are mentioned briefly

localization of shapes using statistical models and stochastic optimization in this paper we present a new model for deformations of shapes a pseudolikelihood is based on the statistical distribution of the gradient vector field of the gray level the prior distribution is based on the probabilistic principal component analysis ppca we also propose a new model based on mixtures of ppca that is useful in the case of greater variability in the shape a criterion of global or local object specificity based on a preliminary color segmentation of the image is included into the model the localization of a shape in an image is then viewed as minimizing the corresponding gibbs field we use the exploration selection e s stochastic algorithm in order to find the optimal deformation this yields a new unsupervised statistical method for localization of shapes in order to estimate the statistical parameters for the gradient vector field of the gray level we use an iterative conditional estimation ice procedure the color segmentation of the image can be computed with an exploration selection estimation ese procedure

a multiphase godunov method for compressible multifluid and multiphase flows we propose a new model and a solution method for two phase compressible flows the model involves six equations obtained from conservation principles applied to each phase completed by a seventh equation for the evolution of the volume fraction this equation is necessary to close the overall system the model is valid for fluid mixtures as well as for pure fluids the system of partial differential equations is hyperbolic hyperbolicity is obtained because each phase is considered to be compressible two difficulties arise for the solution one of the equations is written in non conservative form non conservative terms exist in the momentum and energy equations we propose robust and accurate discretisation of these terms the method solves the same system at each mesh point with the same algorithm it allows the simulation of interface problems between pure fluids as well as multiphase mixtures several test cases where fluids have compressible behavior are shown as well as some other test problems where one of the phases is incompressible the method provides reliable results is able to compute strong shock waves and deals with complex equations of state

nonlocal means based speckle filtering for ultrasound images in image processing restoration is expected to improve the qualitative inspection of the image and the performance of quantitative image analysis techniques in this paper an adaptation of the nonlocal nl means filter is proposed for speckle reduction in ultrasound us images originally developed for additive white gaussian noise we propose to use a bayesian framework to derive a nl means filter adapted to a relevant ultrasound noise model quantitative results on synthetic data show the performances of the proposed method compared to well established and state of the art methods results on real images demonstrate that the proposed method is able to preserve accurately edges and structural details of the image

application of the space time conservation element and solution element method to one dimensional convection diffusion problems abstract in the space time conservation element and solution element ce se method the independent marching variables used comprise not only the mesh values of the physical dependent variables but also in contrast to a typical numerical method the mesh values of the spatial derivatives of these physical variables the use of the extra marching variables results from the need to construct the two level explicit and nondissipative schemes which are at the core of the ce se development it also results from the need to minimize the stencil while maintaining accuracy in this paper using the 1d a scheme as an example the effect of this added complication on consistency accuracy and operation count is assessed as part of this effort an equivalent yet more efficient form of the a scheme in which the independent marching variables are the local fluxes tied to each mesh point is introduced also the intriguing relations that exist among the a leapfrog and dufort frankel schemes are further explored in addition the redundancy of the leapfrog dufort frankel and lax schemes and the remedy for this redundancy are discussed this paper is concluded with the construction and evaluation of a ce se solver for the inviscid burgers equation

central upwind schemes for the system of shallow water equations with horizontal temperature gradients we introduce a central upwind scheme for one and two dimensional systems of shallow water equations with horizontal temperature gradients the ripa system the scheme is well balanced positivity preserving and does not develop spurious pressure oscillations in the neighborhood of temperature jumps that is near the contact waves such oscillations would typically appear when a conventional godunov type finite volume method is applied to the ripa system and the nature of the oscillation is similar to the ones appearing at material interfaces in compressible multifluid computations the idea behind the proposed approach is to utilize the interface tracking method originally developed in chertock et al m2an math model numer anal 42 991 1019 2008 for compressible multifluids the resulting scheme is highly accurate preserves two types of lake at rest steady states and is oscillation free across the temperature jumps as it is illustrated in a number of numerical experiments

fuzzy density weight based support vector regression for image denoising support vector machine svm is a popular machine learning technique and its variant least squares support vector regression ls svr is effective for image denoising however conventional ls svr does not fully consider the sampling distribution of noisy images which may degrade the performance of the algorithm in this paper we propose a new fuzzy density weight svr fdw svr denoising algorithm which assigns fuzzy priority to each sample according to its density weight fdw is designed to estimate the joint probability density function via the fuzzy theory based on the pixel density and neighborhood density extensive experimental results show that fdw svr is superior to those state of the art denoising techniques in light of both subjective and objective evaluations

the space time cese scheme for shallow water equations incorporating variable bottom topography and horizontal temperature gradients abstract the effects of bottom topography and horizontal temperature gradients on the shallow water flows are theoretically investigated the considered systems of partial differential equations pdes are non strictly hyperbolic and non conservative due to the presence of non conservative differential terms on the right hand side the solutions of these model equations are very challenging for a numerical scheme thus our primary goal is to introduce an improved numerical scheme which can handle the non conservative differential terms efficiently and accurately in this paper the space time conservation element and solution element cese method is extended to approximate these model equations the proposed scheme has capability to overcome all difficulties posed by this nonlinear system of pdes the performance of the scheme is analyzed by considering several case studies of practical interest and the results of suggested scheme are compared with those of central nt scheme the accuracy of the scheme is verified qualitatively and quantitatively

on the estimation of the coefficient of variation for anisotropic diffusion speckle filtering in this paper we focus on the problem of speckle removal by means of anisotropic diffusion and specifically on the importance of the correct estimation of the statistics involved first we derive an anisotropic diffusion filter that does not depend on a linear approximation of the speckle model assumed which is the case of a previously reported filter namely srad then we focus on the problem of estimation of the coefficient of variation of both signal and noise and of noise itself our experiments indicate that neighborhoods used for parameter estimation do not need to coincide with those used in the diffusion equations then we show that as long as the estimates are good enough the filter proposed here and the srad perform fairly closely a fact that emphasizes the importance of the correct estimation of the coefficients of variation

oriented speckle reducing anisotropic diffusion ultrasound imaging systems provide the clinician with noninvasive low cost and real time images that can help them in diagnosis planning and therapy however although the human eye is able to derive the meaningful information from these images automatic processing is very difficult due to noise and artifacts present in the image the speckle reducing anisotropic diffusion filter was recently proposed to adapt the anisotropic diffusion filter to the characteristics of the speckle noise present in the ultrasound images and to facilitate automatic processing of images we analyze the properties of the numerical scheme associated with this filter using a semi explicit scheme we then extend the filter to a matrix anisotropic diffusion allowing different levels of filtering across the image contours and in the principal curvature directions we also show a relation between the local directional variance of the image intensity and the local geometry of the image which can justify the choice of the gradient and the principal curvature directions as a basis for the diffusion matrix finally different filtering techniques are compared on a 2 d synthetic image with two different levels of multiplicative noise and on a 3 d synthetic image of a y junction and the new filter is applied on a 3 d real ultrasound image of the liver

anisotropic diffusion filter with memory based on speckle statistics for ultrasound images ultrasound us imaging exhibits considerable difficulties for medical visual inspection and for development of automatic analysis methods due to speckle which negatively affects the perception of tissue boundaries and the performance of automatic segmentation methods with the aim of alleviating the effect of speckle many filtering techniques are usually considered as a preprocessing step prior to automatic analysis methods or visual inspection most of the state of the art filters try to reduce the speckle effect without considering its relevance for the characterization of tissue nature however the speckle phenomenon is the inherent response of echo signals in tissues and can provide important features for clinical purposes this loss of information is even magnified due to the iterative process of some speckle filters e g diffusion filters which tend to produce over filtering because of the progressive loss of relevant information for diagnostic purposes during the diffusion process in this paper we propose an anisotropic diffusion filter with a probabilistic driven memory mechanism to overcome the over filtering problem by following a tissue selective philosophy in particular we formulate the memory mechanism as a delay differential equation for the diffusion tensor whose behavior depends on the statistics of the tissues by accelerating the diffusion process in meaningless regions and including the memory effect in regions where relevant details should be preserved results both in synthetic and real us images support the inclusion of the probabilistic memory mechanism for maintaining clinical relevant structures which are removed by the state of the art filters

wall position and thickness estimation from sequences of echocardiographic images presents a new method for endocardial inner and epicardial outer contour estimation from sequences of echocardiographic images the framework herein introduced is fine tuned for parasternal short axis views at the papillary muscle level the underlying model is probabilistic it captures the relevant features of the image generation physical mechanisms and of the heart morphology contour sequences are assumed to be two dimensional noncausal first order markov random processes each variable has a spatial index and a temporal index the image pixels are modeled as rayleigh distributed random variables with means depending on their positions inside endocardium between endocardium and pericardium or outside pericardium the complete probabilistic model is built under the bayesian framework as estimation criterion the maximum a posteriori map is adopted to solve the optimization problem one is led to joint estimation of contours and distributions parameters the authors introduce an algorithm herein named iterative multigrid dynamic programming imdp it is a fully data driven scheme with no ad hoc parameters the method is implemented on an ordinary workstation leading to computation times compatible with operational use experiments with simulated and real images are presented