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

robust noise region based active contour model via local similarity factor for image segmentation abstract image segmentation using a region based active contour model could present difficulties when its noise distribution is unknown to overcome this problem this paper proposes a novel region based model for the segmentation of objects or structures in images by introducing a local similarity factor which relies on the local spatial distance within a local window and local intensity difference to improve the segmentation results by using this local similarity factor the proposed method can accurately extract the object boundary while guaranteeing certain noise robustness furthermore the proposed algorithm completely avoids the pre processing steps typical of region based contour model segmentation resulting in a higher preservation of image details experiments performed on synthetic images and real word images demonstrate that the proposed algorithm as compared with the state of art algorithms is more efficient and robust to higher noise level manifestations in the images

on the periodic intermediate long wave equation the authors discuss some properties of a physically interesting nonlinear integro differential equation with periodic boundary conditions it is the natural periodic analogue of the intermediate long wave equation and it provides a periodic analogue of the benjamin ono equation in the appropriate limit due to the speciality of the integral operator the equation admits a backlund transformation an infinity of motion constants etc two simple periodic solutions are exhibited the equation may be transformed into more than one kind of bilinear equation

periodic solutions of the intermediate long wave equation a nonlinear superposition principle periodic stationary wave solutions of the intermediate long wave ilw equation are derived using the bilinear transformation method and a new expression for the dispersion relation is obtained the class of physically important real valued solutions is identified these solutions may be represented as an infinite superposition of solitary wave profiles a property shared by the related korteweg de vries kdv and benjamin ono bo equation this nonlinear superposition principle which has been the subject of various interpretations in the literature is discussed the ilw periodic solution approximates to a sinusoidal wave and a solitary wave in the limits of small and large amplitudes respectively for intermediate amplitudes the solution can be well approximated by either a sine wave or solitary wave in the shallow water kdv limit the ilw periodic solution leads to the familiar cnoidal wave whereas the deep water bo limit yields benjamin s periodic wave a previously unknown expression for the cnoidal wave dispersion relation in terms of theta functions is obtained

discontinuous galerkin finite element method for the wave equation the symmetric interior penalty discontinuous galerkin finite element method is presented for the numerical discretization of the second order wave equation the resulting stiffness matrix is symmetric positive definite and the mass matrix is essentially diagonal hence the method is inherently parallel and leads to fully explicit time integration when coupled with an explicit time stepping scheme optimal a priori error bounds are derived in the energy norm and the l 2 norm for the semidiscrete formulation in particular the error in the energy norm is shown to converge with the optimal order cal o h min s ell with respect to the mesh size h the polynomial degree ell and the regularity exponent s of the continuous solution under additional regularity assumptions the l 2 error is shown to converge with the optimal order cal o h min s ell numerical results confirm the expected convergence rates and illustrate the versatility of the method

geometric active contours without re initialization for image segmentation a geometric active contour model without re initialization that can be used for grey and color image segmentation is presented in this paper it combines directional information about edge location based on cumani operator as a part of driving force with the improved geodesic active contours containing bays error based statistical region information moreover an extra term that penalizes the deviation of the level set function from a signed distance function is also included in the model thus the costly re initialization procedure can be completely eliminated and all these measures are integrated in a unified frame experimental results on real grey and color images have shown that our model can precisely extract contours of images and its performance is much better and faster than the geodesic aided c v gacv model

a multiphase level set framework for image segmentation using the mumford and shah model we propose a new multiphase level set framework for image segmentation using the mumford and shah model for piecewise constant and piecewise smooth optimal approximations the proposed method is also a generalization of an active contour model without edges based 2 phase segmentation developed by the authors earlier in t chan and l vese 1999 in scale space 99 m nilsen et al eds lncs vol 1682 pp 141 151 and t chan and l vese 2001 ieee ip 10 2 266 277 the multiphase level set formulation is new and of interest on its own by construction it automatically avoids the problems of vacuum and overlaps it needs only log n level set functions for n phases in the piecewise constant cases it can represent boundaries with complex topologies including triple junctionss in the piecewise smooth case only two level set functions formally suffice to represent any partition based on the four color theorem finally we validate the proposed models by numerical results for signal and image denoising and segmentation implemented using the osher and sethian level set method

the special modular transformation for polycnoidal waves of the korteweg de vries equation the modular transformation of the riemann theta function is used to show that the implicit dispersion relation for the n polycnoidal waves of the korteweg de vries equation has a countable infinity of branches for n 2 although the transformation also implies that each branch or mode can be written in a countable infinity of ways it is also shown that there is a unique physical representation for each mode such that the parameters of the theta function can be interpreted as wavenumbers and amplitudes in the limit of either very small or very large amplitude unfortunately the small amplitude physical representation is different by a modular transformation from the large amplitude physical representation for a given mode but this difference explains an apparent paradox as described in the text the general modular transformation expresses the theta function in terms of complex wavenumbers phase speeds and coordinates that have no physical relevance to the korteweg de vries equation but it is shown that for n 2 there is a subgroup here dubbed the special modular transformation which gives a real result this subgroup is explicitly constructed for general n and presented as a table for n 2

interior penalty discontinuous galerkin time domain method based on wave equation for 3 d electromagnetic modeling built on the vector wave equation an interior penalty discontinuous galerkin time domain ipdg we method is presented for 3 d real life electromagnetic modeling in this paper we develop the interior penalty fluxes corresponding to different types of boundary conditions which are commonly used in electromagnetic modeling to construct the ipdg we system in local elements in addition to model the incident wave excitation the total field scattered field approach is incorporated into the proposed method the stability of the ipdg we method is studied analytically and demonstrated numerically we also compare the performance between wave equation based finite element time domain method the maxwell s equation based discontinuous galerkin time domain method and the proposed method both in cpu time and memory usage which demonstrates that the ipdg we method is very competitive among time domain solvers besides the presented method shows good characteristics including the energy conservation and the optimal convergence rate of o h p 1 numerical examples are presented to illustrate the validity versatility and potential of the proposed method in 3 d electromagnetic problems modeling

an efficient discontinuous galerkin finite element method for highly accurate solution of maxwell equations a discontinuous galerkin finite element method dg fem with a highly accurate time integration scheme for solving maxwell equations is presented the new time integration scheme is in the form of traditional predictor corrector algorithms pe ce m but it uses coefficients that are obtained using a numerical scheme with fully controllable accuracy numerical results demonstrate that the proposed dg fem uses larger time steps than dg fem with classical pe ce m schemes when high accuracy which could be obtained using high order spatial discretization is required

hierarchal vector basis functions of arbitrary order for triangular and tetrahedral finite elements new vector finite elements are proposed for electromagnetics the new elements are triangular or tetrahedral edge elements tangential vector elements of arbitrary polynomial order they are hierarchal so that different orders can be used together in the same mesh and p adaption is possible they provide separate representation of the gradient and rotational parts of the vector field explicit formulas are presented for generating the basis functions to arbitrary order the basis functions can be used directly or after a further stage of partial orthogonalization to improve the matrix conditioning matrix assembly for the frequency domain curl curl equation is conveniently carried out by means of universal matrices application of the new elements to the solution of a parallel plate waveguide problem demonstrates the expected convergence rate of the phase of the reflection coefficient for tetrahedral elements to order 4 in particular the full order elements have only the same asymptotic convergence rate as elements with a reduced gradient space such as the whitney element however further tests reveal that the optimum balance of the gradient and rotational components is problem dependent

theta functions gaussian series and spatially periodic solutions of the korteweg de vries equation it has been shown by novikov funct anal appl 8 236 1974 dubrovin et al russian math surveys 31 59 1976 lax commun pure appl math 28 141 1975 mckean and van moerbeke inv math 30 217 1975 and others that the nonlinear evolution equations which admit solitary waves also have spatially periodic exact solutions polycnoidal waves which can be expressed in terms of multidimensional riemann theta functions here it is shown that via poisson summation the fourier series that define the theta functions can be transformed into an infinite series of gaussian functions because the lowest terms of the gaussian series generate the usual solitary waves it is possible to intimately explore the relationship between solitary waves and these spatially periodic polycnoidal waves also by using the gaussian series one can perturbatively calculate phase velocities and wave structure for the polycnoidal wave even in the strongly nonlinear regime for which the soliton or mult

interior penalty discontinuous galerkin finite element method for the time dependent first order maxwell s equations an interior penalty discontinuous galerkin method is described with a conformal perfectly matched layer pml for solving the two first order maxwell s equations in the time domain both central and upwind fluxes are studied in this work in both cases the proposed method is explicit and conditionally stable additionally a local time stepping strategy is applied to increase efficiency and reduce the computational time finally numerical examples are presented to validate the method

direct and inverse scattering problems of the nonlinear intermediate long wave equation the inverse scattering transformation method associated with a nonlinear singular integrodifferential equation is discussed the equation describes long internal gravity waves in a stratified fluid of finite depth and reduces to the korteweg de vries equation as shallow water limit and the benjamin ono equation as deep water limit both limits of the method and novel aspects of the theory are also discussed

on the periodic solution of the burgers equation a unified approach for the most part the various known expressions for the periodic solution to the burgers equation have been derived by a mixture of ad hoc argument and approximation methods these include the well known solutions due to r d fay and d f parker remarkably these solutions were obtained without recourse to the celebrated hopf cole transformation which linearizes the burgers equation to the heat conduction equation we present here an alternative approach to the periodic problem which uses the fact that the riemann theta functions solve the burgers equation via the hopf cole transformation and thereby provide a unifying framework in which all previous representations of the periodic solution find their natural place yet another expression for the periodic solution in the form of an amplitude modulated sine wave is given and would appear to be new the limiting forms of the periodic solution as t rightarrow 0 embryonic sawtooth profile and t rightarrow infty old age sinusoidal profile are examined in detail the representation due to d f parker which expresses the periodic wave as a superposition of spreading taylor shock profiles is discussed within the context of a nonlinear superposition principle the composite asymptotic expansion due to m b lesser and d g crighton is examined in the light of our results the curious behaviour of this expansion in the embryonic region t ll 1 whereby a first order approximation yields an exact periodic solution the fay solution is explained

peakons and coshoidal waves traveling wave solutions of the camassa holm equation abstract camassa and holm 1 have recently derived a new integrable wave equation for the special case 0 they showed it has solitary waves of the form c exp x ct which they named peakons in this work we derive a perturbation series for general which converges even at the peakon limit we also give three analytical representations for the spatially periodic generalization of the peakon the coshoidal wave the three representations are i a closed form analytical solution ii a fourier series with coefficients that are explicit rational functions and iii an imbricate fourier series which is the superposition of an infinite number of peakons each separated from its neighbors by distance p where p is the spatial period lastly we have numerically tested the soliton superposition principle although the camassa holm equation is integrable for general it appears that imbricating solitary waves generates an exact spatially periodic solution only for the special cases 0 c 1 2 however the imbricate soliton series is a very good approximate solution for general even when the spatial period is small and the solution resembles a sine wave more than a solitary wave

on exact solutions of the regularized long wave equation a direct approach to partially integrable equations i solitary wave and solitons hitherto the bilinear transformation method has been used to obtain analytic solutions of completely integrable or nonlinear evolution equations in this first of two studies designated i and ii it is shown that the method may apply equally well to those nonlinear wave equations dubbed partially integrable here the regularized long wave rlw and rlw boussinesq rlwb equations are considered as examples in each case the bilinear form is found to have an extra equation which would appear to signal their nonintegrability their solitary wave solutions are reconstructed and the nonexistence of multisoliton solutions is demonstrated the present work provides the basis for the construction of periodic solutions in ii

rapid and brief communication gacv geodesic aided c v method a novel algorithm for image segmentation is proposed the proposed method incorporates geodesic curves and c v method to raise active contours performance on image segmentation moreover we extend our method to color images by practical experiments it is verified that our model obtains better results than original methods especially with respect to images within holes complex background weak edges and noise

the double cnoidal wave of the korteweg de vries equation an overview earlier work of the author on the spatially periodic solutions of the korteweg de vries equation is here extended via an in depth treatment of a special case the double cnoidal wave is the simplest generalization of the ordinary cnoidal wave discovered by korteweg and de vries in 1895 in the limit of small amplitude the double cnoidal wave is the sum of two noninteracting linear sine waves in the oppositie limit of large amplitude it is the sum of solitary waves of two different heights repeated periodically over all space although special the double cnoidal wave is important because it is but the particular case n 2 of a broad family of solutions known variously as n polycnoidal waves finite gap finite zone solutions waves on a circle or n phase wave trains it has been shown by others that the set of n polycnoidal waves gives the general initial value solution to the korteweg de vries equation this present work is the core of a three part treatment of the double cnoidal wave this part the overview presents graphic examples in all the important parameter regimes explains how collision phase shifts alter the average speed of the two wave phases from the free velocities of the two solitary waves describes the different branches or modes of the double cnoidal wave it is possible to have many solitary waves on each spatial period provided they are of only two distinct sizes and contrasts the results of this work with the very limited numerical calculations of previous authors the second part describes how the problem of numerically calculating the double cnoidal wave can be reduced down to solving four algebraic equations by perturbation theory the third part explains how the so called modular transformation of the riemann theta functions is important in interpreting n polycnoidal waves

a comparative study of three finite element based explicit numerical schemes for solving maxwell s equations three finite element based explicit numerical algorithms named the dual field domain decomposition at the element level dfdd eld the discontinuous galerkin time domain method with upwind fluxes dgtd upwind and the discontinuous galerkin time domain method with central fluxes dgtd central are investigated and compared in terms of accuracy and efficiency all three algorithms can perform an efficient domain decomposition and avoid the inversion of a global system matrix yet the study shows that they differ from each other in terms of accuracy and efficiency hybrid implicit explicit schemes which can relax the restriction on the time step size imposed by the smallest elements in the computational domain are also investigated for both dfdd and dgtd and compared in terms of efficiency

periodic solutions of the camassa holm equation based on the bilinear form since the famous work of camassa and holm various analytic techniques have been used to find the exact solutions of camassa holm ch equation and many interesting results have been found by the different methods in this paper we first give an extended bilinear form of the ch equation which contains four more free parameters than those in the results proposed in parkers finding for soliton solutions thus we construct the smooth periodic solution of the ch equation in a parametric form based on the previous work of nakumura we also show that the periodic solution degenerates into the smooth solitary wave solution by limiting behavior of is the parameter appeared from the riemann theta function

on the camassa holm equation and a direct method of solution i bilinear form and solitary waves over the last decade a variety of techniques has been used to find exact solutions both analytic and other of the camassaholm equation the different approaches have met with varying measures of

construction of lighthill s unitary functions the imbricate series of unity the poisson sum theorem implies that every spatially periodic function f x can be written as a so called imbricate series that is as the superposition of an infinite number of evenly space copies of a pattern function a x the pattern is the fourier transform of a function a n that specifies the usual fourier coefficients because there are many a n which coincide with a given set of fourier coefficients aj when n is an integer the pattern function a x is not unique in this work we show how to construct pattern functions of the form a x f x w x where f x is the periodic function itself the imbrication of a x and where w x is what lighthill called a unitary function we derive an explicit formula to construct all possible unitary functions and tabulate eight examples we also prove that all unitary functions are pattern functions of unity that is for the imbricate series that sums to f x 1 x

short note an explicit expression for the penalty parameter of the interior penalty method we derive an explicit expression for the penalty parameter of the interior penalty method for elliptic problems the expression yields a coercive bilinear form and is valid for general meshes comprising of geometrically nonconforming simplical elements

cnoidal waves as exact sums of repeated solitary waves new series for elliptic functions via poisson summation of the corresponding fourier series it is shown that the cnoidal wave of the korteweg de vries equation can be written as an infinite sum of periodically repeated solitary waves a result first proved by toda through a different method similar series of hyperbolic secant or tangent functions are also derived for the elliptic dn sn and cn functions which make it possible to express the cnoidal wave of almost any evolution equation in terms of a series of the corresponding solitary waves as a by product new series are also obtained for the complete elliptic integral k and modulus k

periodic solutions of the non integrable convective fluid equation in the present paper we have obtained and analyzed a family of exact periodic solutions of the nonlinear evolution partial differential convecting fluid equation cfe by applying a modification of the bilinear transformation method this modification is used in view of the circumstance that cfe is a non integrable nonlinear equation a detailed consideration has been given to the quite important case of balance between the dispersion and nonlinear effects establishing that this balance changes the structure of the equation itself the exact periodic solutions of cfe have been also found in the important case when cfe is identical with the kuramoto sivashinsky equation

penalty factor threshold and time step bound estimations for discontinuous galerkin time domain method based on helmholtz equation in this article penalty factor threshold and time step bound in discontinuous galerkin time method based on vector wave equation dgtd we method are well estimated based on the semidiscrete form of the dgtd we method properties of the system matrices are studied and the stability condition related to the penalty factor is derived by decomposing the global system matrices of the dgtd we method into the local ones and developing an efficient iteration procedure the lower bound threshold of the penalty factor is well estimated to guarantee the positive semidefinite property of the global system matrices with the calculated penalty factor the maximum time step is analytically determined by approximating spectral radius of the local system matrix both the penalty factor bound and the maximal time step are computed element wise instead of a global system matrix operation and thus the proposed method can be efficiently applied into the large scale meshes with different types of the basis functions and boundary conditions numerical examples are presented to demonstrate the validity and good performance of the proposed methods

exact periodic solutions of the sixth order generalized boussinesq equation this paper examines a class of nonlinear sixth order generalized boussinesq like equations sgbe utt uxx 3 u2 xx uxxxx uxxxxxx r depending on the positive parameter hirota s bilinear transformation method is applied to the above class of non integrable equations and exact periodic solutions have been obtained the results confirmed the well known nonlinear superposition principle

solitons from sine waves analytical and numerical methods for non integrable solitary and cnoidal waves abstract the fkdv equation u t uu x u xxxxx 0 is used as a testbed for a variety of analytical and numerical methods that can be applied to solitary waves and cnoidal waves of non integrable differential equations that is to say to equations which cannot be solved by the inverse scattering transform the basic tools are i pade approximants formed from power series in the amplitude ii a newton kantorovich pseudospectral fourier continuation numerical method iii singular perturbation theory for two interacting solitons of almost identical phase speed iv bifurcation and branch switching methods v the imbricate soliton series a number of new results for the fkdv equation are obtained including extensive numerical calculations of the spatially periodic solutions with one peak cnoidal wave and two peaks bicnoidal wave per period an analytical expression for the double peaked soliton bion calculation of both the limit and bifurcation points for the bicnoidal wave and finally the computation of accurate analytical approximations to the cnoidal wave for all amplitudes more important all of these analytical and numerical tools are highly effective for this equation in spite of the fact that it cannot be solved by the inverse scattering transform work now in progress will apply these methods to non integrable equations in two space dimensions

interior penalty discontinuous galerkin method for maxwell s equations energy norm error estimates we develop the symmetric interior penalty discontinuous galerkin dg method for the time dependent maxwell equations in second order form we derive optimal a priori error estimates in the energy norm for smooth solutions we also consider the case of low regularity solutions that have singularities in space

perturbation series for the double cnoidal wave of the korteweg de vries equation by means of the theorems proved earlier by the author the problem of the double cnoidal wave of the korteweg de vries equation is reduced to four algebraic equations in four unknowns two of the unknowns are the nonlinear phase speeds c1 and c2 another is a physically irrelevant integration constant the fourth unknown is the off diagonal element of the symmetric 2 2 theta matrix which in turn gives the explicit coefficients of the riemann theta function the double cnoidal wave u x t is then obtained by taking the second x derivative of the logarithm of the theta function two separate forms of these four nonlinear residual equations are given one is obtained from the fourier series of the theta function and is useful for small wave amplitude the other is based on the gaussian series of the theta function and is highly efficient in the large amplitude regime where the double cnoidal wave is the sum of two solitary waves both sets of residual equations can be solved via perturbation theory and

periodic solutions of the dabo equation as a sum of repeated solitons it is shown that the periodic solution of the non linear dabo equation can be written as an infinite sum of an equally spaced row of identical lorentzian solitons this may be considered as a generalisation of a similar result which has been found for the kdv equation and is related to the clean interaction properties of colliding solitons under non linear coupling

estimation of penalty parameters for symmetric interior penalty galerkin methods this paper presents computable lower bounds of the penalty parameters for stable and convergent symmetric interior penalty galerkin methods in particular we derive the explicit dependence of the coercivity constants with respect to the polynomial degree and the angles of the mesh elements numerical examples in all dimensions and for different polynomial degrees are presented we show the numerical effects of loss of coercivity

a global minimization hybrid active contour model with applications to oil spill images active contour model is popularly and widely used in the field of image segmentation which is based on superior theoretical properties and efficient numerical methods nevertheless one of the prominent disadvantages of this kind of model is the existence of local minima in its functional energy in this paper we propose a novel global minimization hybrid active contour model this model effectively integrates the edge information the local region information and the global region information of the image which is relatively sufficient to extract the object boundaries furthermore we introduce an efficient and fast numerical approach to globally minimize the proposed model which is through a dual formulation of the minimization problem and easy to implement the proposed model is robust enough to the initial condition and does not need to initialize the contour in a distance function and re initialize it periodically during the evolution process specially we applied the proposed model to segment oil spill images in which there usually exist the noise blurry boundaries and intensity inhomogeneity compared with the state of the art models experiment results demonstrate the performance and effectiveness of the proposed model with applications to synthetical and real images especially for oil spill images