euler s elastica and curvature based inpainting image inpainting is a special image restoration problem for which image prior models play a crucial role euler s elastica was first introduced to computer vision by mumford algebraic geometry and its applications springer verlag new york 1994 pp 491 506 as a curve prior model by functionalizing the elastica energy masnou and morel proceedings of the 5th ieee international conference image processing 3 1998 pp 259 263 proposed an elastica based variational inpainting model the current paper is intended to contribute to the development of its mathematical foundation and the study of its properties and connections to the earlier works of bertalmio sapiro caselles and ballester siggraph 2000 acm press new york 2000 and chan and shen j visual comm image rep 12 2001 pp 436 449 a computational scheme based on numerical pdes is presented which allows the automatic handling of topologically complex inpainting domains

segmentation with depth a level set approach segmentation with depth is the challenging problem of obtaining three dimensional information from a single two dimensional image unlike the standard segmentation problem the goal of segmentation with depth is to determine not only the boundaries of objects that appear in the image but also their relative distances to the observer by making use of occlusion relations nitzberg mumford and shiota the 2 1d sketch in proceedings of the third international conference on computer vision osaka japan 1990 filtering segmentation and depth lecture notes in comput sci 662 springer verlag berlin 1993 proposed a variational formulation of this problem according to their model called the 2 1d sketch model the regions that the objects occupy and their relative depth are to be extracted from the two dimensional image by minimizing a curvature based functional numerically this is a highly nontrivial problem as the functional involves curvatures of the unknown contours in this paper we develop a level set based procedure for minimizing the nitzberg mumford shiota energy unlike the minimization technique of nitzberg mumford shiota filtering segmentation and depth lecture notes in comput sci 662 springer verlag berlin 1993 our technique represents contours implicitly and thus allows for connections between t junctions to take place automatically

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

identification of delays and discontinuity points of unknown systems by using synchronization of chaos in this paper we present an approach in which synchronization of chaos is used to address identification problems in particular we are able to identify i the discontinuity points of systems described by piecewise dynamical equations and ii the delays of systems described by delay differential equations delays and discontinuities are widespread features of the dynamics of both natural and manmade systems the foremost goal of the paper is to present a general and flexible methodology that can be used in a broad variety of identification problems

self adaptive hp finite element method with iterative mesh truncation technique accelerated with adaptive cross approximation abstract to alleviate the computational bottleneck of a powerful two dimensional self adaptive h p finite element method fem for the analysis of open region problems which uses an iterative computation of the integral equation over a fictitious boundary for truncating the fem domain we propose the use of adaptive cross approximation aca to effectively accelerate the computation of the integral equation it will be shown that in this context aca exhibits a robust behavior yields good accuracy and compression levels up to 90 and provides a good fair control of the approximants which is a crucial advantage for h p adaptivity theoretical and empirical results of performance computational complexity comparing the accelerated and non accelerated versions of the method are presented several canonical scenarios are addressed to resemble the behavior of aca with h p and h p adaptive strategies and higher order methods in general

a hybrid method combining the multitemporal resolution time domain method of moments with the time domain geometrical theory of diffraction for thin wire antenna problems in this paper a hybrid method combining a multitemporal resolution mtr enhanced time domain method of moments td mom with the td geometrical theory of diffraction gtd is presented which allows to efficiently calculate the transient fields radiated by antennas in presence of large objects the mtr scheme tailors the time step size and thus implicitly the duration of the temporal basis function on the basis of the distance between source and test element additionally the voltage induced by source elements far away from the test element is interpolated in time the hybrid method is applied to calculate the radiation properties of thin wire antennas in presence of perfectly conducting flat scatterers to demonstrate its basic features and advantages

a variational model for segmentation of overlapping objects with additive intensity value we propose a variant of the mumford shah model for the segmentation of a pair of overlapping objects with additive intensity value unlike standard segmentation models it does not only determine distinct objects in the image but also recover the possibly multiple membership of the pixels to accomplish this some a priori knowledge about the smoothness of the object boundary is integrated into the model additivity is imposed through a soft constraint which allows the user to control the degree of additivity and is more robust than the hard constraint we also show analytically that the additivity parameter can be chosen to achieve some stability conditions to solve the optimization problem involving geometric quantities efficiently we apply a multiphase level set method segmentation results on synthetic and real images validate the good performance of our model and demonstrate the model s applicability to images with multiple channels and multiple objects

a highly effective preconditioner for solving the finite element boundary integral matrix equation of 3 d scattering a highly effective preconditioner is presented for solving the system of equations obtained from the application of the hybrid finite element boundary integral fe bi method to three dimensional 3 d electromagnetic scattering problems different from widely used algebraic preconditioners the proposed one is based on a physical approximation and is constructed from the finite element method fem using an absorbing boundary condition abc on the truncation boundary it is shown that the large eigenvalues of the finite element fe abc system are similar to those of the fe bi system hence the preconditioned system has a spectrum distribution clustered around 1 in the complex plane consequently when a krylov subspace based method is employed to solve the preconditioned system the convergence can be greatly accelerated numerical results show that the proposed preconditioner can improve the convergence of an iterative solution by approximately two orders of magnitude for large problems

a multiresolution stochastic level set method for mumford shah image segmentation the mumford shah model is one of the most successful image segmentation models however existing algorithms for the model are often very sensitive to the choice of the initial guess to make use of the model effectively it is essential to develop an algorithm which can compute a global or near global optimal solution efficiently while gradient descent based methods are well known to find a local minimum only even many stochastic methods do not provide a practical solution to this problem either in this paper we consider the computation of a global minimum of the multiphase piecewise constant mumford shah model we propose a hybrid approach which combines gradient based and stochastic optimization methods to resolve the problem of sensitivity to the initial guess at the heart of our algorithm is a well designed basin hopping scheme which uses global updates to escape from local traps in a way that is much more effective than standard stochastic methods in our experiments a very high quality solution is obtained within a few stochastic hops whereas the solutions obtained with simulated annealing are incomparable even after thousands of steps we also propose a multiresolution approach to reduce the computational cost and enhance the search for a global minimum furthermore we derived a simple but useful theoretical result relating solutions at different spatial resolutions

analysis of antennas on board arbitrary structures modeled by nurbs surfaces an accurate and efficient numerical scheme has been developed for predicting high frequency radiation patterns of antennas mounted on arbitrary structures modeled by parametric surfaces the method is based on geometric optics go and the uniform theory of diffraction utd nonuniform rational b splines nurbs surfaces have been used to describe the geometry of the structure as most of the computer aided geometric design cagd tools available in the industry are biased on nurbs the scheme can perform the electromagnetic analysis without any new or additional remeshing of the geometrical model a special ray tracing technique that combines go and utd with nurbs has been developed this technique uses some selective criteria in order to identify rapidly the nurbs where a ray impact may occur impact point coordinates are obtained by means of an optimization procedure based on the conjugate gradient method cgm the accuracy and efficiency of the approach are shown comparing it with other methods

finite element solution to electromagnetic scattering problems by means of the robin boundary condition iteration method a new numerical method called the robin boundary condition iteration rbci is proposed for the finite element fe solution of electromagnetic scattering problems in open boundary domains the unbounded domain is truncated to a bounded one by means of a fictitious boundary that contains the scatterer and on which a suitable nonhomogeneous robin mixed boundary condition is assumed for the helmholtz equation in the bounded domain the robin condition is expressed by means of an integral formula the second green identity in terms of the field in the interior of the bounded domain with the integration surface being a surface strictly enclosed by the truncation boundary the discretized differential and integral equations are then coupled together to solve the problem the formulation is completely immune from the well known interior resonance problems a simple and effective iterative solving scheme is described examples are also provided to validate rbci and compare it with other methods

analysis of antenna around nurbs surface with hybrid mom po technique the hybrid method of moments and physical optics mom po approach is used to calculate the radiation pattern of antenna around arbitrarily shaped structure the structure is modeled with non uniform rational b spline nurbs surfaces the hybrid mom po approach is implemented by modifying the impedance matrix of the mom region with po formula for the scattered po field is deduced for cases of antenna located around nurbs surface the stationary phase method spm is applied for the integral of the induced current in the po region results obtained from this method and from mom po approach based on triangle facet model agree well while the former is more efficient in execution time

efficient algorithm for the evaluation of the physical optics scattering by nurbs surfaces with relatively general boundary condition an adaptive integration algorithm is presented for the computation of the physical optics po electric and magnetic field scattered by electrically large objects modeled by non uniform rational b splines nurbs the algorithm is the customization of a more general purpose result that has been recently published by using a unique formulation both impenetrable e g impedance surfaces coated conductors as well as transparent thin sheet materials e g thin dielectric panels or frequency selective surfaces are treated via their fresnel reflection and transmission coefficients the po radiation integral is evaluated over the nurbs parametric domain since most of the computer aided geometric design cagd tools are based on nurbs the proposed algorithm allows a straightforward electromagnetic analysis of the structures by exploiting the standard available geometrical description with no need of generating new geometrical models furthermore the proposed adaptive sampling requires a number of integration points that is found to be drastically smaller than that resulting from standard nyquist based sampling integration algorithms such reduction of the sampling points is achieved by resorting to high frequency technique concepts and allows a significant reduction of the cpu computational burden therefore the algorithm is efficient and particulary suitable for the electromagnetic characterization of real life electrically large objects

a hybrid sbr mom technique for analysis of scattering from small protrusions on a large conducting body a hybrid technique combining the shooting and bouncing ray sbr method and the method of moments mom is presented for analyzing scattering by large conducting bodies having small protrusions in this technique the mom with an approximate green s function is used to characterize the small protrusions yielding an admittance matrix which when multiplied with the incident field on the protrusions yields the currents induced on the protrusions the incident field in the presence of the large bodies is calculated using the sbr method the field radiated by the currents on the protrusions is also calculated using the sbr method with the aid of reciprocity furthermore an iterative approach is developed which can reduce the error introduced by the use of the approximate green s function numerical results are given to demonstrate the accuracy and capability of the hybrid technique

a hybrid febi mlfmm utd method for numerical solutions of electromagnetic problems including arbitrarily shaped and electrically large objects numerical solutions of electromagnetic scattering and radiation problems including arbitrarily shaped objects are obtained by solving integral equations with the method of moments mom fast and efficient solution of the integral equation with low computation and memory complexity is provided by the multilevel fast multipole method mlfmm the presence of electrically large conducting objects leads to hybrid mom techniques with high frequency methods for ray based high frequency methods no discretization of the electrically large objects is needed resulting into a more efficient numerical treatment of the problem however in order to retain low computation and memory complexity the high frequency fields must be taken into account in the matrix vector product computations in the various levels of the mlfmm in this contribution a ray based hybridization of the mlfmm with the uniform geometrical theory of diffraction utd is proposed within a hybrid finite element boundary integral febi technique using the combined field integral equation cfie resulting into a hybrid febi mlfmm utd method the hybridization is performed at the translation procedure on the various levels of the mlfmm using a far field approximation of the appropriate translation operator to obtain the high frequency incident fields at the critical points of the utd the formulation of this new hybrid technique is presented and numerical results are shown

optimal approximations by piecewise smooth functions and associated variational problems abstract this reprint will introduce and study the most basic properties of three new variational problems which are suggested by applications to computer vision in computer vision a fundamental problem is to appropriately decompose the domain r of a function g x y of two variables this problem starts by describing the physical situation which produces images assume that a three dimensional world is observed by an eye or camera from some point p and that g1 rho represents the intensity of the light in this world approaching the point sub 1 from a direction rho if one has a lens at p focusing this light on a retina or a film in both cases a plane domain r in which we may introduce coordinates x y then let g x y be the strength of the light signal striking r at a point with coordinates x y g x y is essentially the same as sub 1 rho possibly after a simple transformation given by the geometry of the imaging syste the function g x y defined on the plane domain r will be called an image what sort of function is g the light reflected off the surfaces si of various solid objects o sub i visible from p will strike the domain r in various open subsets r sub i when one object o1 is partially in front of another object o2 as seen from p but some of object o2 appears as the background to the sides of o1 then the open sets r1 and r2 will have a common boundary the edge of object o1 in the image defined on r and one usually expects the image g x y to be discontinuous along this boundary jhd

fully coupled hybrid fem utd method using nurbs for the analysis of radiation problems a novel hybrid finite element method fem uniform theory of diffraction utd method for the analysis of radiating structures in the presence of electrically large objects is presented the hybridization is done in a fully coupled way taking into account mutual interactions between the fem and utd regions the utd objects are modeled using non uniform rational b spline nurbs surfaces ray acceleration techniques and simple clustering strategies are used to speed up the computation time numerical results are presented showing the validity of the method

evaluation of physical optics integrals from b spline surfaces by means of a fast locating algorithm of stationary points a novel modeling method based on the parametric domain decomposition is proposed for the b spline surfaces this method combines the advantages of conventional b spline and bezier surfaces moreover a fast algorithm based on the new modeling method is presented to locate the stationary points including inner and boundary stationary points of physical optics po integrals from targets modeled with double quadratic b spline surfaces in this algorithm the locating problem is reduced to a numerical or analytical solution no approximation is involved in the proposed modeling method and locating algorithm the stationary phase method by means of the fast locating algorithm is employed to evaluate po integrals the cpu time is independent of the incident frequency and physical dimension of scattered surfaces the accuracy and performance of the presented methods are validated by comparing them with those of the brute force method

a nonstandard schwarz domain decomposition method for finite element mesh truncation of infinite arrays a nonstandard schwarz domain decomposition method is proposed as finite element mesh truncation for the analysis of infinite arrays the proposed methodology provides an asymptotic numerically exact radiation condition regardless of the distance to the sources of the problem and without disturbing the original sparsity of the finite element matrices furthermore it works as a multi floquet mode propagating and evanescent absorbing boundary condition numerical results illustrating main features of the proposed methodology are shown

hybrid sup 2 combining the three dimensional hybrid finite element boundary integral technique for planar multilayered media with the uniform geometrical theory of diffraction the fully three dimensional 3 d hybrid finite element fe boundary integral bi technique is extended by further hybridization with the uniform geometrical theory of diffraction utd resulting in a so called hybrid sup 2 fe bi utd approach the formulation is capable of modeling arbitrarily shaped strongly inhomogeneous objects together with electrically large obstacles of relatively simple shape within the common environment of a planar multilayered medium the arbitrarily shaped inhomogeneous objects are discretized by finite elements whereas the electrically large obstacles are described by the utd and both of these models are included into an integral equation derived from the equivalence principle for planar multilayered media thus full electromagnetic coupling is realized between all parts of the formulation the integral equation is implemented using mixed potentials with appropriate green s functions derived from sommerfeld integral representations for planar multilayered media the utd contributions are accounted for by corresponding modifications of the green s functions and the fe technique is coupled to the integral equation via introduction of equivalent surface current densities in the bounding surfaces of the discretized objects after presenting the formulation of this novel fully 3 d hybrid sup 2 technique the implemented computer code is validated against conventional hybrid fe bi computations and a wireless base station antenna is analyzed in several situations of complex real world microcell environments

a novel hybridization of higher order finite element and boundary integral methods for electromagnetic scattering and radiation problems a novel hybridization of the finite element fe and boundary integral methods is presented for an efficient and accurate numerical analysis of electromagnetic scattering and radiation problems the proposed method derives an adaptive numerical absorbing boundary condition abc for the finite element solution based on boundary integral equations unlike the standard finite element boundary integral approach the proposed method is free of interior resonance and produces a purely sparse system matrix which can be solved very efficiently unlike the traditional finite element absorbing boundary condition approach the proposed method uses an arbitrarily shaped truncation boundary placed very close to the scatterer radiator to minimize the computational domain and more importantly the method produces a solution that converges to the true solution of the problem to demonstrate its great potential the proposed method is implemented using higher order curvilinear vector elements a mixed functional is designed to yield both electric and magnetic fields on an integration surface without numerical differentiation to be used in the calculation of the adaptive abc the required evaluation of boundary integrals is carried out using the multilevel fast multipole algorithm which greatly reduces both the memory requirement and cpu time the finite element equations are solved efficiently using the multifrontal algorithm a mathematical analysis is conducted to study the convergence of the method finally a number of numerical examples are given to illustrate its accuracy and efficiency