multimodality image registration by maximization of mutual information a new approach to the problem of multimodality medical image registration is proposed using a basic concept from information theory mutual information mi or relative entropy as a new matching criterion the method presented in this paper applies mi to measure the statistical dependence or information redundancy between the image intensities of corresponding voxels in both images which is assumed to be maximal if the images are geometrically aligned maximization of mi is a very general and powerful criterion because no assumptions are made regarding the nature of this dependence and no limiting constraints are imposed on the image content of the modalities involved the accuracy of the mi criterion is validated for rigid body registration of computed tomography ct magnetic resonance mr and photon emission tomography pet images by comparison with the stereotactic registration solution while robustness is evaluated with respect to implementation issues such as interpolation and optimization and image content including partial overlap and image degradation our results demonstrate that subvoxel accuracy with respect to the stereotactic reference solution can be achieved completely automatically and without any prior segmentation feature extraction or other preprocessing steps which makes this method very well suited for clinical applications

the angular difference function and its application to image registration the estimation of large motions without prior knowledge is an important problem in image registration in this paper we present the angular difference function adf and demonstrate its applicability to rotation estimation the adf of two functions is defined as the integral of their spectral difference along the radial direction it is efficiently computed using the pseudopolar fourier transform which computes the discrete fourier transform of an image on a near spherical grid unlike other fourier based registration schemes the suggested approach does not require any interpolation thus it is more accurate and significantly faster

real time affine global motion estimation using phase correlation and its application for digital image stabilization we propose a fast and robust 2d affine global motion estimation algorithm based on phase correlation in the fourier mellin domain and robust least square model fitting of sparse motion vector field and its application for digital image stabilization rotation scale translation rst approximation of affine parameters is obtained at the coarsest level of the image pyramid thus ensuring convergence for a much larger range of motions despite working at the coarsest resolution level using subpixel accurate phase correlation provides sufficiently accurate coarse estimates for the subsequent refinement stage of the algorithm the refinement stage consists of ransac based robust least square model fitting for sparse motion vector field estimated using block based subpixel accurate phase correlation at randomly selected high activity regions in finest level of image pyramid resulting algorithm is very robust to outliers such as foreground objects and flat regions we investigate the robustness of the proposed method for digital image stabilization application experimental results show that the proposed algorithm is capable of estimating larger range of motions as compared to another phase correlation method and optical flow algorithm

global existence for the einstein vacuum equations in wave coordinates we prove global stability of minkowski space for the einstein vacuum equations in harmonic wave coordinate gauge for the set of restricted data coinciding with the schwarzschild solution in the neighborhood of space like infinity the result contradicts previous beliefs that wave coordinates are unstable in the large and provides an alternative approach to the stability problem originally solved for unrestricted data in a different gauge and with a precise description of the asymptotic behavior at null infinity by d christodoulou and s klainerman

a new smoothing newton type method for second order cone programming problems a new smoothing function of the well known fischer burmeister function is given based on this new function a smoothing newton type method is proposed for solving second order cone programming at each iteration the proposed algorithm solves only one system of linear equations and performs only one line search this algorithm can start from an arbitrary point and it is q quadratically convergent under a mild assumption numerical results demonstrate the effectiveness of the algorithm

scattering for the quasilinear wave equations with null conditions in two dimensions abstract we give a detailed description of the scattering theory of solutions to the quasilinear wave equations with null conditions and small initial data in two dimensions the scattering profile is shown to be the same as the one conjectured by alinhac 1 1995 our proof is based on a framework of fourier transform by deng and pusateri 6 2018 and an expansion of oscillatory integral together with the global well posedness of the solutions by alinhac 2 2001

pseudopolar based estimation of large translations rotations and scalings in images one of the major challenges related to image registration is the estimation of large motions without prior knowledge this work presents a fourier based approach that estimates large translations scalings and rotations the algorithm uses the pseudopolar pp fourier transform to achieve substantial improved approximations of the polar and log polar fourier transforms of an image thus rotations and scalings are reduced to translations which are estimated using phase correlation by utilizing the pp grid we increase the performance accuracy speed and robustness of the registration algorithms scales up to 4 and arbitrary rotation angles can be robustly recovered compared to a maximum scaling of 2 recovered by state of the art algorithms the algorithm only utilizes one dimensional fast fourier transform computations whose overall complexity is significantly lower than prior works experimental results demonstrate the applicability of the proposed algorithms

almost global existence for 2 d incompressible isotropic elastodynamics author s lei z sideris tc zhou y abstract 2015 american mathematical society we consider the cauchy problem for 2 d incompressible isotropic elastodynamics standard energy methods yield local solutions on a time interval 0 t for initial data of the form u0 where t depends only on some sobolev norm of u0 we show that for such data there exists a unique solution on a time interval 0 exp t provided that is sufficiently small this is achieved by careful consideration of the structure of the nonlinearity the incompressible elasticity equation is inherently linearly degenerate in the isotropic case in other words the equation satisfies a null condition this is essential for time decay estimates the pressure which arises as a lagrange multiplier to enforce the incompressibility constraint is estimated in a novel way as a nonlocal nonlinear term with null structure the proof employs the generalized energy method of klainerman enhanced by weighted l2 estimates and the ghost weight introduced by alinhac

an adaptable multilayer fractional fourier transform approach for image registration a novel adaptable accurate way for calculating polar fft and log polar fft is developed in this paper named multilayer fractional fourier transform mlfft mlfft is a necessary addition to the pseudo polar fft for the following reasons it has lower interpolation errors in both polar and log polar fourier transforms it reaches better accuracy with the nearly same computing complexity as the pseudo polar fft it provides a mechanism to increase the accuracy by increasing the user defined computing level this paper demonstrates both mlfft itself and its advantages theoretically and experimentally by emphasizing applications of mlfft in image registration with rotation and scaling our experiments suggest two major advantages of mlfft 1 scaling up to 5 and arbitrary rotation angles or scales up to 10 without rotation can be recovered by mlfft while currently the result recovered by the state of the art algorithms is the maximum scaling of 4 2 no iteration is needed to obtain large rotation and scaling values of images by mlfft hence it is more efficient than the pseudopolar based fft methods for image registration

global existence of null form wave equations on small asymptotically euclidean manifolds abstract we prove the global existence of the small solutions to the cauchy problem for quasilinear wave equations satisfying the null condition on r 3 g where the metric g is a small perturbation of the flat metric and approaches the euclidean metric like 1 x 2 2 with 1 global and almost global existence for systems without the null condition are also discussed for certain small time dependent perturbations of the flat metric in appendix a

uniform bound of sobolev norms of solutions to 3d nonlinear wave equations with null condition abstract this article concerns the time growth of sobolev norms of classical solutions to the 3d quasi linear wave equations with the null condition given initial data in h s h s 1 with compact supports the global well posedness theory has been established independently by klainerman 13 and christodoulou 3 respectively for a relatively large integer s however the highest order sobolev energy namely the h s energy of solutions may have a logarithmic growth in time in this paper we show that the h s energy of solutions is also uniformly bounded for s 5 the proof employs the generalized energy method of klainerman enhanced by weighted l 2 estimates and the ghost weight introduced by alinhac

multisensor image registration via implicit similarity this paper presents an approach to the registration of significantly dissimilar images acquired by sensors of different modalities a robust matching criterion is derived by aligning the locations of gradient maxima the alignment is achieved by iteratively maximizing the magnitudes of the intensity gradients of a set of pixels in one of the images where the set is initialized by the gradient maxima locations of the second image no explicit similarity measure that uses the intensities of both images is used the computation utilizes the full spatial information of the first image and the accuracy and robustness of the registration depend only on it false matchings are detected and adaptively weighted using a directional similarity measure by embedding the scheme in a coarse to fine formulation we were able to estimate affine and projective global motions even when the images were characterized by complex space varying intensity transformations the scheme is especially suitable when one of the images is of considerably better quality than the other noise blur etc we demonstrate these properties via experiments on real multisensor image sets

intensity based image registration by nonparametric local smoothing image registration is used widely in applications for mapping one image to another existing image registration methods are either feature based or intensity based feature based methods first extract relevant image features and then find the geometrical transformation that best matches the two corresponding sets of features extracted from the two images because identification and extraction of image features is often a challenging and time consuming process intensity based image registration by which the mapping transformation is estimated directly from the observed image intensities of the two images has received much attention recently in the literature most existing intensity based image registration methods estimate the mapping transformation globally by solving a minimization maximization problem defined by the two entire images to register to this end it needs to be assumed that the mapping transformation has a certain type of parametric form or it is a continuous bivariate function satisfying certain regularity conditions in this paper we propose a novel intensity based image registration method using nonparametric local smoothing by this method the mapping transformation at a given pixel is estimated locally in a neighborhood after certain image features are accommodated in the estimation due to the flexibility of local smoothing this method does not require any parametric form for the mapping transformation it even allows the transformation to be a discontinuous function numerical examples show that it is effective in various applications

blow up for quasi linear wave equations in three space dimensions we consider equations of the form u phi x t u u u 1a for a function u u x 1 x n t u x t here denotes the d alembertian square frac partial 2 partial t 2 vartriangle 1b and u represents the vector of first derivatives u that of second derivatives of u with respect to the x k and t on linearizing 1a shall go over into the classical wave equation u 0 this means that and its first derivatives with respect to u u u shall vanish for u u u 0

a new feature extractor invariant to intensity rotation and scaling of color images this paper proposes a new method for extracting the invariant features of an image based on the concept of principal component analysis and a competitive learning algorithm the proposed algorithm can be applied to binary gray level or colored texture images with a size greater than 256x256 pixels in addition to translation scaling and rotation invariant extraction the extraction of a feature invariant to color intensity can be implemented by using this method in our experiment the proposed method shows the capability to differentiate images having the same shape but different colored textures the experimental results report the effectiveness of this technique and its performance as measured by recognition accuracy rate and computational time these results are also compared with those obtained by classical techniques

global classical solutions of nonlinear wave equations is a formally selfadjoint positive elliptic operator and f is a real c2 function with non negative primitive function we treat both the homogeneous initialboundary value problem over ir x f2 for a smooth open set 2clr and the cauchy problem over ir x 1r for the initial boundary value problem we show that any strong solution of 0 1 known to exist according to heinz and yon wahl 4 if 2rn f j u2 o lul 2j j 0 1 u oo

on a global existence theorem of small amplitude solutions for nonlinear wave equations in an exterior domain soit un domaine non borne dans un espace euclidien a n dimensions r n a frontiere compacte et c on considere le probleme mixte u u f t x d 1 d 1 u f t x dans 0 u 0 sur 0 u 0 x u 0 x t u 0 x u 1 x dans f est une fonction non lineaire a valeur reelle et d 1 d 1 u t j x u 1 j 2

minimum principle of complementary energy of cable networks by using second order cone programming abstract the minimum principle of complementary energy is established for cable networks involving only stress components as variables in geometrically nonlinear elasticity it is rather amazing that the complementary energy always attains minimum value at the equilibrium state irrespective of the stability of cable networks contrary to the fact that only the stationary principles have been presented for elastic trusses and continua even in the case of stable equilibrium state in order to show the strong duality between the minimization problems of total potential energy and complementary energy the convex formulations of these problems are investigated which can be embedded into a primal dual pair of second order cone programming problems the existence and uniqueness of solution are also investigated for the minimization problem of complementary energy

contact analysis of cable networks by using second order cone programming a method based on mathematical programming is proposed for large deformation and contact analysis of cable networks by explicitly considering these nonsmooth behaviors we formulate the linear complementarity problems over symmetric cones under some practically acceptable assumptions we also present the equivalent second order cone programming socp problems which can be regarded as the minimization problem of total potential energy and complementary energy with the subsidiary constraints on the displacements and contact forces respectively by solving the presented socp problems by using the primal dual interior point method the equilibrium configurations and internal forces of several cable networks are obtained without any assumptions on stress states and contact conditions

global existence of classical solutions to the cauchy problem for a kind of quasilinear hyperbolic system abstract this paper deals with the cauchy problem for a kind of quasilinear hyperbolic system with the linear elastodynamic system as its principal part and the nonlinear terms depending on quadratic terms of the first derivatives of u a system of new null conditions is given by which the author shows the global existence of the problem

numerical validation of blow up solutions of ordinary differential equations abstract this paper focuses on blow up solutions of ordinary differential equations odes we present a method for validating blow up solutions and their blow up times which is based on compactifications and the lyapunov function validation method the necessary criteria for this construction can be verified using interval arithmetic techniques some numerical examples are presented to demonstrate the applicability of our method

global smooth axisymmetric solutions to 2d compressible euler equations of chaplygin gases with non zero vorticity abstract for 2d compressible isentropic euler equations of polytropic gases s alinhac establishes that the axisymmetric smooth solution blows up in the present paper for 2d compressible isentropic euler equations of chaplygin gases we show that the small perturbed smooth solution exists globally when the rotationally invariant initial data are a perturbation of size e 0 of a rest state near the light cone 2d euler equations of chaplygin gases can be transformed into a second order quasilinear wave equation which satisfies both the null conditions this will lead to that the corresponding second order quasilinear wave equation admits a global smooth solution near the light cone however away from the light cone the hydrodynamical waves have no decay in time and strongly affect the related acoustical waves by introducing a nonlinear ode we can distinguish the fast decay part and non decay part so that the global energy estimates are derived

combined effects of two nonlinearities in lifespan of small solutions to semi linear wave equations this paper investigates the combined effects of two distinctive power type nonlinear terms with parameters p q 1 in the lifespan of small solutions to semi linear wave equations we determine the full region of p q to admit global existence of small solutions at least for spatial dimensions n 2 3 moreover for many p q when there is no global existence we obtain sharp lower bound of the lifespan which is of the same order as the upper bound of the lifespan

combined interior point method and semismooth newton method for frictionless contact problems in the present paper a solution scheme is proposed for frictionless contact problems of linear elastic bodies which are discretized using the finite element method with lower order elements an approach combining the interior point method and the semismooth newton method is proposed in this method an initial active set for the semismooth newton method is obtained from the approximate optimal solution by the interior point method the simplest node to node contact model is considered in the present paper that is pairs of matching nodes exist on the contact surfaces however the discussions can be easily extended to a node to segment or segment to segment contact model in order to evaluate the proposed method a number of illustrative examples of the frictionless contact problem are shown the proposed combined method is compared with the interior point method and the semismooth newton method two numerical examples that are difficult to solve using the semismooth newton method are solved effectively using the proposed combined method it is shown that the proposed method converges within far fewer iterations than the semismooth newton methods or the interior point method

on nonparametric image registration image registration ir aims to map one image to another of a same scene it is a fundamental task in many imaging applications most existing ir methods assume that the mapping transformation has a parametric form or satisfies certain regularity conditions e g it is a smooth function with continuous first or higher order derivatives they often estimate the mapping transformation globally by solving a global minimization maximization problem such global smoothing methods usually cannot preserve singularities e g discontinuities and other features of the mapping transformation well further the ill posed nature of the ir problem namely the mapping transformation is not well defined at certain places including the place where the true image intensity surface is straight is not handled properly by such methods in this article we suggest solving the ir problem locally by first studying the local properties of a mapping transformation to this end some concepts for describing such local prop

multi sensor image registration based on intensity and edge orientation information this paper presents a method for registering multi sensor images such as visible and infrared images registration is achieved by iteratively minimizing an objective function through updating transformation parameters of deformation a new entropy based objective function is proposed on the basis of a 3 d joint histogram incorporating intensity information and edge orientation information to complement the entropy based objective function a weighting function is also introduced through the use of a coincidence measure of edge orientations experimental results show that the proposed method provides more robust registration results than the existing approaches

nonresonance and global existence of prestressed nonlinear elastic waves this article considers the existence of global classical solutions to the cauchy problem in nonlinear elastodynamics the unbounded elastic medium is assumed to be homogeneous isotropic and hyperelastic as in the theory of 3d nonlinear wave equations in three space dimensions global existence hinges on two basic assumptions first the initial deformation must be a small displacement from equilibrium in this case a prestressed homogeneous dilation of the reference conflguration and equally important the nonlinear terms must obey a type of nonresonance or null condition the omission of either of these assumptions can lead to the breakdown of solutions in flnite time in particular nonresonance complements the genuine nonlinearity condition of f john under which arbitrarily small spherically symmetric displacements develop singularities although one expects this to carry over to the nonsymmetric case as well 4 john also showed that small solutions exist almost globally 5 see also 10 formation of singularities for large displacements was illustrated by tahvildar zadeh 16 the nonresonance condition introduced here represents a substantial improvement over our previous work on this topic 13 to explain the difierence roughly our earlier version of the null condition forced the cancellation of all nonlinear wave interactions to flrst order along the characteristic cones here only the cancellation of nonlinear wave interactions among individual wave families is required the di culty in realizing this weaker version is that the decomposition of elastic waves into their longitudinal and transverse components involves the nonlocal helmholtz projection which is ill suited to nonlinear analysis however our decay estimates make clear that only the leading contribution of the resonant interactions along the characteristic cones is potentially dangerous and this permits the usage of approximate local decompositions

almost global existence to nonlinear wave equations in three space dimensions on considere l existence a t grand de solutions de petite amplitude pour des equations d onde d ordre 2 non lineaires a 4 dimensions d espace temps

on one dimension semi linear wave equations with null conditions abstract it is well known that in space dimensions at least three semilinear wave equations with null conditions admit global solutions for small initial data it is also known that in space dimension two such result still holds for a certain class of quasi linear wave equations with null conditions the proofs are based on the decay mechanism of linear waves however in one space dimension waves do not decay nevertheless we will prove that small data still lead to global solutions if the null condition is satisfied

estimation of two dimensional affine transformations through polar curve matching and its application to image mosaicking and remote sensing data registration this paper presents a new and effective method for estimating two dimensional affine transformations and its application to image registration the method is based on matching polar curves obtained from the radial projections of the image energies defined as the squared magnitudes of their fourier transforms such matching is formulated as a simple minimization problem whose optimal solution is found with the levenberg marquardt algorithm the analysis of affine transformations in the frequency domain exploits the well known property whereby the translational displacement in this domain can be factored out and separately estimated through phase correlation after the four remaining degrees of freedom of the affine warping have been determined another important contribution of this paper emphasized through one example of image mosaicking and one example of remote sensing image registration consists in showing that affine motion can be accurately estimated by applying our algorithm to the shapes of macrofeatures extracted from the images to register the excellent performance of the algorithm is also shown through a synthetic example of motion estimation and its comparison with another standard registration technique

polynomial convergence of primal dual algorithms for the second order cone program based on the mz family of directions in this paper we study primal dual path following algorithms for the second order cone programming socp based on a family of directions that is a natural extension of the monteiro zhang mz family for semidefinite programming we show that the polynomial iteration complexity bounds of two well known algorithms for linear programming namely the short step path following algorithm of kojima et al and monteiro and adler and the predictor corrector algorithm of mizuno et al carry over to the context of socp that is they have an o loge 1 iteration complexity to reduce the duality gap by a factor of e where n is the number of second order cones since the mz type family studied in this paper includes an analogue of the alizadeh haeberly and overton pure newton direction we establish for the first time the polynomial convergence of primal dual algorithms for socp based on this search direction

applications of second order cone programming in a second order cone program socp a linear function is minimized over the intersection of an affine set and the product of second order quadratic cones socps are nonlinear convex problems that include linear and convex quadratic programs as special cases but are less general than semidefinite programs sdps several efficient primaldual interior point methods for socp have been developed in the last few years after reviewing the basic theory of socps we describe general families of problems that tan be recast as socps these include robust linear programming and robust leastsquares problems problems involving sums or maxima of norms or with convex hyperbolic constraints we discuss a variety of engineering applications such as filter design antenna array weight design truss design and grasping forte optimization in robotics we describe an efficient primaldual interior point method for solving socps which shares many of the features of primaldual interior point methods for linear program

on some results concerning the reciprocal formulation for the signorini s problem abstract in the paper the relationship between two formulations of the signorini s problem is investigated the first one is based on the minimum potential energy theorem and is expressed in terms of displacements in the second one the so called reciprocal formulation the unknown function appears to be a contact pressure based on ekeland temam s results concerning the duality theory the equivalance of both formulations is shown for the sake of some numerical experience the simple example of a beam supported on elastic supports is considered numerical results fully confirm the theoretical investigations

fast parametric elastic image registration we present an algorithm for fast elastic multidimensional intensity based image registration with a parametric model of the deformation it is fully automatic in its default mode of operation in the case of hard real world problems it is capable of accepting expert hints in the form of soft landmark constraints much fewer landmarks are needed and the results are far superior compared to pure landmark registration particular attention has been paid to the factors influencing the speed of this algorithm the b spline deformation model is shown to be computationally more efficient than other alternatives the algorithm has been successfully used for several two dimensional 2 d and three dimensional 3 d registration tasks in the medical domain involving mri spect ct and ultrasound image modalities we also present experiments in a controlled environment permitting an exact evaluation of the registration accuracy test deformations are generated automatically using a random hierarchical fractional wavelet based generator

on the blowup of classical solutions to the 3 d pressure gradient systems the 3 d pressure gradient system arises from the splitting of the three dimensional compressible euler system which can be reduced into such a nonlinear wave equation t2v div ev v 0 where div ev v i 13 i ev iv i xi 1 i 3 and x x1 x2 x3 in this paper we will establish a blowup result of classical solutions to the 3 d pressure gradient systems when the initial data are of small perturbations with respect to constant states

smoothing functions for second order cone complementarity problems smoothing functions have been much studied in the solution of optimization and complementarity problems with nonnegativity constraints in this paper we extend smoothing functions to problems in which the nonnegative orthant is replaced by the direct product of second order cones these smoothing functions include the chen mangasarian class and the smoothed fischer burmeister function we study the lipschitzian and differential properties of these functions and in particular we derive computable formulas for these functions and their jacobians these properties and formulas can then be used to develop and analyze noninterior continuation methods for solving the corresponding optimization and complementarity problems in particular we establish the existence and uniqueness of the newton direction when the underlying mapping is monotone

second order cone programming second order cone programming socp problems are convex optimization problems in which a linear function is minimized over the intersection of an affine linear manifold with the cartesian product of second order lorentz cones linear programs convex quadratic programs and quadratically constrained convex quadratic programs can all be formulated as socp problems as can many other problems that do not fall into these three categories these latter problems model applications from a broad range of fields from engineering control and finance to robust optimization and combinatorial optimization on the other hand semidefinite programming sdp that is the optimization problem over the intersection of an affine set and the cone of positive semidefinite matrices includes socp as a special case therefore socp falls between linear lp and quadratic qp programming and sdp like lp qp and sdp problems socp problems can be solved in polynomial time by interior point methods the computational effort per iteration required by these methods to solve socp problems is greater than that required to solve lp and qp problems but less than that required to solve sdp s of similar size and structure because the set of feasible solutions for an socp problem is not polyhedral as it is for lp and qp problems it is not readily apparent how to develop a simplex or simplex like method for socp while socp problems can be solved as sdp problems doing so is not advisable both on numerical grounds and computational complexity concerns for instance many of the problems presented in the survey paper of vandenberghe and boyd vb96 as examples of sdps can in fact be formulated as socps and should be solved as such in 2 3 below we give socp formulations for four of these examples the convex quadratically constrained quadratic programming qcqp problem problems involving fractional quadratic functions rutcor rutgers university e mail alizadeh rutcor rutgers edu research supported in part by the u s national science foundation grant ccr 9901991 ieor columbia university e mail gold ieor columbia edu research supported in part by the department of energy grant de fg02 92er25126 national science foundation grants dms 94 14438 cda 97 26385 and dms 01 04282

fast and accurate global motion estimation algorithm using pixel subsampling global motion generally describes the motion of a camera although it may comprise motions of large objects global motions are often modeled by parametric transformations of two dimensional images the process of estimating the motions parameters is called global motion estimation gme gme is widely employed in many applications such as video coding image stabilization and super resolution to estimate global motion parameters the levenburg marquardt algorithm lma is typically used to minimize an objective function iteratively since the region of support for the global motion representation consists of the entire image frame the minimization process tends to be very expensive computationally by involving all the pixels within an image frame in order to significantly reduce the computational complexity of the lma we proposed to select only a small subset of the pixels for estimating the motion parameters based on several subsampling patterns and their combinations simulation results demonstrated that the proposed method could speed up the conventional gme approach by over ten times with only a very slight loss less than 0 1db in estimation accuracy the proposed method was also found to outperform several state of the art fast gme methods in terms of the speed accuracy tradeoffs

global existence of radial solutions for general semilinear hyperbolic systems in 3d abstract we study the well posedness of radial solutions for general nonlinear hyperbolic systems in three dimensions we give a proof of the global existence of radial solutions for general semilinear hyperbolic systems in 3d under null condition with small scaling invariant w 2 1 r 3 data we obtain a bilinear estimate that is effective for hyperbolic systems which do not have any time decay it allows us to achieve the boundedness of the weighted bv norm of the radial solutions

the small data solutions of general 3 d quasilinear wave equations ii abstract this paper is a continuation of the work in 8 where the authors established the global existence of smooth small data solutions to the general 3 d quasilinear wave equation i j 0 3 g i j u u i j 2 u 0 when the weak null condition holds in the present paper we show that the smooth small data solutions of equation i j 0 3 g i j u u i j 2 u 0 will blow up in finite time when the weak null condition does not hold and a generic nondegenerate condition on the initial data is satisfied moreover a precise blowup time is completely determined therefore collecting the main results in this paper and 8 we have given a basically complete study on the blowup or global existence of small data solutions to the 3 d quasilinear wave equation i j 0 3 g i j u u i j 2 u 0

optimal magnetic shield design with second order cone programming in this paper we consider a continuous version of the convex network flow problem which involves the integral of the euclidean norm of the flow and its square in the objective function a discretized version of this problem can be cast as a secondorder cone program for which efficient primal dual interior point algorithms have been developed recently an optimal magnetic shielding design problem of the maglev train a new bullet train under development in japan is formulated as the continuous convex network flow problem and is solved with the primal dual interiorpoint algorithm taking advantage of its efficiency and stability the algorithm is further applied to robust design of the magnetic shielding

global solutions of nonlinear wave equations in time dependent inhomogeneous media we consider the problem of small data global existence for a class of semilinear wave equations with null condition on a lorentzian background mathbb r 3 1 g with a time dependent metric g coinciding with the minkowski metric outside the cylinder t x x leq r we show that the small data global existence result can be reduced to two integrated local energy estimates and demonstrate that these estimates work in the particular case when g is merely c1 close to the minkowski metric one of the novel aspects of this work is that it applies to equations on backgrounds which do not settle to any particular stationary metric

anisotropic membrane wrinkling theory and analysis abstract a complete theory of wrinkling of anisotropic elastic membranes is presented based on the notion of relaxed energy function the theory is obtained as a particular case of a general theory of saturated elasticity it is shown that when any given hyperelastic constitutive law is supplemented with a saturation condition the right cauchy green strain tensor abides by an additive decomposition law governed by a normality rule for the case of wrinkling these results are implemented into a numerical procedure and examples are presented

regularized laplacian zero crossings as optimal edge integrators we view the fundamental edge integration problem for object segmentation in a geometric variational framework first we show that the classical zero crossings of the image laplacian edge detector as suggested by marr and hildreth inherently provides optimal edge integration with regard to a very natural geometric functional this functional accumulates the inner product between the normal to the edge and the gray level image gradient along the edge we use this observation to derive new and highly accurate active contours based on this functional and regularized by previously proposed geodesic active contour geometric variational models we also incorporate a 2d geometric variational explanation to the haralick edge detector into the geometric active contour framework

lagrange multipliers and optimality lagrange multipliers used to be viewed as auxiliary variables introduced in a problem of constrained minimization in order to write first order optimality conditions formally as a system of equations modern applications with their emphasis on numerical methods and more complicated side conditions than equations have demanded deeper understanding of the concept and how it fits into a larger theoretical picture a major line of research has been the nonsmooth geometry of one sided tangent and normal vectors to the set of points satisfying the given constraints another has been the game theoretic role of multiplier vectors as solutions to a dual problem interpretations as generalized derivatives of the optimal value with respect to problem parameters have also been explored lagrange multipliers are now being seen as arising from a general rule for the subdifferentiation of a nonsmooth objective function which allows black and white constraints to be replaced by penalty expressions this paper traces su

fast motion estimation using bidirectional gradient methods gradient based motion estimation methods gms are considered to be in the heart of state of the art registration algorithms being able to account for both pixel and subpixel registration and to handle various motion models translation rotation affine and projective these methods estimate the motion between two images based on the local changes in the image intensities while assuming image smoothness this paper offers two main contributions the first is enhancement of the gm technique by introducing two new bidirectional formulations of the gm these improve the convergence properties for large motions the second is that we present an analytical convergence analysis of the gm and its properties experimental results demonstrate the applicability of these algorithms to real images

global smooth solutions of 3 d null form wave equations in exterior domains with neumann boundary conditions abstract the paper is devoted to investigating long time behavior of smooth small data solutions to 3 d quasilinear wave equations outside of compact convex obstacles with neumann boundary conditions concretely speaking when the surface of a 3 d compact convex obstacle is smooth and the quasilinear wave equation fulfills the null condition we prove that the smooth small data solution exists globally provided that the neumann boundary condition on the exterior domain is given one of the main ingredients in the current paper is the establishment of local energy decay estimates of the solution itself as an application of the main result the global stability to 3 d static compressible chaplygin gases in exterior domain is shown under the initial irrotational perturbation with small amplitude

semilinear hyperbolic systems violating the null condition we consider systems of semilinear wave equations in three space dimensions with quadratic nonlinear terms not satisfying the null condition we prove small data global existence of the classical solution under a new structural condition related to the weak null condition for two component systems satisfying this condition we also observe a new kind of asymptotic behavior only one component is dissipated and the other one behaves like a non trivial free solution in the large time

arbitrary lagrangian eulerian finite element analysis of large deformation in contacting bodies the primary aim of this research is to implement the arbitrary lagrangian eulerian finite element description to model large deformation of interacting bodies a pure lagrangian description is often incapable of representing their contact with sufficient precision in this work the arbitrary lagrangian eulerian ale description has been extended to the surface nodes of interacting bodies to overcome these limitations a penalty formulation has been implemented to account for the impenetrability constraint the materials have been characterized as elastic viscoplastic implicit integration schemes have been used at the global and constitutive levels for improved stability

efficient local transformation estimation using lie operators conventional translation only motion estimation algorithms cannot cope with transformations of objects such as scaling rotations and deformations motion models characterizing non translation motions are thus beneficial as they offer more accurate motion estimation and compensation in this paper we introduce low complexity transformation estimation methods with four motion models based on lie operators which are linear operators that have found applications in optical character recognitions we show that individual lie operators are capable of capturing small degrees of object transformations we propose an efficient local transformation estimation algorithm in order to further improve the accuracy of the translation only estimation by integrating all four motion models simulations with an mpeg 2 video codec on two video sequences show that the proposed transformation estimation approach can noticeably improve the motion compensation performance of the translation only method by achieving higher psnr peak signal to noise ratio values for the predicted frames with only a small fraction of the complexity required by the translation motion search

small data solutions of 3 d quasilinear wave equations under null condition abstract for the 3 d quasilinear wave equation i j 0 3 g i j u i j u 0 a global existence result has been shown by h lindblad in this paper we consider this 3 d quasilinear wave equation i j 0 3 g i j u i j u i j 0 3 f i j i u j u with small initial data and f i j satisfying null condition through deriving decay estimates of low derivatives and energy estimates for high derivatives combined with the properties of null condition a global existence solution is also established by continuous induction

lower bounds for the life span of solutions of nonlinear wave equations in higher dimensions when m 0 writing 1 as a quasilinear symmetric hyperbolic system it is known that a classical solution exists locally in time provided that f g are small and sufficiently smooth the time interval o t for which this classical solution exists depends on the size of the initial data more precisely if f and g go where fo go are fixed the largest time t t e for which the classical solution of 1 is assured by the local existence theorem is of order l for the one dimensional genuine nonliner wave equation i e m 0 n 1 in 1 and cy 1 in 2 lax l has shown that this estimate is sharp in this case when the genuine nonlinearity condition is violated i e ly 1 klainerman and majda 2 have shown that t e 0 l and that this estimate is also sharp for e sufficiently small in contrast to the one dimensional case john has shown that in higher dimensions the existence time of classical solutions can be significantly improved in fact he proved for the case m 0 y 1 that t e 0 l s for n 4 5 3 and recently t e u l 8 for

fuzzy relation equations for coding decoding processes of images and videos we adopt fuzzy relation equations with continuous triangular norms for compression decompression processes of grey images colour images in the rgb space and frames of videos by comparing the results of the reconstructed images with standard methods like jpeg and mpeg 4 any image is subdivided in blocks and each block is coded decoded using arbitrary fuzzy sets as coders in the fuzzy equations we evaluate the peak signal to noise ratio psnr on the decompressed images for several values of the compression rates as measure of the quality of images and frames reconstructed the original frames of a video are classified in intra frames and predictive frames by using a similarity measure based on the well known lukasiewicz t norm

a time stepping complementarity approach for frictionless systems of rigid bodies this paper presents a time stepping complementarity approach for computing a numerical trajectory of a system of rigid bodies under frictionless contact such a system is formulated as a time dependent ordinary differential complementarity problem dcp which consists of an ordinary differential equation ode coupled with a complementarity condition the phenomenon of impact plays an essential role when modeling a mechanical system of this type within the time stepping scheme which uses a high order ode discretization we include an impact detection routine and an impact law governing the behavior of the system over the duration of an impact we report computational results for the application of the overall numerical scheme to computing the solution trajectories of several realistic mechanical systems

lower bounds for the life span of solutions of nonlinear wave equations in three dimensions abstract the paper deals with strict solutions u x t u x1 x2 x3 t of an equation formula see text where du is the set of four first derivatives of u for given initial values u x 0 ef x ut x 0 eg x the life span t e is defined as the supremum of all t to which the local solution can be extended for all x blowup in finite time corresponds to t e examples show that this can occur for arbitrarily small e on the other hand t e must at least be very large for small e by assuming that aik f g unk c that aik 0 0 and that f g have compact support it is shown that formula see text for every n this result had been established previously only for n 4

life span of small solutions to a system of wave equations abstract we study the cauchy problem with small initial data for a system of semilinear wave equations u v q v t u p in n dimensional space when n 2 we prove that blow up can occur for arbitrarily small data if p q lies below a curve in the p q plane on the other hand we show a global existence result for n 3 which asserts that a portion of the curve is in fact the borderline between global in time existence and finite time blow up we also estimate the maximal existence time and get its upper bound which is sharp at least for n p q 2 2 2 and 3 2 2

a complementary energy formulation of no tension masonry like solids in the present work a complementary energy formulation for the solution of the static equilibrium problem of no tension solids is presented the main feature of the work is systematic use of the augmented lagrangian approach for the regularisation of the nonsmooth and nondifferentiable anelastic deformation potential the proposed formulation is applied to derive a finite element formulation using the subspace of the self equilibrated stresses as primal variables the code implements the augmented lagrangian algorithm for the determination of the inelastic deformations some numerical examples are included to illustrate the performance of the proposed approach

global solutions of quasilinear wave equations we show global small data existence for a class of quasilinear wave equations related to einstein s equations in harmonic coordinates these equations do not satisfy the classical null condition and the asymptotic behavior of solutions is not free but the light cones bend at infinity

efficient robust and fast global motion estimation for video coding in this paper we propose an efficient robust and fast method for the estimation of global motion from image sequences the method is generic in that it can accommodate various global motion models from a simple translation to an eight parameter perspective model the algorithm is hierarchical and consists of three stages in the first stage a low pass image pyramid is built then an initial translation is estimated with full pixel precision at the top of the pyramid using a modified n step search matching in the third stage a gradient descent is executed at each level of the pyramid starting from the initial translation at the coarsest level due to the coarse initial estimation and the hierarchical implementation the method is very fast to increase robustness to outliers we replace the usual formulation based on a quadratic error criterion with a truncated quadratic function we have applied the algorithm to various test sequences within an mpeg 4 coding system from the experimental results we conclude that global motion estimation provides significant performance gains for video material with camera zoom and or pan the gains result from a reduced prediction error and a more compact representation of motion we also conclude that the robust error criterion can introduce additional performance gains without increasing computational complexity

global solutions of nonlinear hyperbolic equations for small initial data on considere des systemes quasilineaires d equations hyperboliques d ordre 2 qui sont des deformations non lineaires de l equation d onde on etudie l existence globale et le comportement asymptotique des solutions du probleme de cauchy quand la donnee initiale est suffisamment petite

coupled deformations of elastic curves and surfaces an equilibrium theory for the coupled finite deformations of elastic curves and surfaces is described possible wrinkling of the curve or surface is taken into account by using a relaxed version of the theory obtained from minimum energy considerations the relaxed theory admits a dual formulation leading to extremum principles and uniqueness of the equilibrium stress distribution a number of examples are treated using spatial finite differences together with a dynamic relaxation method in which equilibrium configurations are obtained in the long time limit of a damped dynamical problem

robust regression methods for computer vision a review regression analysis fitting a model to noisy data is a basic technique in computer vision robust regression methods that remain reliable in the presence of various types of noise are therefore of considerable importance we review several robust estimation techniques and describe in detail the least median of squares lmeds method the method yields the correct result even when half of the data is severely corrupted its efficiency in the presence of gaussian noise can be improved by complementing it with a weighted least squares based procedure the high time complexity of the lmeds algorithm can be reduced by a monte carlo type speed up technique we discuss the relationship of lmeds with the ransac paradigm and its limitations in the presence of noise corrupting all the data and we compare its performance with the class of robust m estimators references to published applications of robust techniques in computer vision are also given

the first darboux problem for wave equations with a nonlinear positive source term abstract we consider the first darboux problem for nonlinear wave equations with positive power nonlinearity source term depending on the power of nonlinearity we investigate the problem on a global existence and blow up of solutions of the first darboux problem the question of local solvability of the problem is also considered