efficient evaluation of 1 d and 2 d polynomials at equispaced points an extension to the two dimensional case of a previously published fast algorithm for evaluating exponential functions and polynomials over periodically distributed points is generalized to evaluate two dimensional polynomials efficiently over general periodic parallelograms the problem of getting the initial values required for other fast algorithms is treated in a general manner fast algorithms are presented for computing initial values in both cases of one and two dimensional polynomials it is observed that the two dimensional recursion is not always advantageous compared with taking the one dimensional recursion for each variable separately

active contours without edges we propose a new model for active contours to detect objects in a given image based on techniques of curve evolution mumford shah 1989 functional for segmentation and level sets our model can detect objects whose boundaries are not necessarily defined by the gradient we minimize an energy which can be seen as a particular case of the minimal partition problem in the level set formulation the problem becomes a mean curvature flow like evolving the active contour which will stop on the desired boundary however the stopping term does not depend on the gradient of the image as in the classical active contour models but is instead related to a particular segmentation of the image we give a numerical algorithm using finite differences finally we present various experimental results and in particular some examples for which the classical snakes methods based on the gradient are not applicable also the initial curve can be anywhere in the image and interior contours are automatically detected

coupling fluid flow with porous media flow the transport of substances back and forth between surface water and groundwater is a very serious problem we study herein the mathematical model of this setting consisting of the stokes equations in the fluid region coupled with the darcy equations in the porous medium coupled across the interface by the beavers joseph saffman conditions we prove existence of weak solutions and give a complete analysis of a finite element scheme which allows a simulation of the coupled problem to be uncoupled into steps involving porous media and fluid flow subproblems this is important because there are many legacy codes available which have been optimized for uncoupled porous media and fluid flow

on fast evaluation of bivariate polynomials at equispaced arguments the initial value problem arising in the recursive evaluation of a 2d polynomial at equispaced points is treated in detail the results facilitate efficient implementation of bose s recursive algorithm the computational complexity is compared with that involved in a direct computation and some general observations are made for an alternative scheme proposed by x nie and r unbehauen 1989

using dynamic programming for solving variational problems in vision dynamic programming is discussed as an approach to solving variational problems in vision dynamic programming ensures global optimality of the solution is numerically stable and allows for hard constraints to be enforced on the behavior of the solution within a natural and straightforward structure as a specific example of the approach s efficacy applying dynamic programming to the energy minimizing active contours is described the optimization problem is set up as a discrete multistage decision process and is solved by a time delayed discrete dynamic programming algorithm a parallel procedure for decreasing computational costs is discussed

encoding of a priori information in active contour models the theory of active contours models the problem of contour recovery as an energy minimization process the computational solutions based on dynamic programming require that the energy associated with a contour candidate can be decomposed into an integral of local energy contributions in this paper we propose a grammatical framework that can model different local energy models and a set of allowable transitions between these models the grammatical encodings are utilized to represent a priori knowledge about the shape of the object and the associated signatures in the underlying images the variability encountered in numerical experiments is addressed with the energy minimization procedure which is embedded in the grammatical framework we propose an algorithmic solution that combines a nondeterministic version of the knuth morris pratt algorithm for string matching with a time delayed discrete dynamic programming algorithm for energy minimization the numerical experiments address practical problems encountered in contour recovery such as noise robustness and occlusion

korn s inequalities for piecewise h 1 vector fields korn s inequalities for piecewise h 1 vector fields are established they can be applied to classical nonconforming finite element methods mortar methods and discontinuous galerkin methods

snakes active contour models a snake is an energy minimizing spline guided by external constraint forces and influenced by image forces that pull it toward features such as lines and edges snakes are active contour models they lock onto nearby edges localizing them accurately scale space continuation can be used to enlarge the capture region surrounding a feature snakes provide a unified account of a number of visual problems including detection of edges lines and subjective contours motion tracking and stereo matching we have used snakes successfully for interactive interpretation in which user imposed constraint forces guide the snake near features of interest

efficient evaluation of polynomials and exponentials of polynomials for equispaced arguments a kth order polynomial can be evaluated by means of k additions and no multiplications when done in a recursive fashion at equispaced arguments the evaluation of an exponential of a kth order polynomial can be accomplished by k multiplications and no additions or exponentiations combinations of rational functions and exponentials can therefore be realized very efficiently by combining these properties

a theoretical analysis of the properties of median filters necessary and sufficient conditions for a signal to be invariant under a specific form of median filtering are derived these conditions state that a signal must be locally monotone to pass through a median filter unchanged it is proven that the form of successive median filtering of a signal i e the filtered output is itself again filtered eventually reduces the original signal to an invariant signal called a root signal for a signal of length l samples a maximum of frac 1 2 l 2 repeated filterings produces a root signal

new finite element methods in computational fluid dynamics by h div elements in this paper the authors present two formulations for the stokes problem which make use of the existing h rm div elements of the raviart thomas type originally developed for the second order elliptic problems in addition two new h rm div elements are constructed and analyzed particularly for the new formulations optimal order error estimates are established for the corresponding finite element solutions in various sobolev norms the finite element solutions feature a full satisfaction of the continuity equation when existing raviart thomas type elements are employed in the numerical scheme

h div conforming finite element methods for the coupled stokes and darcy problem this paper proposes and analyzes a numerical method for solving the coupled stokes and darcy problem an interface problem between a fluid governed by stokes equations and a flow in a porous medium governed by darcy equations the method employs h div conforming finite elements for the velocity field in both stokes and darcy subdomains optimal order error estimates are established

efficient evaluation of multivariate polynomials over multidimensional grids let p x 1 x 2 x n be a multivariate polynomial in n variables x 1 x 2 x n and suppose that p x 1 x 2 x n is of degree m i in x i i 1 2 n it is shown how p x 1 x 2 x n may be evaluated at x i x 0i n i i for n i 0 1 2 and i 1 2 n using not more than m 1 m 2 m n additions per point feasibility of reduction from this upper bound is demonstrated in the n 2 case

a unified stabilized method for stokes and darcy s equations we use the lowest possible approximation order piecewise linear continuous velocities and piecewise constant pressures to compute solutions to stokes equation and darcy s equation applying an edge stabilization term to avoid locking we prove that the formulation satisfies the discrete inf sup condition we prove an optimal a priori error estimate for both problems the formulation is then extended to the coupled case using a nitsche type weak formulation allowing for different meshes in the two subdomains finally we present some numerical examples verifying the theoretical predictions and showing the flexibility of the coupled approach

multilevel nonlinear filters for edge detection and noise suppression two new classes of multilevel nonlinear filters are introduced for simultaneous edge detection and noise suppression which the authors call a nested median filter median averaging filter nmf maf pair and a delayed decision filter embedded median trimmed filter ddf emtf pair median filters and median related filter cause an edge shift in the presence of an impulse near the edge the proposed filters reduce such edge shifting while suppressing impulsive as well as nonimpulsive noise it is shown that at the noisy edge point the nmf and the ddf are substantially superior both theoretically and experimentally to the median filter the spl alpha tm filter and the stm filter in two respects 1 the output bias error and 2 the output mean square error it is also shown that in the noisy homogeneous region nonedge point the bias errors of the maf are zero and the output mean square errors of the maf are substantially close to those of the optimized single level filters the averager the median filter and the min max filter under gaussian laplacian and uniform noise respectively test results confirm that the nmf maf pair and the ddf emtf structure are each robust in preserving sharp edges inhibiting edge shifting and suppressing a wide variety of noise

polynomial phase signal analysis based on the polynomial derivatives decompositions an exact decomposition of the derivatives of any order of a polynomial spl phi t is proposed in terms of spl phi t t sub 0 spl phi t t sub n this result allows us to introduce generalized time frequency distributions for studying signals having a polynomial phase and a constant amplitude in order to determine the degree and the coefficients of the corresponding phase the relationships between these distributions and the already known polynomial distributions i e the polynomial phase transform and the polynomial wigner ville distribution are discussed illustrations by example are proposed

an observation on korn s inequality for nonconforming finite element methods by utilizing a simple observation on traces of rigid motions we are able to strengthen a result of brenner 2004 on korn s inequality for nonconforming finite element methods the approach here is tightly connected to the theory developed in brenner s work our motivation for the analysis was the desire to show that a robust darcy stokes element satisfies korn s inequality and to achieve this the stronger result seems necessary

a generalization of median filtering using linear combinations of order statistics we consider a class of nonlinear filters whose output is given by a linear combination of the order statistics of the input sequence assuming a constant signal in white noise the coefficients in the linear combination are chosen to minimize the output mse for several noise distributions it is shown that the optimal order statistic filter osf tends toward the median filter as the noise becomes more impulsive the optimal osf is applied to an actual noisy image and is shown to perform well combining properties of both the averaging and median filters a more general design scheme for applications involving nonconstant signals is also given

nonlinear mean filters in image processing the use of nonlinear means in image processing is introduced the properties of these means in the presence of different types of noise are investigated it is shown that nonlinear filters based on these means behave well for both additive and impulse noise their performance in the presence of signal dependent noise is satisfactory they preserve the edges better than linear filters and they reject the noise better than median filters

fast geodesic active contours we use an unconditionally stable numerical scheme to implement a fast version of the geodesic active contour model the proposed scheme is useful for object segmentation in images like tracking moving objects in a sequence of images the method is based on the weickert romeney viergever additive operator splitting aos scheme it is applied at small regions motivated by the adalsteinsson sethian level set narrow band approach and uses sethian s 1996 fast marching method for re initialization experimental results demonstrate the power of the new method for tracking in color movies

snakes shapes and gradient vector flow snakes or active contours are used extensively in computer vision and image processing applications particularly to locate object boundaries problems associated with initialization and poor convergence to boundary concavities however have limited their utility this paper presents a new external force for active contours largely solving both problems this external force which we call gradient vector flow gvf is computed as a diffusion of the gradient vectors of a gray level or binary edge map derived from the image it differs fundamentally from traditional snake external forces in that it cannot be written as the negative gradient of a potential function and the corresponding snake is formulated directly from a force balance condition rather than a variational formulation using several two dimensional 2 d examples and one three dimensional 3 d example we show that gvf has a large capture range and is able to move snakes into boundary concavities

generating discriminating cartoon faces using interacting snakes as a computational bridge between the high level a priori knowledge of object shape and the low level image data active contours or snakes are useful models for the extraction of deformable objects we propose an approach for manipulating multiple snakes iteratively called interacting snakes that minimizes the attraction energy functionals on both contours and enclosed regions of individual snakes and the repulsion energy functionals among multiple snakes that interact with each other we implement the interacting snakes through explicit curve parametric active contours representation in the domain of face recognition we represent human faces semantically via facial components such as eyes mouth face outline and the hair outline each facial component is encoded by a closed or open snake that is drawn from a 3d generic face model a collection of semantic facial components form a hypergraph called semantic face graph which employs interacting snakes to align the general facial topology onto the sensed face images experimental results show that a successful interaction among multiple snakes associated with facial components makes the semantic face graph a useful model for face representation including cartoon faces and caricatures and recognition

region competition unifying snakes region growing and bayes mdl for multiband image segmentation we present a novel statistical and variational approach to image segmentation based on a new algorithm named region competition this algorithm is derived by minimizing a generalized bayes minimum description length mdl criterion using the variational principle the algorithm is guaranteed to converge to a local minimum and combines aspects of snakes balloons and region growing the classic snakes balloons and region growing algorithms can be directly derived from our approach we provide theoretical analysis of region competition including accuracy of boundary location criteria for initial conditions and the relationship to edge detection using filters it is straightforward to generalize the algorithm to multiband segmentation and we demonstrate it on gray level images color images and texture images the novel color model allows us to eliminate intensity gradients and shadows thereby obtaining segmentation based on the albedos of objects it also helps detect highlight regions

statistical region snake based segmentation adapted to different physical noise models algorithms for object segmentation are crucial in many image processing applications during past years active contour models snakes have been widely used for finding the contours of objects this segmentation strategy is classically edge based in the sense that the snake is driven to fit the maximum of an edge map of the scene we propose a region snake approach and we determine fast algorithms for the segmentation of an object in an image the algorithms developed in a maximum likelihood approach are based on the calculation of the statistics of the inner and the outer regions defined by the snake it has thus been possible to develop optimal algorithms adapted to the random fields which describe the gray levels in the input image if we assume that their probability density function family are known we demonstrate that this approach is still efficient when no boundary s edge exists in the image we also show that one can obtain fast algorithms by transforming the summations over a region for the calculation of the statistics into summations along the boundary of the region finally we will provide numerical simulation results for different physical situations in order to illustrate the efficiency of this approach

the discrete polynomial phase transform the discrete polynomial phase transform dpt is a new tool for analyzing constant amplitude polynomial phase signals the main properties of the dpt are its ability to identify the degree of the phase polynomial and to estimate its coefficients the transform is robust to deviations from the ideal signal model such as slowly varying amplitude additive noise and nonpolynomial phase the authors define the dpt derive its basic properties and use it to develop computationally efficient estimation and detection algorithms a statistical accuracy analysis of the estimated parameters is also presented

fir median hybrid filters this paper introduces a new generalized class of median type filters which we call fir median hybrid fmh filters the input signal x n is filtered with m linear phase fir filters and the output of the fmh filter is the median of the outputs of the fir filters the statistical properties of the fmh filters are analyzed for input signals with gaussian double exponential and uniform density functions it is shown that fmh filters have essentially the same statistical properties and same type of root signals as the standard median sm filters fmh filters preserve corner points and ramps and attenuate impulsive type noise components effectively an interesting subclass of the fmh filters requiring only one scaling multiplier two additions and three compare swap operations irrespective of the filter length is introduced in the examples speed improvement by a factor of 450 is obtained over an otherwise approximately equivalent sm filter

a relationship between the z transform and the fourier transform a relationship between the one sided z transform and the one sided discrete time fourier transform is discussed every discrete time function that can result from the sampling of a periodic continuous time function is considered to be periodic a simple general equation is presented and discussed

a robust finite element method for darcy stokes flow finite element methods for a family of systems of singular perturbation problems of a saddle point structure are discussed the system is approximately a linear stokes problem when the perturbation parameter is large while it degenerates to a mixed formulation of poisson s equation as the perturbation parameter tends to zero it is established basically by numerical experiments that most of the proposed finite element methods for stokes problem or the mixed poisson s system are not well behaved uniformly in the perturbation parameter this is used as the motivation for introducing a new robust finite element which exhibits this property

estimating the doa and the polarization of a polynomial phase signal using a single polarized vector sensor this paper introduces a novel algorithm to estimate the direction of arrival doa and the polarization of a completely polarized polynomial phase signal of an arbitrary degree the algorithm utilizes a polarized vector sensor comprising a spatially collocated six component electromagnetic vector sensor a dipole triad or a loop triad this esprit based algorithm is based on a time invariant matrix pencil pair derived from the time delayed data sets collected by a single polarized vector sensor the high order difference function of the signal s phase constructs the invariant factor used in the esprit algorithm the steering vector is estimated from the signal subspace eigenvector of the data correlation matrix following which the closed form doa and polarization can be obtained given the degree of the polynomial phase signal this approach resolves the two dimensional azimuth elevation angle and the polarization of the source and requires neither a priori knowledge of the polynomial phase signal s coefficients nor a priori knowledge of the polynomial phase signal s frequency spectrum the efficacy of the proposed algorithm is verified by monte carlo simulations estimation accuracies of the doa and the polarization parameters are evaluated by the closed form cramer rao bounds which are independent of the polynomial coefficients the degree of the polynomial phase signal and the azimuth angle of the source

on fixed point roundoff error analysis the author points out the existence of work published by the author us dept of commerce tech rep ad a086826 57 pp apr 1980 prior to the appearance of the paper by barnes et al ibid vol assp 33 p 595 606 june 1985 covering the same subject

edge preserving filtering by combining nonlinear mean and median filters a very general class of nonlinear filters called mapping order statistics filters mosfs is introduced a subclass of the mosfs called l sub p mean median filters l sub p mmfs is discussed the l sub p mmf shows better properties in preserving edges and attenuating positive and negative impulse noise simultaneously than do the nonlinear mean filters in the analysis of the deterministic properties of the l sub p mmf the concept of a monotonic trend region is introduced a necessary condition for a signal to be a root signal is given this necessary condition is also valid for the known finite impulse response median hybrid filter

application of two dimensional generalized mean filtering for removal of impulse noises from images a new method for removing impulse noises from images is proposed the filtering scheme is based on replacing the central pixel value by the generalized mean value of all pixels inside a sliding window the concepts of thresholding and complementation which are shown to improve the performance of the generalized mean filter are introduced the threshold is derived using a statistical theory the actual performance of the proposed filter is compared with that of file commonly used median filter by filtering noise corrupted real images the hardware complexity of the two types of filters are also compared indicating the advantages of the generalized mean filter

locally conservative coupling of stokes and darcy flows a locally conservative numerical method for solving the coupled stokes and darcy flows problem is formulated and analyzed the approach employs the mixed finite element method for the darcy region and the discontinuous galerkin method for the stokes region a discrete inf sup condition and optimal error estimates are derived

new efficient ls and svd based techniques for high resolution frequency estimation new least squares and singular value decomposition based methods for the estimation of the frequencies of complex sinusoids in white noise are presented the methods are based on a new symmetric prediction problem that has some very useful properties leading to algorithms that have considerably reduced complexity the new symmetric predictor is superior in performance as compared to the well known symmetric smoother and has a performance comparable to other well known methods finally a new ls based method which combines the new prediction technique with the fblp method is proposed this method performs slightly better than the fblp offering at the same time a significant computational saving as a by product in the derivation of the new methods is the establishment of some useful properties concerning the eigenstructure of hermitian and persymmetric matrices

a multiple active contour model for cardiac boundary detection on echocardiographic sequences tracing of left ventricular epicardial and endocardial borders on echocardiographic sequences is essential for quantification of cardiac function the authors designed a method based on an extension of active contour models to detect both epicardial and endocardial borders on short axis cardiac sequences spanning the entire cardiac cycle they validated the results by comparing the computer generated boundaries to the boundaries manually outlined by four expert observers on 44 clinical data sets the mean boundary distance between the computer generated boundaries and the manually outlined boundaries was 2 80 mm spl sigma 1 28 mm for the epicardium and 3 61 spl sigma 1 68 mm for the endocardium these distances were comparable to interobserver distances which had a mean of 3 79 mm spl sigma 1 53 mm for epicardial borders and 2 67 mm spl sigma 0 88 mm for endocardial borders the correlation coefficient between the areas enclosed by the computer generated boundaries and the average manually outlined boundaries was 0 95 for epicardium and 0 91 for endocardium the algorithm is fairly insensitive to the choice of the initial curve thus the authors have developed an effective and robust algorithm to extract left ventricular boundaries from echocardiographic sequences