particle swarm optimization in electromagnetics the particle swarm optimization pso new to the electromagnetics community is a robust stochastic evolutionary computation technique based on the movement and intelligence of swarms this paper introduces a conceptual overview and detailed explanation of the pso algorithm as well as how it can be used for electromagnetic optimizations this paper also presents several results illustrating the swarm behavior in a pso algorithm developed by the authors at ucla specifically for engineering optimizations ucla pso also discussed is recent progress in the development of the pso and the special considerations needed for engineering implementation including suggestions for the selection of parameter values additionally a study of boundary conditions is presented indicating the invisible wall technique outperforms absorbing and reflecting wall techniques these concepts are then integrated into a representative example of optimization of a profiled corrugated horn antenna

invariant palm and related disintegrations via skew factorization let g be a measurable group with haar measure acting properly on a space s and measurably on a space t then any finite jointly invariant measure m on s t admits a disintegration nu otimes mu into an invariant measure on s and an invariant kernel from s to t here we construct and by a general skew factorization which extends an approach by rother and zahle for homogeneous spaces s over g this leads to easy extensions of some classical propositions for invariant disintegration previously known in the homogeneous case the results are applied to the palm measures of jointly stationary pairs where is a random measure on s and is a random element in t

noise robust image edge detection based upon the automatic anisotropic gaussian kernels this paper presents a novel noise robust edge detector based upon the automatic anisotropic gaussian kernels angks which also addresses the current problem that the seminal canny edge detector may miss some obvious crossing edge details firstly automatic angks are designed according to the noise suppression edge resolution and localization precision which also conciliate the conflict between them secondly reasons why cross edge points are missing from canny detector results using isotropic gaussian kernel are analyzed thirdly the automatic angks are used to smooth image and a revised edge extraction method is used to extract edges finally the aggregate test receiver operating characteristic roc curves and pratt s figure of merit fom are used to evaluate the proposed detector against state of the art edge detectors the experiment results show that the proposed algorithm can obtain better performance for noise free and noisy images

automated analytic continuation method for the analysis of dispersive materials all dielectrics are dispersive this frequency dependence of materials must be modeled in a well defined way whenever microwave structures are expected to operate over broad bands of frequency the well known analytic properties of the permittivity can be used to generate such models by fitting them to experimental data using non linear optimizers however in that approach the questions of convergence to the true global solution and the sensitivity to experimental noise remain open here it is shown that an automated deterministic approach to generate such a model for the important case of multi debye relaxation materials can be implemented the method is compared to a recently proposed alternate approach hybrid particle swarm least squares optimization method pso ls that was demonstrated on idealized data sets with bandwidths in excess of 10 000 1 in our case no arbitrary parameters need be set to guarantee convergence nor need any constants be added after the fact to match the data the case of materials with dc conductivity imaginary permittivity growing to infinity at dc is as easily dealt with as the conventional pure debye case physically realizable results are generated even when the data is realistically noisy and spans a frequency bandwidth as small as 18 1

ergodic properties of poissonian id processes we show that a stationary idp process i e an infinitely divisible stationary process without gaussian part can be written as the independent sum of four stationary idp processes each of them belonging to a different class characterized by its levy measure the ergodic properties of each class are respectively nonergodicity weak mixing mixing of all order and bernoullicity to obtain these results we use the representation of an idp process as an integral with respect to a poisson measure which more generally has led us to study basic ergodic properties of these objects

reversibility in infinite hamiltonian systems with conservative noise the set of stationary measures of an infinite hamiltonian system with noise is investigated the model consists of particles moving in r 3 with bounded velocities and subject to a noise that does not violate the classical laws of conservation see ovy following lo we assume that the noise has also a finite radius of interaction and prove that translation invariant stationary states of finite specific entropy are reversible with respect to the stochastic component of the evolution therefore the results of lo imply that such invariant measures are superpositions of gibbs states

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

contour detection and hierarchical image segmentation this paper investigates two fundamental problems in computer vision contour detection and image segmentation we present state of the art algorithms for both of these tasks our contour detector combines multiple local cues into a globalization framework based on spectral clustering our segmentation algorithm consists of generic machinery for transforming the output of any contour detector into a hierarchical region tree in this manner we reduce the problem of image segmentation to that of contour detection extensive experimental evaluation demonstrates that both our contour detection and segmentation methods significantly outperform competing algorithms the automatically generated hierarchical segmentations can be interactively refined by user specified annotations computation at multiple image resolutions provides a means of coupling our system to recognition applications

the equivalence of ensembles for classical systems of particles for systems of particles in classical phase space with standard hamiltonian we consider spatially averaged microcanonical gibbs distributions in finite boxes we show that infinite volume limits along suitable subsequences exist and are grand canonical gibbs measures on the way we establish a variational formula for the thermodynamic entropy density as well as a variational characterization of grand canonical gibbs measures

on non equilibrium dynamics of multidimensional infinite particle systems in the translation invariant case it is shown that for a set of full measure with respect to any translation invariant probability distribution on the space of initial configurarations of classical particle systems on d with interaction given by a smooth superstable potential of finite range there is a solution to the newtonian equations of motion provided that the specific energy and the particle density of the initial configuration exist a s

time evolution of two dimensional systems with infinitely many particles mutually interacting via very singular forces we study the existence and uniqueness of the time evolution via the newton law of a two dimensional system of infinitely many particles with very singular mutual interactions it is an improvement of the result by fritz and dobrushin given in comm math phys 57 67 81 1977 for inverse power like singular interactions

edge preserving filtering of images with low photon counts edge preserving filters such as local m smoothers or bilateral filtering are usually designed for gaussian noise this paper investigates how these filters can be adapted in order to efficiently deal with poissonian noise in addition the issue of photometry invariance is addressed by changing the way filter coefficients are normalized the proposed normalization is additive instead of being multiplicative and leads to a strong connection with anisotropic diffusion experiments show that ensuring the photometry invariance leads to comparable denoising performances in terms of the root mean square error computed on the signal

existence of gibbsian point processes with geometry dependent interactions we establish the existence of stationary gibbsian point processes for interactions that act on hyperedges between the points for example such interactions can depend on delaunay edges or triangles cliques of voronoi cells or clusters of k nearest neighbors the classical case of pair interactions is also included the basic tools are an entropy bound and stationarity

a second order dispersive fdtd algorithm for transverse electric maxwell s equations with complex interfaces this work overcomes the difficulty of the finite difference time domain fdtd algorithm in solving the transverse electric te maxwell s equations with inhomogeneous dispersive media for such te problems the electric fields are discontinuous across the dispersive interfaces moreover such discontinuities are time variant a novel matched interface and boundary time domain mibtd method is proposed to solve such problems through new developments in both mathematical formulations and numerical algorithms mathematically instead of handling all zeroth and first order jump conditions in a local coordinate we directly construct the te jump conditions which are needed in the fdtd computations in the cartesian coordinate such cartesian direction conditions depend on the time as well as tangential and normal components of the electric flux driven by the jump condition modeling we adopt the standard maxwell s equations in coupling with the debye auxiliary differential equations for the electric flux as the governing equations computationally the leapfrog scheme is employed for integrating the maxwell system and time dependent jump conditions sophisticated interface treatments are developed in both producing the te jump conditions and enforcing them in the fdtd algorithm based on a staggered yee lattice the numerical accuracy stability and efficiency of the proposed scheme are investigated by considering dispersive interfaces of various shapes the mibtd method achieves a spatially second order of convergence in all tests to the best of our knowledge the present mibtd scheme is the first fdtd method in the literature that can restore second order accuracy in treating curved dispersive interfaces for the te maxwell system

a general method for fdtd modeling of wave propagation in arbitrary frequency dispersive media a general formulation is presented for finite difference time domain fdtd modeling of wave propagation in arbitrary frequency dispersive media two algorithmic approaches are outlined for incorporating dispersion into the fdtd time stepping equations the first employs a frequency dependent complex permittivity denoted form 1 and the second employs a frequency dependent complex conductivity denoted form 2 a pade representation is used in z transform space to represent the frequency dependent permittivity form 1 or conductivity form 2 this is a generalization over several previous methods employing either debye lorentz or drude models the coefficients of the pade model may be obtained through an optimization process leading directly to a finite difference representation of the dispersion relation without introducing discretization error stability criteria for the dispersive fdtd algorithms are given we show that several previously developed dispersive fdtd algorithms can be cast as special cases of our more general framework simulation results are presented for a one dimensional 1 d air muscle example considered previously in the literature and a three dimensional 3 d radiation problem in dispersive lossy soil using measured soil data

palm distributions and local approximation of regenerative processes for a regenerative process x with associated local time random measure the distribution relative to some fixed times has a simple description in terms of the excursion kernel r and the palm distributions qt with respect to under suitable regularity conditions on the qt admit versions with strong continuity and regularity properties using the latter versions we may establish some local invariance and mixing properties of x and show that the multivariate palm distributions can be approximated by ordinary conditional distributions

edge detection with embedded confidence computing the weighted average of the pixel values in a window is a basic module in many computer vision operators the process is reformulated in a linear vector space and the role of the different subspaces is emphasized within this framework wellknown artifacts of the gradient based edge detectors such as large spurious responses can be explained quantitatively it is also shown that template matching with a template derived from the input data is meaningful since it provides an independent measure of confidence in the presence of the employed edge model the widely used three step edge detection procedure gradient estimation non maxima suppression hysteresis thresholding is generalized to include the information provided by the confidence measure the additional amount of computation is minimal and experiments with several standard test images show the ability of the new procedure to detect weak edges

piecewise linear recursive convolution for dispersive media using fdtd electromagnetic propagation through linear dispersive media can be analyzed using the finite difference time domain fdtd method by employing the recursive convolution rc approach to evaluate the discrete time convolution of the electric field and the dielectric susceptibility function the rc approach results in a fast and computationally efficient algorithm however the accuracy achieved is not generally as good as that obtained with other methods a new piecewise linear recursive convolution plrc method is described here that has greatly improved accuracy over the original rc approach but retains its speed and efficiency advantages

on the impact of anisotropic diffusion on edge detection content aware edge preserving smoothing techniques have gained visibility in recent years however they have had a rather limited impact on the edge detection literature compared to content unaware linear techniques often based on gaussian filters in this work we focus on anisotropic diffusion covering its initial definition by perona and malik and subsequent extensions a visual case study is used to illustrate their features we perform a quantitative evaluation of the performance of the canny method for edge detection when substituting linear gaussian smoothing filters by anisotropic diffusion highlightsreviewing the main trends in anisotropic diffusion identifying the practical scenarios on which anisotropic diffusion fails quantifying the improvement of edge detection when anisitropic diffusion is applied

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

susan a new approach to low level image processing this paper describes a new approach to low level image processing in particular edge and corner detection and structure preserving noise reduction non linear filtering is used to define which parts of the image are closely related to each individual pixel each pixel has associated with it a local image region which is of similar brightness to that pixel the new feature detectors are based on the minimization of this local image region and the noise reduction method uses this region as the smoothing neighbourhood the resulting methods are accurate noise resistant and fast details of the new feature detectors and of the new noise reduction method are described along with test results

noise robust edge detector combining isotropic and anisotropic gaussian kernels a new noise robust edge detector is proposed which combines a small scaled isotropic gaussian kernel and large scaled anisotropic gaussian kernels angks to obtain edge maps of images its main advantage is that noise reduction is attained while maintaining high edge resolution from the angks anisotropic directional derivatives andds are derived to capture the locally directional variation of an image the andd based edge strength map esm is constructed its noise robustness is determined by the scale alone and its edge resolution by the ratio of the scale to the anisotropic factor moreover the edge stretch effect in anisotropic smoothing is revealed the andd based esm and the gradient based esm with a small scaled isotropic gaussian kernel are fused into a noise robust esm with high edge resolution and little edge stretch embedding the fused esm into the routine of canny detector a noise robust edge detector is developed which includes two additional modifications contrast equalization and noise dependent lower threshold the aggregate test receiver operating characteristic roc curves and the pratt s figure of merit fom are used to evaluate the proposed detector by abundant experiments the experimental results show that the proposed detector can obtain high quality edge maps for noise free and noisy images

coherence enhancing diffusion filtering the completion of interrupted lines or the enhancement of flow like structures is a challenging task in computer vision human vision and image processing we address this problem by presenting a multiscale method in which a nonlinear diffusion filter is steered by the so called interest operator second moment matrix structure tensor an m dimensional formulation of this method is analysed with respect to its well posedness and scale space properties an efficient scheme is presented which uses a stabilization by a semi implicit additive operator splitting aos and the scale space behaviour of this method is illustrated by applying it to both 2 d and 3 d images

debye function expansions of complex permittivity using a hybrid particle swarm least squares optimization approach with appropriate modifications the finite difference time domain fdtd method can be used to analyze propagation through linear isotropic dispersive media although materials characterized by the debye permittivity model can be analyzed accurately and efficiently using well established methods the treatment of other types of frequency dependence is more difficult this paper proposes the use of a weighted sum of debye functions to approximate more general complex permittivity functions a combination of the particle swarm optimization method and linear least squares optimization is used to find the relaxation frequencies and weights in the expansion which can then be accommodated in the fdtd method using one of the established methods two key advantages of the proposed approach are that the relaxation frequencies are bandlimited and the weights are always positive these two characteristics help to maintain the accuracy and stability of the fdtd solution it is also shown that the correlation between the imaginary parts of two debye functions is the same as that between the real parts

some remarks on nonequilibrium dynamics of infinite particle systems classical mechanics of infinitely many particles in dimensions one and two is considered particles interacting by a superstable pair potential of finite range the group of motion generated by newton s equations is constructed in the space of locally finite configurations with a logarithmic order of energy fluctuations at infinity a core of the liouville operator is also described results of dobrushin and the author and of marchioro pellegrinotti pulvirenti are improved

large deviations and the maximum entropy principle for marked point random fields we establish large deviation principles for the stationary and the individual empirical fields of poisson and certain interacting random fields of marked point particles in d the underlying topologies are induced by a class of not necessarily bounded local functions and thus finer than the usual weak topologies our methods yield further that the limiting behaviour of conditional poisson distributions as well as certain distributions of gibbsian type is governed by the maximum entropy principle we also discuss various applications and examples

on edge detection edge detection is the process that attempts to characterize the intensity changes in the image in terms of the physical processes that have originated them a critical intermediate goal of edge detection is the detection and characterization of significant intensity changes this paper discusses this part of the edge detection problem to characterize the types of intensity changes derivatives of different types and possibly different scales are needed thus we consider this part of edge detection as a problem in numerical differentiation we show that numerical differentiation of images is an ill posed problem in the sense of hadamard differentiation needs to be regularized by a regularizing filtering operation before differentiation this shows that this part of edge detection consists of two steps a filtering step and a differentiation step following this perspective the paper discusses in detail the following theoretical aspects of edge detection 1 the properties of different types of filters with minimal uncertainty with a bandpass spectrum and with limited support are derived minimal uncertainty filters optimize a tradeoff between computational efficiency and regularizing properties 2 relationships among several 2 d differential operators are established in particular we characterize the relation between the laplacian and the second directional derivative along the gradient zero crossings of the laplacian are not the only features computed in early vision 3 geometrical and topological properties of the zero crossings of differential operators are studied in terms of transversality and morse theory

behavioral analysis of anisotropic diffusion in image processing in this paper we analyze the behavior of the anisotropic diffusion model of perona and malik 1990 the main idea is to express the anisotropic diffusion equation as coming from a certain optimization problem so its behavior can be analyzed based on the shape of the corresponding energy surface we show that anisotropic diffusion is the steepest descent method for solving an energy minimization problem it is demonstrated that an anisotropic diffusion is well posed when there exists a unique global minimum for the energy functional and that the ill posedness of a certain anisotropic diffusion is caused by the fact that its energy functional has an infinite number of global minima that are dense in the image space we give a sufficient condition for an anisotropic diffusion to be well posed and a sufficient and necessary condition for it to be ill posed due to the dense global minima the mechanism of smoothing and edge enhancement of anisotropic diffusion is illustrated through a particular orthogonal decomposition of the diffusion operator into two parts one that diffuses tangentially to the edges and therefore acts as an anisotropic smoothing operator and the other that flows normally to the edges and thus acts as an enhancement operator

using canny s criteria to derive a recursively implemented optimal edge detector a highly efficient recursive algorithm for edge detection is presented using canny s design 1 we show that a solution to his precise formulation of detection and localization for an infinite extent filter leads to an optimal operator in one dimension which can be efficiently implemented by two recursive filters moving in opposite directions in addition to the noise truncature immunity which results the recursive nature of the filtering operations leads with sequential machines to a substantial saving in computational effort five multiplications and five additions for one pixel independent of the size of the neighborhood the extension to the two dimensional case is considered and the resulting filtering structures are implemented as two dimensional recursive filters hence the filter size can be varied by simply changing the value of one parameter without affecting the time execution of the algorithm performance measures of this new edge detector are given and compared to canny s filters various experimental results are shown

fundamental relationship between bilateral filtering adaptive smoothing and the nonlinear diffusion equation in this paper the relationship between bilateral filtering and anisotropic diffusion is examined the bilateral filtering approach represents a large class of nonlinear digital image filters we first explore the connection between anisotropic diffusion and adaptive smoothing and then the connection between adaptive smoothing and bilateral filtering previously adaptive smoothing was considered to be an inconsistent approximation to the nonlinear diffusion equation we extend adaptive smoothing to make it consistent thus enabling a unified viewpoint that relates nonlinear digital image filters and the nonlinear diffusion equation

time domain matched interface and boundary mib modeling of debye dispersive media with curved interfaces a new finite difference time domain fdtd method is introduced for solving transverse magnetic maxwell s equations in debye dispersive media with complex interfaces and discontinuous wave solutions based on the auxiliary differential equation approach a hybrid maxwell debye system is constructed which couples the wave equation for the electric component with maxwell s equations for the magnetic components this hybrid formulation enables the calculation of the time dependent parts of the interface jump conditions so that one can track the transient changes in the regularities of the electromagnetic fields across a dispersive interface effective matched interface and boundary mib treatments are proposed to rigorously impose the physical jump conditions which are not only time dependent but also couple both cartesian directions and both magnetic field components based on a staggered yee lattice the proposed mib scheme can deal with arbitrarily curved interfaces and nonsmooth interfaces with sharped edges second order convergences are numerically achieved in solving dispersive interface problems with constant curvatures general curvatures and nonsmooth corners

fdtd schemes for wave propagation in davidson cole dispersive media using auxiliary differential equations two finite difference time domain fdtd schemes based on the use of auxiliary differential equations are proposed for modeling time domain wave propagation in dispersive davidson cole media the main difficulty in fdtd implementations for such media is the appearance of fractional derivatives in the time domain polarization relation to circumvent this difficulty the relative complex permittivity of the medium is approximated by pade approximants resulting in auxiliary differential equations of integer order moreover it is proven that under certain conditions the pade approximation is equivalent to one given by a sum of debye terms hence an alternative set of auxiliary differential equations is derived over a wideband frequency domain the comparisons between analytical and calculated values of the relative complex permittivity as well as of the transfer function inside the dispersive medium illustrate the efficiency of both fdtd schemes

a new interpretation and improvement of the nonlinear anisotropic diffusion for image enhancement the purpose of the article is to give an analysis of the anisotropic diffusion ad and propose adaptive nonlinear filtering based on a judicious choice of the conductance function cf and the edgeness threshold a new undesirable effect which we call the pinhole effect may result when ad is introduced for the first time a robust solution to this effect is proposed and evaluated through experimental data the evolution of the diffused signal is analyzed through a physical model using the optical flow technique oft the overall strategy is evaluated through experimental results obtained on synthetic and actual images

bivariate cox processes some models for bivariate spatial point patterns summary from certain points of view the range of probability models currently available for describing the joint behaviour of two point processes is rather limited in this paper we explore the structure of some further models and apply our results to the statistical analysis of bivariate spatial point patterns in many branches of science there is interest in the study and description of data which represent the locations of objects as points in an essentially planar region in the present paper we assume that the objects are of two qualitatively distinguishable types and refer to the data as a bivariate spatial point pattern a statistical analysis of such data should seek to provide some meaningful summary descriptions of the separate point patterns for each of the two types of object and of any possible inter relationship between these two patterns for example fig 1 shows the locations of 173 newly emergent and 155 1 year old bramnble 0 a a tv t to 0 x t

an auxiliary differential equation method for fdtd modeling of wave propagation in cole cole dispersive media a method for modeling time domain wave propagation in dispersive cole cole media is presented the cole cole model can describe the frequency dependence of the electromagnetic properties of various biological tissues with great accuracy over a wide frequency range and plays a key role in microwave medical imaging the main difficulty in the time domain modeling of cole cole media is the appearance of fractional time derivatives in the proposed method a pade approximation is employed resulting in auxiliary differential equations of integer order a finite difference time domain method is developed to solve the differential equations obtained the comparison of analytical and calculated relative complex permittivity values over wideband frequency domain proves the validity of the method

partial regularity for the stochastic navier stokes equations the effects of random forces on the emergence of singularities in the navier stokes equations are investigated in spite of the presence of white noise the paths of a martingale suitable weak solution have a set of singular points of one dimensional hausdorff measure zero furthermore statistically stationary solutions with finite mean dissipation rate are analysed for these stationary solutions it is proved that at any time t the set of singular points is empty the same result holds true for every martingale solution starting from 0 a e initial condition u 0 where 0 is the law at time zero of a stationary solution finally the previous result is non trivial when the noise is sufficiently non degenerate since for any stationary solution the measure 0 is supported on the whole space h of initial conditions

nonequilibrium dynamics of infinite particle systems with infinite range interactions we discuss the existence and uniqueness of nonequilibrium dynamics of infinitely many particles interacting via superstable pair interactions in one and two dimensions the interaction is allowed to be of infinite range and singular at the origin under suitable regularity conditions on the interaction potential we show that if the potential decreases polynomially as the distance between interacting two particles increases then the tempered solution to the system of hamiltonian equations exists moreover if the potential satisfies further that either it has a subexponential decreasing rate or it is everywhere two times continuously differentiable then we show that the tempered solution is unique the results extend those of dobrushin and fritz obtained for finite range interactions

time evolution of an infinitely extended vlasov system with singular mutual interaction we study the time evolution of an infinitely extended system in the mean field approximation governed by the vlasov equation this system is confined in an unbounded cylinder by an external force singular on the border the mutual interaction is assumed singular at short distance as 1 r alpha with alpha 2 3 or alpha 1 in case of an external lorentz force and with a short range the initial density is assumed bounded differently from studies which assume initial data compact in space and or in velocities here we consider a system having infinite mass and an exponential bound on the velocities according to the maxwell boltzmann law

on support measures in minkowski spaces and contact distributions in stochastic geometry this paper is concerned with contact distribution functions of a random closed set n 1 n in r d where the n are assumed to be random nonempty convex bodies these distribution functions are defined here in terms of a distance function which is associated with a strictly convex gauge body structuring element that contains the origin in its interior support measures with respect to such distances will be introduced and extended to sets in the local convex ring these measures will then be used in a systematic way to derive and describe some of the basic properties of contact distribution functions most of the results are obtained in a general nonstationary setting only the final section deals with the stationary case

an efficient cost scaling algorithm for the assignment problem the cost scaling push relabel method has been shown to be efficient for solving minimum cost flow problems in this paper we apply the method to the assignment problem and investigate implementations of the method that take advantage of assignment s special structure the results show that the method is very promising for practical use

edge based compression of cartoon like images with homogeneous diffusion edges provide semantically important image features in this paper a lossy compression method for cartoon like images is presented which is based on edge information edges together with some adjacent grey colour values are extracted and encoded using a classical edge detector binary compression standards such as jbig and state of the art encoders such as paq when decoding information outside these encoded data is recovered by solving the laplace equation i e we inpaint with the steady state of a homogeneous diffusion process for the discrete reconstruction problem we prove existence and uniqueness and establish a maximum minimum principle furthermore we describe an efficient multigrid algorithm the result is a simple codec that is able to encode and decode in real time we show that for cartoon like images this codec can outperform the jpeg standard and even its more advanced successor jpeg2000

a nonlinear derivative scheme applied to edge detection this paper presents a nonlinear derivative approach to addressing the problem of discrete edge detection this edge detection scheme is based on the nonlinear combination of two polarized derivatives its main property is a favorable signal to noise ratio snr at a very low computation cost and without any regularization a 2d extension of the method is presented and the benefits of the 2d localization are discussed the performance of the localization and snr are compared to that obtained using classical edge detection schemes tests of the regularized versions and a theoretical estimation of the snr improvement complete this work

non equilibrium dynamics of three dimensional infinite particle systems we show existence and uniqueness for the solutions to the newton equations relative to a system of infinitely many particles in the space interacting by means of a positive and short range potential the initial conditions are chosen in a set sufficiently large to be the support of any reasonable non equilibrium state we extend previous results in one and two dimensions obtained by lanford and by fritz and dobrushin respectively many years ago

random time evolution and direct integrals constants of the motion and the mass operator the members h p2 v x of ergodic families of random operators defined in h l2 rd are considered as acting in fibers in a direct integral decomposition of k l2 p d h p being the underlying probability space such a formulation may turn out to be useful in providing a rigorous background for theoretical physical methods employed in treating random systems as an example a rigorous definition of the mass operator z is presented and the formulation of transport equations in a functional analytic setting is briefly indicated in case there is translational invariance in the probability law the operator h is shown to be unitarily equivalent to an operator h which can be decomposed h h k in a way that diagonalizes p thus problems about averaged time evolution can be formulated entirely in terms of h k in l2 p

multigrid anisotropic diffusion a multigrid anisotropic diffusion algorithm for image processing is presented the multigrid implementation provides an efficient hierarchical relaxation method that facilitates the application of anisotropic diffusion to time critical processes through a multigrid v cycle the anisotropic diffusion equations are successively transferred to coarser grids and used in a coarse to fine error correction scheme when a coarse grid with a trivial solution is reached the coarse grid estimates of the residual error can be propagated to the original grid and used to refine the solution the main benefits of the multigrid approach are rapid intraregion smoothing and reduction of artifacts due to the elimination of low frequency error the theory of multigrid anisotropic diffusion is developed then the intergrid transfer functions relaxation techniques diffusion coefficients and boundary conditions are discussed the analysis includes the examination of the storage requirements the computational cost and the solution quality finally experimental results are reported that demonstrate the effectiveness of the multigrid approach

a geometric approach to edge detection this paper describes edge detection as a composition of four steps conditioning feature extraction blending and scaling we examine the role of geometry in determining good features for edge detection and in setting parameters for functions to blend the features we find that 1 statistical features such as the range and standard deviation of window intensities can be as effective as more traditional features such as estimates of digital gradients 2 blending functions that are roughly concave near the origin of feature space ran provide visually better edge images than traditional choices such as the city block and euclidean norms 3 geometric considerations ran be used to specify the parameters of generalized logistic functions and takagi sugeno input output systems that yield a rich variety of edge images and 4 understanding the geometry of the feature extraction and blending functions is the key to using models based on computational learning algorithms such as neural networks and fuzzy systems for edge detection edge images derived from a digitized mammogram are given to illustrate various facets of our approach

incorporation of attenuation into time domain computations of seismic wave fields the only numerically tractable way yet found to incorporate attenuation into numerical time domain computations of seismic wave fields is to approximate the viscoelastic modulus by a low order rational function of frequency the coefficients of this function can be determined by the pade approximation our test computations show however that this approximation generally is of poor quality therefore we suggest a new approach which is based on the rheological model of the generalized maxwell body which has a modulus of the desired rational form we choose the relaxation frequencies logarithmically equidistant in the frequency band of interest and determine the weight factors by simple numerical curve fitting to an arbitrary q law this approach is superior to the method above both in accuracy and in computational efficiency for most practical applications approximations of orders 2 or 3 are sufficient the computing time and memory requirements for a finite difference calculation are then approximately twice those of a purely elastic calculation as a first application of the method we compute sh channel waves in discontinuous coal seams with q 50 within the coal the results show that the high frequency airy phase is strongly attenuated this indicates that care has to be taken in comparing the results of purely elastic model calculations of the propagation of seam waves with experimental data

incorporating the havriliak negami dielectric model in the fd td method we derive and analyze an efficient algorithm to incorporate the anomalously dispersive havriliak negami dielectric model of induced polarization in the finite difference time domain fd td method our algorithm implements this dielectric model which in the time domain involves fractional derivatives and fractional differential operators with a preset error over the desired computational time interval 0 t c o m p and correctly takes into account the singularity at t 0 of the corresponding time domain dielectric susceptibility the overall algorithm is shown to be second order accurate in space and time and to obey the standard fd td stability condition numerical experiments confirm our analysis

on candidates selection for hysteresis thresholds in edge detection manual determination of hysteresis thresholds is time consuming several methods approach the problem of unsupervised determination of edge detector parameters but they require human intervention to establish the initial range of values in which to detect the best parameter value and the result depends on the range of values initially used in this paper a method is proposed to determine candidates to hysteresis thresholds in an unsupervised manner the method provides a criterion to reduce in a significant way the number of initial values to be considered as threshold candidates the proposed method can be applied to any feature image provided by an edge detector upon which hysteresis must be implemented

a computational approach to edge detection this paper describes a computational approach to edge detection the success of the approach depends on the definition of a comprehensive set of goals for the computation of edge points these goals must be precise enough to delimit the desired behavior of the detector while making minimal assumptions about the form of the solution we define detection and localization criteria for a class of edges and present mathematical forms for these criteria as functionals on the operator impulse response a third criterion is then added to ensure that the detector has only one response to a single edge we use the criteria in numerical optimization to derive detectors for several common image features including step edges on specializing the analysis to step edges we find that there is a natural uncertainty principle between detection and localization performance which are the two main goals with this principle we derive a single operator shape which is optimal at any scale the optimal detector has a simple approximate implementation in which edges are marked at maxima in gradient magnitude of a gaussian smoothed image we extend this simple detector using operators of several widths to cope with different signal to noise ratios in the image we present a general method called feature synthesis for the fine to coarse integration of information from operators at different scales finally we show that step edge detector performance improves considerably as the operator point spread function is extended along the edge

a shearlet approach to edge analysis and detection it is well known that the wavelet transform provides a very effective framework for analysis of multiscale edges in this paper we propose a novel approach based on the shearlet transform a multiscale directional transform with a greater ability to localize distributed discontinuities such as edges indeed unlike traditional wavelets shearlets are theoretically optimal in representing images with edges and in particular have the ability to fully capture directional and other geometrical features numerical examples demonstrate that the shearlet approach is highly effective at detecting both the location and orientation of edges and outperforms methods based on wavelets as well as other standard methods furthermore the shearlet approach is useful to design simple and effective algorithms for the detection of corners and junctions

nonlinear image filtering with edge and corner enhancement the authors describe a model of nonlinear image filtering for noise reduction and edge enhancement using anisotropic diffusion the method is designed to enhance not only edges but corners and t junctions as well the method roughly corresponds to a nonlinear diffusion process with backward heat flow across the strong edges such a process is ill posed making the results depend strongly on how the algorithm differs from the diffusion process two ways of modifying the equations using simulations on a variable grid are studied

stability and phase error analysis of fd td in dispersive dielectrics four fd td extensions for the modeling of pulse propagation in debye or lorentz dispersive media are analyzed through studying the stability and phase error properties of the coupled difference equations corresponding to maxwell s equations and to the equations for the dispersion for good overall accuracy the author shows that all schemes should be run at their courant stability limit and that the timestep should finely resolve the medium timescales particularly for debye schemes it should be at least spl delta t 10 sup spl minus 3 spl tau while for lorentz schemes it should be spl delta t 10 sup spl minus 2 spl tau where spl tau is a typical medium relaxation time a numerical experiment with a debye medium confirms this the author has determined that two of the discretizations for debye media are totally equivalent in the lorentz medium case the author establishes that the method that uses the polarization differential equation to model dispersion is stable for all wavenumbers and that the method using the local in time constitutive relation is weakly unstable for modes with wavenumber k such that k spl delta x spl pi 2

poisson process fock space representation chaos expansion and covariance inequalities we consider a poisson process on an arbitrary measurable space with an arbitrary sigma finite intensity measure we establish an explicit fock space representation of square integrable functions of as a consequence we identify explicitly in terms of iterated difference operators the integrands in the wiener ito chaos expansion we apply these results to extend well known variance inequalities for homogeneous poisson processes on the line to the general poisson case the poincare inequality is a special case further applications are covariance identities for poisson processes on strictly ordered spaces and harris fkg inequalities for monotone functions of

combined nonparametric inference and state estimation for mixed poisson processes given independent identically distributed copies of a mixed poisson process n on a lccb space e i e a cox process whose directing measure is of the form m where 0 is a random variable with distribution and m is a measure on e we construct strongly consistent and asymptotically normal estimators of m and the laplace transform l methods are presented for estimating the directing measure of the n 1 st process by combining the data for that process with estimates of appropriate quantities the latter based on the first n processes the case where different processes are observed over different sets is addressed

contour and texture analysis for image segmentation this paper provides an algorithm for partitioning grayscale images into disjoint regions of coherent brightness and texture natural images contain both textured and untextured regions so the cues of contour and texture differences are exploited simultaneously contours are treated in the intervening contour framework while texture is analyzed using textons each of these cues has a domain of applicability so to facilitate cue combination we introduce a gating operator based on the texturedness of the neighborhood at a pixel having obtained a local measure of how likely two nearby pixels are to belong to the same region we use the spectral graph theoretic framework of normalized cuts to find partitions of the image into regions of coherent texture and brightness experimental results on a wide range of images are shown

a novel piecewise linear recursive convolution approach for dispersive media using the finite difference time domain method two novel methods for implementing recursively the convolution between the electric field and a time dependent electric susceptibility function in the finite difference time domain fdtd method are presented both resulting algorithms are straightforward to implement and employ an inclusive susceptibility function which holds as special cases the lorentz debye and drude media relaxations the accuracy of the new proposed algorithms is found to be systematically improved when compared to existing standard piecewise linear recursive convolution plrc approaches it is conjectured that the reason for this improvement is that the new proposed algorithms do not make any assumptions about the time variation of the polarization density in each time interval no finite difference or semi implicit schemes are used for the calculation of the polarization density the only assumption that these two new methods make is that the first time derivative of the electric field is constant within each fdtd time interval

high order fdtd methods for transverse magnetic modes with dispersive interfaces a new finite difference time domain fdtd algorithm is introduced to solve two dimensional 2d transverse magnetic tm modes with a straight dispersive interface driven by the consideration of simplifying interface jump conditions the auxiliary differential equation of the debye constitution model is rewritten to form a new debye maxwell tm system interface auxiliary differential equations are utilized to describe the transient changes in the regularities of electromagnetic fields across a dispersive interface the resulting time dependent jump conditions are rigorously enforced in the fdtd discretization by means of a matched interface and boundary scheme higher order convergences are numerically achieved for the first time in the literature in 2d fdtd simulations of dispersive inhomogeneous media

the stable doubly infinite pedigree process of supercritical branching populations an individual is sampled randomly from a supercritical general branching population and the pedigree process which centers around this ego individual is studied the process describes not only lineage backwards and forwards but also the lives of all individuals involved under mild conditions and in several senses the process is shown to stabilize as time passes the limit is a doubly infinite population process which generalizes the stable age distribution of branching processes and demography it displays a nice independence structure and can easily be constructed from the original branching law the results are applied to certain kin number problems the process of ego s ancestors births and to the flm curve of cell kinetics

optimal matching problem in detection and recognition performance evaluation abstract this paper proposes a principle of one to one correspondence in performance evaluation of a general class of detection and recognition algorithms such a correspondence between ground truth entities and algorithm declared entities is essential in accurately computing objective performance measures such as the detection recognition and false alarm rates we mathematically define the correspondence by formulating a combinatorial optimal matching problem in addition to evaluating detection performance this methodology is also capable of evaluating recognition performance our study shows that the proposed principle for detection performance evaluation is simple general and mathematically sound the derived performance evaluation technique is widely applicable precise consistent and efficient

drift and diffusion for a mechanical system we consider a mechanical system in the plane consisting of a vertical rod of length l with its center moving on the horizontal axis subject to elastic collisions with the particles of a free gas and to a constant forcef assuming a suitable initial measure we show that the evolution of the system as seen from the rod is described by an exponentially ergodic irreducible harris chain implying convergence to a stationary invariant measure ast we deduce that in the proper scaling the motion of the rod is described as a drift plus a diffusion we prove in conclusion that the diffusion is nondegenerate and that the drift is nonzero iff 0 and has the same sign off

positive dependence properties of point processes there are many ways of describing positive dependence for example the strong fkg inequalities and association it is known that for bernoulli random variables the strong fkg inequalities are equivalent to all the conditional distributions being associated which is in turn equivalent to all the conditional distributions having positively correlated marginals these and similar definitions are extended to point processes on r d examples are given to show that these conditions are no longer equivalent

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

time evolution of infinitely many particles an existence theorem in this paper we deal with systems of infinitely many particles in 3 given by a two body short range potential and an external potential depending on the position of the particles we show the existence of dynamics for a set of initial configurations which has measure one with respect to the gibbs measure induced by a suitable family of hamiltonians

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