non self adjoint zakharov shabat operator with a potential of the finite asymptotic values i direct spectral and scattering problems the zakharov and shabat equation for the scattering problem is studied the estimates analytical properties and asymptotic expansions of the jost solution are presented for a general class of the potentials q x not vanishing at infinity the existence of the similarity transformation is also shown for q x vanishing at infinity the continuous part of the spectrum doubly degenerates however nonvanishing finite asymptotic values of q x dissolve the degeneracy completely the expansion theorem is given in c 0 2 r and for a class of q x we prove that the zakharov and shabat equation yields a non self adjoint spectral operator in the hilbert space in the sense of dunford and schwartz

intelligent meshing technique for 2d resistivity inverse problems abstractin geophysical inverse problems an a priori structured mesh is often used for inversion and mesh refinement is applied if needed by the user after observation of inversion results we have developed a new intelligent self adaptive unstructured finite element meshing technique for electrical resistivity tomography inverse problems this new approach uses harris corner and edge detectors that are based on the local autocorrelation function of 2d distribution of pixels this meshing technique optimizes the size of the inverse problem by refining areas where variations in the physical property structure are sensed to be important the meshing technique also generates a more appropriate and optimum mesh for the inverse problem that is dependent on the problem itself tests on modeled data have demonstrated that the proposed intelligent meshing technique can reduce data misfit produce a better reconstruction of the true physical properties and minimize the size of the inverse problem the synthetic m

simplifying mixture models through function approximation the finite mixture model is widely used in various statistical learning problems however the model obtained may contain a large number of components making it inefficient in practical applications in this paper we propose to simplify the mixture model by minimizing an upper bound of the approximation error between the original and the simplified model under the use of the l 2 distance measure this is achieved by first grouping similar components together and then performing local fitting through function approximation the simplified model obtained can then be used as a replacement of the original model to speed up various algorithms involving mixture models during training e g bayesian filtering belief propagation and testing e g kernel density estimation support vector machine svm testing encouraging results are observed in the experiments on density estimation clustering based image segmentation and simplification of svm decision functions

a front tracking method for multiphase free boundary problems a front tracking method for the solution of multiphase free boundary problems is presented based on the method of lines with invariant imbedding this method is sufficiently general to allow the solution of problems with three or more phases and problems in which phases appear and disappear a discussion of the method for the three phase stefan problem and for the moving contact problem as well as a proof of convergence for the latter is included in addition the method is demonstrated for a free boundary problem with a combination of stefan and ablation boundary conditions and for the two dimensional contact problem numerical results indicate that this front tracking method is fast enough to solve a wide range of problems on a personal computer

solution of the cauchy problem for a generalized sine gordon equation we consider a spectral problem generating a hierarchy of nonlinear evolution equations including the sine gordon equation and a physically interesting generalization in the laboratory coordinates the direct and inverse problems are treated the time evolution of the spectral data is explicitly given and therefore the cauchy problem for the related equations is solved

spectral transform and solitons for the three wave coupling model with nontrivial boundary conditions a nonlinear three wave coupling model with nontrivial boundary conditions is analyzed in the framework of the inverse spectral transform spectral data are determined and their evolution is derived it is shown that there exists mutual cancellation of divergences of the scattering matrix elements in branching points on the plane of a spectral parameter a regular dark soliton type solution is obtained

ridge regression biased estimation for nonorthogonal problems in multiple regression it is shown that parameter estimates based on minimum residual sum of squares have a high probability of being unsatisfactory if not incorrect if the prediction vectors are not orthogonal proposed is an estimation procedure based on adding small positive quantities to the diagonal of x x introduced is the ridge trace a method for showing in two dimensions the effects of nonorthogonality it is then shown how to augment x x to obtain biased estimates with smaller mean square error

comparison of finite element techniques for solidification problems the accuracies of the computed temperatures of a liquid in a corner region under freezing conditions are compared for various fixed grid finite element techniques using the analytical solution for this problem as a reference in the finite element formulation of the problem different time stepping schemes are compared the implicit euler backward algorithm combined with an iterative scheme and two three time level methods the lees algorithm and a dupont algorithm which are both applied as non iterative schemes furthermore different methods for handling the evolution of latent heat are examined an approximation method suggested by lemmon and one suggested by del giudice both using the enthalpy formulation as well as a fictitious heat flow method presented by rolph and bathe results of calculations performed with the consistent heat capacity matrix are compared with those performed with a lumped heat capacity matrix

a numerical method to compute the dissolution of second phases in ternary alloys abstract dissolution of stoichiometric multi component particles in ternary alloys is an important process occurring during the heat treatment of as cast aluminium alloys prior to hot extrusion a mathematical model is proposed to describe such a process in this model an equation is given to determine the position of the particle interface in time using two diffusion equations which are coupled by nonlinear boundary conditions at the interface some results concerning existence uniqueness and monotonicity are given furthermore for an unbounded domain an analytical approximation is derived the main part of this work is the development of a numerical solution method finite differences are used on a grid which changes in time the discretization of the boundary conditions is important to obtain an accurate solution the resulting nonlinear algebraic system is solved by the newton raphson method numerical experiments illustrate the accuracy of the numerical method the numerical solution is compared with the analytical approximation

threshold solutions and sharp transitions for nonautonomous parabolic equations on mathbb r n this paper is devoted to a class of nonautonomous parabolic equations of the form ut u f t u on mathbb r n we consider a monotone one parameter family of initial data with compact support such that for small values of the parameter the corresponding solutions decay to zero whereas for large values they exhibit a different behavior either blowup in finite time or locally uniform convergence to a positive constant steady state we are interested in the set of intermediate values of the parameter for which neither of these behaviors occurs we refer to such values as threshold values and to the corresponding solutions as threshold solutions we prove that the transition from decay to the other behavior is sharp there is just one threshold value we also describe the behavior of the threshold solution it is global bounded and asymptotically symmetric in the sense that all its limit profiles as t are radially symmetric about the same center our proofs rely on parabolic liouville theorems asymptotic symmetry results for nonlinear parabolic equations and theorems on exponential separation and principal floquet bundles for linear parabolic equations

learning to match deriving optimal template matching algorithms from probabilistic image models finding correspondences between images by template matching is a common problem in image understanding although a variety of solutions have been proposed most of them rely on the arbitrary choice of a template and a matching function often different cost functions lead to different results and the choice of a good cost for a specific application remains an art statistical models on the other hand allow us to derive optimal learning and matching algorithms from modeling assumptions using likelihood maximization principles the key contribution of this paper is the development of a statistical framework for learning what function to optimize from training examples we present a family of statistical models for grayscale images which allow us to derive optimal template matching algorithms the intensity at each pixel is described by a random variable whose distribution is encoded by a deformable template firstly we assume the intensity distribution to be gaussian and derive an intensity matching algorithm which is a generalization of the classical sum of squared differences then we introduce a hidden segmentation variable in the probabilistic model and derive a segmentation matching algorithm that can handle photometric variations both models are exemplified on the automatic detection of anatomical landmarks in brain magnetic resonance images

nonlinear systems related to an arbitrary space time dependence of the spectral transform a general algebraic analytic scheme for the spectral transform of solutions of nonlinear evolution equations is proposed this allows one to give the general nonlinear evolution corresponding to an arbitrary time and space dependence of the spectral transform in general nonlinear and with nonanalytic dispersion relations the main theorem is that the compatibility conditions always give a true nonlinear evolution because it can always be written as an identity between polynomials in the spectral variable k this general result is then used to obtain first a method to generate a new class of solutions to the nonlinear schrodinger equation and second to construct the spectral transform theory for solving initial boundary value problems for resonant wave coupling processes like self induced transparency in two level media or stimulated brillouin scattering of plasma waves or else stimulated raman scattering in nonlinear optics etc

a mathematical model for the dissolution of particles in multi component alloys dissolution of stoichiometric multi component particles is an important process occurring during the heat treatment of as cast aluminum alloys prior to hot extrusion a mathematical model is proposed to describe such a process in this model equations are given to determine the position of the particle interface in time using a number of diffusion equations which are coupled by nonlinear boundary conditions at the interface this problem is known as a vector valued stefan problem a necessary condition for existence of a solution of the moving boundary problem is proposed and investigated using the maximum principle for the parabolic partial differential equation furthermore for an unbounded domain and planar co ordinates an asymptotic approximation based on self similarity is derived the asymptotic approximation is used to gain insight into the influence of all components on the dissolution subsequently a numerical treatment of the vector valued stefan problem is described the numerical solution is compared with solutions obtained by the analytical methods finally an example is shown

robust image corner detection through curvature scale space this paper describes a novel method for image corner detection based on the curvature scale space css representation the first step is to extract edges from the original image using a canny detector 1986 the corner points of an image are defined as points where image edges have their maxima of absolute curvature the corner points are detected at a high scale of the css and tracked through multiple lower scales to improve localization this method is very robust to noise and we believe that it performs better than the existing corner detectors an improvement to canny edge detector s response to 45 spl deg and 135 spl deg edges is also proposed furthermore the css detector can provide additional point features curvature zero crossings of image edge contours in addition to the traditional corners

existence of many positive solutions of semilinear elliptic equations on annulus abstract we study the existence of many nonradial positive solutions in an annulus of rn it is an improvement of results in c v coffman a nonlinear boundary value problem with many positive solutions j differential equations 54 1984 429 437 an annulus is invariant under many group actions and these group actions act naturaly on the functional and leave the functional invariant therefore when we look for critical points of the functional we can restrict the functional to the manifold consisting of all fixed points under the group action we are going to use different group actions to obtain critical points and furthermore we can distinguish them

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

scale affine invariant interest point detectors in this paper we propose a novel approach for detecting interest points invariant to scale and affine transformations our scale and affine invariant detectors are based on the following recent results 1 interest points extracted with the harris detector can be adapted to affine transformations and give repeatable results geometrically stable 2 the characteristic scale of a local structure is indicated by a local extremum over scale of normalized derivatives the laplacian 3 the affine shape of a point neighborhood is estimated based on the second moment matrix our scale invariant detector computes a multi scale representation for the harris interest point detector and then selects points at which a local measure the laplacian is maximal over scales this provides a set of distinctive points which are invariant to scale rotation and translation as well as robust to illumination changes and limited changes of viewpoint the characteristic scale determines a scale invariant region for each point we extend the scale invariant detector to affine invariance by estimating the affine shape of a point neighborhood an iterative algorithm modifies location scale and neighborhood of each point and converges to affine invariant points this method can deal with significant affine transformations including large scale changes the characteristic scale and the affine shape of neighborhood determine an affine invariant region for each point we present a comparative evaluation of different detectors and show that our approach provides better results than existing methods the performance of our detector is also confirmed by excellent matching resultss the image is described by a set of scale affine invariant descriptors computed on the regions associated with our points

theoretical and numerical results on the two phase stefan problem the two phase stefan problem in several space dimensions and with an enthalpy dependent source is studied here assuming that a strictly positive temperature is prescribed at the fixed boundary the existence of a solution with an extra space regularity is proven the stability of the implicit euler time discretization algorithm is also shown finally for a temperature dependent source error estimates in l infty 0 t l 2 omega and l infty 0 t l 1 omega are deduced for the enthalpy variable

an algorithm for data driven bandwidth selection the analysis of a feature space that exhibits multiscale patterns often requires kernel estimation techniques with locally adaptive bandwidths such as the variable bandwidth mean shift proper selection of the kernel bandwidth is however a critical step for superior space analysis and partitioning this paper presents a mean shift based approach for local bandwidth selection in the multimodal multivariate case the method is based on a fundamental property of normal distributions regarding the bias of the normalized density gradient this paper demonstrates that within the large sample approximation the local covariance is estimated by the matrix that maximizes the magnitude of the normalized mean shift vector using this property the paper develops a reliable algorithm which takes into account the stability of local bandwidth estimates across scales the validity of the theoretical results is proven in various space partitioning experiments involving the variable bandwidth mean shift

a framework for weighted fusion of multiple statistical models of shape and appearance this paper presents a framework for weighted fusion of several active shape and active appearance models the approach is based on the eigenspace fusion method proposed by hall et al which has been extended to fuse more than two weighted eigenspaces using unbiased mean and covariance matrix estimates to evaluate the performance of fusion a comparative assessment on segmentation precision as well as facial verification tests are performed using the ar equinox and xm2vts databases based on the results it is concluded that the fusion is useful when the model needs to be updated online or when the original observations are absent

solution of three waves interaction type models with nontrivial asymptotic and boundary conditions in the following we introduce a new way to solve the cauchy problem for non vanishing potentials at infinity for the spectral problem of the zakharov and shabat ablowitz kaup newell and segur zs akns hierarchy then we apply the results to solve a class of coupled systems with this nonvanishing condition on the potential and with quite general boundary conditions on the other fields finally we present an application to a physical system governed by a three waves interaction type model

shape based tracking of left ventricular wall motion an approach for tracking and quantifying the nonrigid nonuniform motion of the left ventricular lv endocardial wall from two dimensional 2 d cardiac image sequences on a point by point basis over the entire cardiac cycle is presented given a set of boundaries motion computation involves first matching local segments on one contour to segments on the next contour in the sequence using a shape based strategy results from the match process are incorporated with a smoothness term into an optimization functional the global minimum of this functional is found resulting in a smooth flow field that is consistent with the match data the computation is performed for all pairs of frames in the temporal sequence and equally sampled points on one contour are tracked throughout the sequence resulting in a composite flow field over the entire sequence two perspectives on characterizing the optimization functional are presented which result in a tradeoff resolved by the confidence in the initial boundary segmentation experimental results for contours derived from diagnostic image sequences of three different imaging modalities are presented a comparison of trajectory estimates with trajectories of gold standard markers implanted in the lv wall are presented for validation the results of this comparison confirm that although cardiac motion is a three dimensional 3 d problem two dimensional 2 d analysis provides a rich testing ground for algorithm development

an analysis of a phase field model of a free boundary a mathematical analysis of a new approach to solidification problems is presented a free boundary arising from a phase transition is assumed to have finite thickness the physics leads to a system of nonlinear parabolic differential equations existence and regularity of solutions are proved invariant regions of the solution space lead to physical interpretations of the interface a rigorous asymptotic analysis leads to the gibbs thompson condition which relates the temperature at the interface to the surface tension and curvature

a computational approach for corner and vertex detection corners and vertexes are strong and useful features in computer vision for scene analysis stereo matching and motion analysis here we deal with the development of a computational approach to these important features we consider first a corner model and study analytically its behavior once it has been smoothed using the well known gaussian filter this allows us to clarify the behavior of some well knowncornerness measure based approaches used to detect these points of interest most of these classical approaches appear to detect points that do not correspond to the exact position of the corner a new scale space based approach that combines useful properties from the laplacian and beaudet s measure beaudet 1978 is then proposed in order to correct and detect exactly the corner position an extension of this approach is then developed to solve the problem of trihedral vertex characterization and detection in particular it is shown that a trihedral vertex has two elliptic maxima on extremal contrast surfaces if the contrast is sufficient and this allows us to classify trihedral vertexes in 2 classes vertex and vertex as corner the corner detection approach developed is applied to accurately detect trihedral vertexes using an additional test in order to make a distinction between trihedral vertexes and corners many experiments have been carried out using noisy synthetic data and real images containing corners and vertexes most of the promising results obtained are used to illustrate the experimental section of this paper

learning the dynamics and time recursive boundary detection of deformable objects we propose a principled framework for recursively segmenting deformable objects across a sequence of frames we demonstrate the usefulness of this method on left ventricular segmentation across a cardiac cycle the approach involves a technique for learning the system dynamics together with methods of particle based smoothing as well as nonparametric belief propagation on a loopy graphical model capturing the temporal periodicity of the heart the dynamic system state is a low dimensional representation of the boundary and the boundary estimation involves incorporating curve evolution into recursive state estimation by formulating the problem as one of state estimation the segmentation at each particular time is based not only on the data observed at that instant but also on predictions based on past and future boundary estimates although this paper focuses on left ventricle segmentation the method generalizes to temporally segmenting any deformable object

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

spreading vanishing dichotomy in a diffusive logistic model with a free boundary ii abstract we study the diffusive logistic equation with a free boundary in higher space dimensions and heterogeneous environment such a model may be used to describe the spreading of a new or invasive species with the free boundary representing the expanding front for simplicity we assume that the environment and the solution are radially symmetric in the special case of one space dimension and homogeneous environment this free boundary problem was investigated in du and lin 2010 10 we prove that the spreading vanishing dichotomy established in du and lin 2010 10 still holds in the more general and ecologically realistic setting considered here moreover when spreading occurs we obtain best possible upper and lower bounds for the spreading speed of the expanding front when the environment is asymptotically homogeneous at infinity these two bounds coincide our results indicate that the asymptotic spreading speed determined by this model does not depend on the spatial dimension

a robust technique for matching two uncalibrated images through the recovery of the unknown epipolar geometry abstract this paper proposes a robust approach to image matching by exploiting the only available geometric constraint namely the epipolar constraint the images are uncalibrated namely the motion between them and the camera parameters are not known thus the images can be taken by different cameras or a single camera at different time instants if we make an exhaustive search for the epipolar geometry the complexity is prohibitively high the idea underlying our approach is to use classical techniques correlation and relaxation methods in our particular implementation to find an initial set of matches and then use a robust technique the least median of squares lmeds to discard false matches in this set the epipolar geometry can then be accurately estimated using a meaningful image criterion more matches are eventually found as in stereo matching by using the recovered epipolar geometry a large number of experiments have been carried out and very good results have been obtained regarding the relaxation technique we define a new measure of matching support which allows a higher tolerance to deformation with respect to rigid transformations in the image plane and a smaller contribution for distant matches than for nearby ones a new strategy for updating matches is developed which only selects those matches having both high matching support and low matching ambiguity the update strategy is different from the classical winner take all which is easily stuck at a local minimum and also from loser take nothing which is usually very slow the proposed algorithm has been widely tested and works remarkably well in a scene with many repetitive patterns

statistical shape analysis clustering learning and testing using a differential geometric treatment of planar shapes we present tools for 1 hierarchical clustering of imaged objects according to the shapes of their boundaries 2 learning of probability models for clusters of shapes and 3 testing of newly observed shapes under competing probability models clustering at any level of hierarchy is performed using a minimum variance type criterion and a markov process statistical means of clusters provide shapes to be clustered at the next higher level thus building a hierarchy of shapes using finite dimensional approximations of spaces tangent to the shape space at sample means we implicitly impose probability models on the shape space and results are illustrated via random sampling and classification hypothesis testing together hierarchical clustering and hypothesis testing provide an efficient framework for shape retrieval examples are presented using shapes and images from eth surrey and amcom databases

junctions detection classification and reconstruction junctions are important features for image analysis and form a critical aspect of image understanding tasks such as object recognition we present a unified approach to detecting classifying and reconstructing junctions in images our main contribution is a modeling of the junction which is complex enough to handle all these issues and yet simple enough to admit an effective dynamic programming solution we use a template deformation framework along with a gradient criterium to detect radial partitions of the template we use the minimum description length principle to obtain the optimal number of partitions that best describes the junction the kona detector presented by parida et al 1997 is an implementation of this model we demonstrate the stability and robustness of the detector by analyzing its behavior in the presence of noise using synthetic controlled apparatus we also present a qualitative study of its behavior on real images

an information fusion framework for robust shape tracking existing methods for incorporating subspace model constraints in shape tracking use only partial information from the measurements and model distribution we propose a unified framework for robust shape tracking optimally fusing heteroscedastic uncertainties or noise from measurement system dynamics and a subspace model the resulting nonorthogonal subspace projection and fusion are natural extensions of the traditional model constraint using orthogonal projection we present two motion measurement algorithms and introduce alternative solutions for measurement uncertainty estimation we build shape models offline from training data and exploit information from the ground truth initialization online through a strong model adaptation our framework is applied for tracking in echocardiograms where the motion estimation errors are heteroscedastic in nature each heart has a distinct shape and the relative motions of epicardial and endocardial borders reveal crucial diagnostic features the proposed method significantly outperforms the existing shape space constrained tracking algorithm due to the complete treatment of heteroscedastic uncertainties the strong model adaptation and the coupled tracking of double contours robust performance is observed even on the most challenging cases

the dirac equation and integrable systems of kp type the propagator for the 2d heat equation in an arbitrary linear space is shown to give solutions of the two component kadomtsev petviashvilii kp equations also called davey stewartson system this propagator is subject to the klein gordon equation and its right derivatives are required to be of rank one that imply that it can be expressed in terms of solutions of the dirac equation large families of solutions of the two component kadomtsev petviashvilii equations are constructed in terms of solutions of the heat and dirac equations particular attention is paid to the real reductions of the davey stewartson type recovering in this way the line solitons and the multidromion solutions moreover new solutions to the davey stewartson i are presented as massive deformations of the dromion

merging and splitting eigenspace models we present new deterministic methods that given two eigenspace models each representing a set of n dimensional observations will 1 merge the models to yield a representation of the union of the sets and 2 split one model from another to represent the difference between the sets as this is done we accurately keep track of the mean here we give a theoretical derivation of the methods empirical results relating to the efficiency and accuracy of the techniques and three general applications including the construction of gaussian mixture models that are dynamically updateable

inverse scattering transform for the vector nonlinear schrodinger equation with nonvanishing boundary conditions the inverse scattering transform for the vector defocusing nonlinear schrodinger nls equation with nonvanishing boundary values at infinity is constructed the direct scattering problem is formulated on a two sheeted covering of the complex plane two out of the six jost eigenfunctions however do not admit an analytic extension on either sheet of the riemann surface therefore a suitable modification of both the direct and the inverse problem formulations is necessary on the direct side this is accomplished by constructing two additional analytic eigenfunctions which are expressed in terms of the adjoint eigenfunctions the discrete spectrum bound states and symmetries of the direct problem are then discussed in the most general situation a discrete eigenvalue corresponds to a quartet of zeros poles of certain scattering data the inverse scattering problem is formulated in terms of a generalized riemann hilbert rh problem in the upper lower half planes of a suitable uniformization variable special soliton solutions are constructed from the poles in the rh problem and include dark dark soliton solutions which have dark solitonic behavior in both components as well as dark bright soliton solutions which have one dark and one bright component the linear limit is obtained from the rh problem and is shown to correspond to the fourier transform solution obtained from the linearized vector nls system

combining multiple dynamic models and deep learning architectures for tracking the left ventricle endocardium in ultrasound data we present a new statistical pattern recognition approach for the problem of left ventricle endocardium tracking in ultrasound data the problem is formulated as a sequential importance resampling algorithm such that the expected segmentation of the current time step is estimated based on the appearance shape and motion models that take into account all previous and current images and previous segmentation contours produced by the method the new appearance and shape models decouple the affine and nonrigid segmentations of the left ventricle to reduce the running time complexity the proposed motion model combines the systole and diastole motion patterns and an observation distribution built by a deep neural network the functionality of our approach is evaluated using a dataset of diseased cases containing 16 sequences and another dataset of normal cases comprised of four sequences where both sets present long axis views of the left ventricle using a training set comprised of diseased and healthy cases we show that our approach produces more accurate results than current state of the art endocardium tracking methods in two test sequences from healthy subjects using three test sequences containing different types of cardiopathies we show that our method correlates well with interuser statistics produced by four cardiologists

a conserving discretization for the free boundary in a two dimensional stefan problem the dissolution of a disk likeal2cuparticle is considered a characteristic property is that initially the particle has a nonsmooth boundary the mathematical model of this dissolution process contains a description of the particle interface of which the position varies in time such a model is called a stefan problem it is impossible to obtain an analytical solution for a general two dimensional stefan problem so we use the finite element method to solve this problem numerically first we apply a classical moving mesh method computations show that after some time steps the predicted particle interface becomes very unrealistic therefore we derive a new method for the displacement of the free boundary based on the balance of atoms this method leads to good results also for nonsmooth boundaries some numerical experiments are given for the dissolution of anal2cuparticle in anal cualloy

approximation of the heat equation in a variable domain with application to the stefan problem a discretization of the one dimensional heat equation in a time dependent domain is considered with particular emphasis on a generalization of the crank nicholson scheme for the discretization with respect to time application to a one dimensional stefan problem is given with an iterative algorithm to follow the moving boundary numerical results agree well with the theoretical error bounds

a discrete expression of canny s criteria for step edge detector performances evaluation optimal filters for edge detection are usually developed in the continuous domain and then transposed by sampling to the discrete domain simpler filters are directly defined in the discrete domain we define criteria to compare filter performances in the discrete domain canny has defined 1983 1986 three criteria to derive the equation of an optimal filter for step edge detection good detection good localization and low responses multiplicity these criteria seem to be good candidates for filter comparison unfortunately they have been developed in the continuous domain and their analytical expressions cannot be used in the discrete domain we establish three criteria with the same meaning as canny s some comparisons with experimental results confirm the validity of our approach this study highlights the existence of two classes of derivative operators that are distinguished by whether or not the impulse response of the filter in continuous space domain is continuous on its center these classes exhibit very different properties for the second and third criteria we extend the use of the first and third criteria to the smoothing filters we also define an optimal continuous filter according to the continuous third criterion and an optimal discrete filter according to the discrete third criterion we compare the performances of the sampled version of the continuous filter to those of the optimal discrete filter

solution of vector stefan problems with cross diffusion a general model for the dissolution of particles in multi component alloys is proposed and analyzed the model is based on diffusion equations with cross terms for the several species combined with a stefan condition as the equation of motion of the interface between the particle and diffusive phase several numerical schemes for the solution of the stefan problem are proposed and compared it turns out that diagonalization is useful for numerical purposes however for the case of position dependent diffusion coefficients one has to use a different scheme here we analyze stability and workload of several time integration methods

blow up and asymptotic behavior of solutions for reaction diffusion equations with free boundaries abstract we study the blow up phenomena and the asymptotic behavior of time global solutions for reaction diffusion equations u t u x x a u u p a r and p 1 with free boundaries and initial data x we give a sharp threshold value a p 0 such that the solution blows up in finite time when vanishes i e u 0 as t when and when it converges as t to 0 or to an evenly decreasing positive stationary solution depending on whether a 0 or a 0 moreover when blow up happens we show that the blow up set is compact in the occupying domain of initial data and the free boundaries keep bounded

robust photometric invariant features from the color tensor luminance based features are widely used as low level input for computer vision applications even when color data is available the extension of feature detection to the color domain prevents information loss due to isoluminance and allows us to exploit the photometric information to fully exploit the extra information in the color data the vector nature of color data has to be taken into account and a sound framework is needed to combine feature and photometric invariance theory in this paper we focus on the structure tensor or color tensor which adequately handles the vector nature of color images further we combine the features based on the color tensor with photometric invariant derivatives to arrive at photometric invariant features we circumvent the drawback of unstable photometric invariants by deriving an uncertainty measure to accompany the photometric invariant derivatives the uncertainty is incorporated in the color tensor hereby allowing the computation of robust photometric invariant features the combination of the photometric invariance theory and tensor based features allows for detection of a variety of features such as photometric invariant edges corners optical flow and curvature the proposed features are tested for noise characteristics and robustness to photometric changes experiments show that the proposed features are robust to scene incidental events and that the proposed uncertainty measure improves the applicability of full invariants

analysis on a coupled parabolic system with free boundary abstract the purpose of this paper is to investigate a parabolic problem with coupled reaction terms and free boundary including the existence uniqueness regularity and long time behavior of positive solutions firstly by the contraction mapping theorem we establish the local existence and uniqueness of positive solutions then we prove the solution blows up in finite time with large initial data by comparison principle and give more details for these large initial data by exhibiting an energy condition the simultaneous blow up result of the maximum of u and v is obtained and the blow up set of blow up solutions is a compact subset of 0 h 0 furthermore there is a global and fast solution which decays uniformly at an exponential rate if the initial datum is small while there is a global and slow solution provided that the initial datum is suitably large finally for initial data x x we obtain a trichotomy conclusion by considering the size of parameter

stability and instability of stationary solutions for sublinear parabolic equations abstract in the present paper we study the initial boundary value problem of the sublinear parabolic equation we prove the existence of solutions and investigate the stability and instability of stationary solutions we show that a unique positive and a unique negative stationary solutions are exponentially stable and give the exact exponent we prove that small stationary solutions are unstable for one space dimensional autonomous equations we elucidate the structure of stationary solutions and study the stability of all stationary solutions

cortex segmentation a fast variational geometric approach an automatic cortical gray matter segmentation from a three dimensional 3 d brain images magnetic resonance mr or computed tomography is a well known problem in medical image processing in this paper we first formulate it as a geometric variational problem for propagation of two coupled bounding surfaces an efficient numerical scheme is then used to implement the geodesic active surface model experimental results of cortex segmentation on real 3 d mr data are provided

using simple decomposition for smoothing and feature point detection of noisy digital curves this correspondence presents an algorithm for smoothed polygonal approximation of noisy digital planar curves and feature point detection the resulting smoothed polygonal representation preserves the signs of the curvature function of the curve the algorithm is based on a simple decomposition of noisy digital curves into a minimal number of convex and concave sections the location of each separation point is optimized yielding the minimal possible distance between the smoothed approximation and the original curve curve points within a convex concave section are discarded if their angle signs do not agree with the section sign and if the resulted deviations from the curve are less than a threshold spl epsi which is derived automatically inflection points are curve points between pairs of convex concave sections and cusps are curve points between pairs of convex convex or concave concave sections corners and points of local minimal curvature are detected by applying the algorithm to respective total curvature graphs the detection of the feature points is based on properties of pairs of sections that are determined in an adaptive manner rather than on properties of single points that are based on a fixed size neighborhood the detection is therefore reliable and robust complexity analysis and experimental results are presented

a computational framework and an algorithm for the measurement of visual the robust measurement of visual motion from digitized image sequences has been an important but difficult problem in computer vision this paper describes a hierarchical computational framework for the determination of dense displacement fields from a pair of images and an algorithm consist ent with that framework our framework is based on the separation of the image intensity information as well as the process of measuring motion according to scale the large scale intensity information is first used to obtain rough estimates of image motion which are then refined by using intensity information at smaller scales the estimates are in the form of displacement or velocity vectors for pixels and are accompanied by a direction dependent confidence measure a smoothness constraint is employed to propagate the measurements with high confidence to their neigboring areas where the confidences are low at all levels the computations are pixel parallel uniform across the image and based on information from a small neighborhood of a pixel for our algorithm the local displacement vectors are determind by mini mizing the sum of squared differences ssd of intensities the confidence measures are derived from the shape of the ssd surface and the smoothness constraint is cast in the form of energy minimization results of applying our algorithm to pairs of real images are included in addition to our own

an explicit expression of the dark n soliton solution of the mkdv equation by means of the darboux transformation a darboux transformation is developed for generating dark multi soliton solutions of the mkdv equation the darboux matrices are found explicitly in recursive manner and a system of linear algebraic equations is derived for determining the dark n soliton solutions by means of the binet cauchy formula an explicit expression of the dark n soliton solution is obtained

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

determining optical flow optical flow cannot be computed locally since only one independent measurement is available from the image sequence at a point while the flow velocity has two components a second constraint is needed a method for finding the optical flow pattern is presented which assumes that the apparent velocity of the brightness pattern varies smoothly almost everywhere in the image an iterative implementation is shown which successfully computes the optical flow for a number of synthetic image sequences the algorithm is robust in that it can handle image sequences that are quantized rather coarsely in space and time it is also insensitive to quantization of brightness levels and additive noise examples are included where the assumption of smoothness is violated at singular points or along lines in the image

the curvature primal sketch in this paper we introduce a novel representation of the significant changes in curvature along the bounding contour of planar shape we call the representation the curvature primal sketch because of the close analogy to the primal sketch representation advocated by marr for describing significant intensity changes we define a set of primitive parameterized curvature discontinuities and derive expressions for their convolutions with the first and second derivatives of a gaussian we describe an implemented algorithm that computes the curvature primal sketch by matching the multiscale convolutions of a shape and illustrate its performance on a set of tool shapes several applications of the representation are sketched

darboux transformations for the nonlinear schrodinger equations darboux transformations for the akns zs system are constructed in terms of grammian type determinants of vector solutions of the associated lax pairs with an operator spectral parameter a study of the reduction of the darboux transformation for the nonlinear schrodinger equations with standard and anomalous dispersion is presented two different families of new solutions for a given seed solution of the nonlinear schrodinger equation are given being one family related to a new vector lax pair for it in the first family and associated to diagonal matrices we present topological solutions with different asymptotic argument for the amplitude and nonzero background for the anomalous dispersion case they represent continuous deformations of the bright n soliton solution which is recovered for zero background in particular these solutions contain the combination of multiple homoclinic orbits of the focusing nonlinear schrodinger equation associated with jordan blocks we find rational deformations of the just described solutions as well as pure rational solutions the second family contains not only the solutions mentioned above but also broader classes of solutions for example in the standard dispersion case we are able to obtain the dark soliton solutions

a coarse to fine deformable contour optimization framework this paper introduces a novel coarse to fine deformable contour optimization framework which is composed of two main components the first component uses scale space and information theories to produce a coarser representation of the input image to be used in a coarse to fine optimization scheme the employment of information theory ensures that maximal image information is propagated to the coarse images and employment of scale spaces provides a mechanism to change the image coarseness locally based on the deformable contour model definition the second component of this framework uses a novel combination of dynamic programming and gradient descent methods to optimize the contour energy on coarser representations and then use the obtained coarse contour positions in finer optimizations the motivation in using a combination of dynamic programming and gradient descent method is to take advantage of each method s efficiency and avoid their drawbacks in order to verify the performance of this framework we constructed a deformable contour model for the spatiotemporal tracking of closed contours and optimized the model energy under this framework experiments on this system performed using synthetic images and real world echocardiographic sequences demonstrated the effectiveness and practicality of this framework

restoration of the velocity field of the heart from two dimensional echocardiograms a method to quantify the motion of the heart from digitized sequences of two dimensional echocardiograms 2 d echos was recently proposed this method computes on every point of the 2 d echoes the 2 d apparent velocity vector or optical flow which characterizes its interframe motion however further analysis is required to determine what part of this motion is due to translation rotation contraction and deformation of the myocardium a method to locally obtain this information is presented the proposed method assumes that the interframe velocity field u xy v x y can be locally described by linear equations in the form u x y a ax by v x y b cx dy the additional constraint was introduced in the computation of the local velocity field by the method of projections onto convex sets since this constraint is only valid locally the myocardium must be first divided into sectors and the velocity fields computed independently for each sector

discriminative metric preservation for tracking low resolution targets tracking low resolution lr targets is a practical yet quite challenging problem in real video analysis applications lack of discriminative details in the visual appearance of the lr target leads to the matching ambiguity which confronts most existing tracking methods although artificially enhancing the video resolution by superresolution sr techniques before analyzing might be an option the high demand of computational cost can hardly meet the requirements of the tracking scenario this paper presents a novel solution to track lr targets without explicitly performing sr this new approach is based on discriminative metric preservation that preserves the data affinity structure in the high resolution hr feature space for effective and efficient matching of lr images in addition we substantialize this new approach in a solid case study of differential tracking under metric preservation and derive a closed form solution to motion estimation for lr video in addition this paper extends the basic linear metric preservation method to a more powerful nonlinear kernel metric preservation method such a solution to lr target tracking is discriminative robust and efficient extensive experiments validate the entrustments and effectiveness of the proposed approach and demonstrate the improved performance of the proposed method in tracking lr targets

non linear simulation of dendritic solidification of an undercooled melt two dimensional finite element simulations of solidification for quiescent undercooled pure metals are presented the full non linear transient heat equation is used with phase front tracking which is subject to local curvature and interfacial kinetics during early stages of the waveform instability the simulated solutions match the linear stability analysis with fidelity beyond the valid range of that analysis the numerical solution continues to demonstrate the physically observed exponential growth behaviour and characteristic spacing between fingers whereas the simulations show the sensitivity of dendritic growth to initial conditions as expected for an unstable process the overall pattern formation preserves the characteristic spacing the simulations are terminated after the onset of bifurcation thereafter the numerical model is inappropriate for physical comparison owing to the planar two dimensional limitation

robust shape tracking with multiple models in ultrasound images this paper addresses object tracking in ultrasound images using a robust multiple model tracker the proposed tracker has the following features 1 it uses multiple dynamic models to track the evolution of the object boundary and 2 it models invalid observations outliers reducing their influence on the shape estimates the problem considered in this paper is the tracking of the left ventricle which is known to be a challenging problem the heart motion presents two phases diastole and systole with different dynamics the multiple models used in this tracker try to solve this difficulty in addition ultrasound images are corrupted by strong multiplicative noise which prevents the use of standard deformable models robust estimation techniques are used to address this difficulty the multiple model data association mmda tracker proposed in this paper is based on a bank of nonlinear filters organized in a tree structure the algorithm determines which model is active at each instant of time and updates its state by propagating the probability distribution using robust estimation techniques

non self adjoint zakharov shabat operator with a potential of the finite asymptotic values ii inverse problem the inverse spectral and scattering problem of the zakharov shabat zs operator is studied the similarity transformation between zs operators is examined when their potentials q x have the common nonvanishing asymptotic values q at the infinity the marchenko equation is derived from the parseval equation we give the necessary as well as the sufficient condition of the scattering data for the potential of the specified class

deformable kernels for early vision early vision algorithms often have a first stage of linear filtering that extracts from the image information at multiple scales of resolution and multiple orientations a common difficulty in the design and implementation of such schemes is that one feels compelled to discretize coarsely the space of scales and orientations in order to reduce computation and storage costs a technique is presented that allows 1 computing the best approximation of a given family using linear combinations of a small number of basis functions and 2 describing all finite dimensional families i e the families of filters for which a finite dimensional representation is possible with no error the technique is based on singular value decomposition and may be applied to generating filters in arbitrary dimensions and subject to arbitrary deformations the relevant functional analysis results are reviewed and precise conditions for the decomposition to be feasible are stated experimental results are presented that demonstrate the applicability of the technique to generating multiorientation multi scale 2d edge detection kernels the implementation issues are also discussed

early jump out corner detectors the authors present two new corner detectors one works by using dissimilarity along the contour direction to detect curves in the image contour and the other estimates image curvature along the contour direction these operators are fast robust to noise and require no subjective thresholding

heteroscedastic regression in computer vision problems with bilinear constraint we present an algorithm to estimate the parameters of a linear model in the presence of heteroscedastic noise i e each data point having a different covariance matrix the algorithm is motivated by the recovery of bilinear forms one of the fundamental problems in computer vision which appears whenever the epipolar constraint is imposed or a conic is fit to noisy data points we employ the errors in variables eiv model and show why already at moderate noise levels most available methods fail to provide a satisfactory solution the improved behavior of the new algorithm is due to two factors taking into account the heteroscedastic nature of the errors arising from the linearization of the bilinear form and the use of generalized singular value decomposition gsvd in the computations the performance of the algorithm is compared with several methods proposed in the literature for ellipse fitting and estimation of the fundamental matrix it is shown that the algorithm achieves the accuracy of nonlinear optimization techniques at much less computational cost

intrackability characterizing video statistics and pursuing video representations videos of natural environments contain a wide variety of motion patterns of varying complexities which are represented by many different models in the vision literature in many situations a tracking algorithm is formulated as maximizing a posterior probability in this paper we propose to measure the video complexity by the entropy of the posterior probability called the intrackability to characterize the video statistics and pursue optimal video representations based on the definition of intrackability our study is aimed at three objectives firstly we characterize video clips of natural scenes by intrackability we calculate the intrackabilities of image points to measure the local inferential uncertainty and collect the histogram of the intrackabilities over the video in space and time as the global video statistics we find that a pca scatter plot based on the first two principle components of intrackability histograms can reflect the major variations i e image scaling and object density in natural video clips secondly we show that different video representations including deformable contours tracking kernels with various appearance features dense motion fields and dynamic texture models are connected by the change of intrackability and thus develop a simple criterion for model transition and for pursuing the optimal video representation thirdly we derive the connections between the intrackability measure and other criteria in the literature such as the shi tomasi texturedness measure conditional number and harris stephens r score and compare with the shi tomasi measure in tracking experiments

exponentially small asymptotics of solutions to the defocusing nonlinear schrodinger equation ii the riemann hilbert problem approach is used to derive a special set of leading order exponentially small asymptotics as t such that x t 0 of solutions to the cauchy problem for the defocusing nonlinear schrodinger equation i t u x2 u 2 u 2 1 u 0 with finite density initial data u x 0 x exp i 11 1 o 1 0 2

global existence large time behavior and life span of solutions of a semilinear parabolic cauchy problem we investigate the behavior of the solution u x t of where 1 1 n 2 xi 2 is the laplace operator p 1 is a constant t 0 and is a nonnegative bounded continuous function in r n the main results are for the case when the initial value has polynomial decay near x assuming 1 x 75a with a 0 various questions of global in time existence and nonexistence large time behavior or life span of the solution u x t are answered in terms of simple conditions on a p and the space dimension n

focus of attention from local color symmetries in this paper a continuous valued measure for local color symmetry is introduced the new algorithm is an extension of the successful gray value based symmetry map proposed by reisfeld et al the use of color facilitates the detection of focus points fps on objects that are difficult to detect using gray value contrast only the detection of fps is aimed at guiding the attention of an object recognition system therefore fps have to fulfill three major requirements stability distinctiveness and usability the proposed algorithm is evaluated for these criteria and compared with the gray value based symmetry measure and two other methods from the literature stability is tested against noise object rotation and variations of lighting as a measure for the distinctiveness of fps the principal components of fp centered windows are compared with those of windows at randomly chosen points on a large database of natural images finally usability is evaluated in the context of an object recognition task

the diffusive competition problem with a free boundary in heterogeneous time periodic environment abstract in this paper we consider the diffusive competition problem with a free boundary and sign changing intrinsic growth rate in heterogeneous time periodic environment consisting of an invasive species with density u and a native species with density v we assume that v undergoes diffusion and growth in r n and u exists initially in a ball b h 0 0 but invades into the environment with spreading front r h t the effect of the dispersal rate d 1 the initial occupying habitat h 0 the initial density u 0 of invasive species u and the parameter see 1 3 on the dynamics of this free boundary problem are studied a spreading vanishing dichotomy is obtained and some sufficient conditions for the invasive species spreading and vanishing are provided moreover when spreading of u happens some rough estimates of the spreading speed are also given

evaluation of interest point detectors many different low level feature detectors exist and it is widely agreed that the evaluation of detectors is important in this paper we introduce two evaluation criteria for interest points repeatability rate and information content repeatability rate evaluates the geometric stability under different transformations information content measures the distinctiveness of features different interest point detectors are compared using these two criteria we determine which detector gives the best results and show that it satisfies the criteria well

a novel image representation via local frequency analysis for illumination invariant stereo matching in this paper we propose a novel image representation approach to tackle illumination variations in stereo matching problems images are mapped using their fourier transforms which are convolved with a set of monogenic filters frequency analysis is carried out at different scales to account for most image content the phase congruency and the local weighted mean phase angle are then computed over all the scales the original image is transformed into a new representation using these two mappings this representation is invariant to illumination and contrast variations more importantly it is generic and can be used with most sparse as well as dense stereo matching algorithms in addition sequential feature matching or tracking can also benefit from our approach in varying radiometric conditions we demonstrate the improvements introduced with our image mappings on well established data sets in the literature as well as on our own experimental scenarios that include high dynamic range imagery the experiments include both dense and sparse stereo and sequential matching algorithms where the latter is considered in the very challenging visual odometry framework

scale based description and recognition of planar curves and two dimensional shapes the problem of finding a description at varying levels of detail for planar curves and matching two such descriptions is posed and solved in this paper a number of necessary criteria are imposed on any candidate solution method path based gaussian smoothing techniques are applied to the curve to find zeros of curvature at varying levels of detail the result is the generalized scale space image of a planar curve which is invariant under rotation uniform scaling and translation of the curve these properties make the scale space image suitable for matching the matching algorithm is a modification of the uniform cost algorithm and finds the lowest cost match of contours in the scale space images it is argued that this is preferable to matching in a so called stable scale of the curve because no such scale may exist for a given curve this technique is applied to register a landsat satellite image of the strait of georgia b c manually corrected for skew to a map containing the shorelines of an overlapping area