the klein gordon equation of generalized hulthen potential in complex quantum mechanics we have investigated the reality of exact bound states of complex and or pt symmetric non hermitian exponential type generalized hulthen potential the klein gordon equation has been solved by using the nikiforov uvarov method which is based on solving the second order linear differential equations by reduction to a generalized equation of hypergeometric type in many cases of interest negative and positive energy states have been discussed for different types of complex potentials

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

snakes in movement in this paper we propose a geometric partial differential equation pde for tracking one or several moving objects from a sequence of images which is based on a geometric model for active contours the active contour approach permits us to simultaneously handle both aspects finding the boundaries and tracking them we also describe a numerical scheme to solve the geometric equation and we present some numerical experiments

comparing images using the hausdorff distance the hausdorff distance measures the extent to which each point of a model set lies near some point of an image set and vice versa thus this distance can be used to determine the degree of resemblance between two objects that are superimposed on one another efficient algorithms for computing the hausdorff distance between all possible relative positions of a binary image and a model are presented the focus is primarily on the case in which the model is only allowed to translate with respect to the image the techniques are extended to rigid motion the hausdorff distance computation differs from many other shape comparison methods in that no correspondence between the model and the image is derived the method is quite tolerant of small position errors such as those that occur with edge detectors and other feature extraction methods it is shown that the method extends naturally to the problem of comparing a portion of a model against an image

exact time dependence of solutions to the time dependent schrodinger equation solutions of the schrodinger equation with an exact time dependence are derived as eigenfunctions of dynamical invariants which are constructed from time independent operators using time dependent unitary transformations exact solutions and a closed form expression for the corresponding time evolution operator are found for a wide range of time dependent hamiltonians in d dimensions including non hermitean symmetric hamiltonians hamiltonians are constructed using time dependent unitary spatial transformations comprising dilatations translations and rotations and solutions are found in several forms as eigenfunctions of a quadratic invariant as coherent state eigenfunctions of boson operators as plane wave solutions from which the general solution is obtained as an integral transform by means of the fourier transform and as distributional solutions for which the initial wavefunction is the dirac function for the isotropic harmonic oscillator in d dimensions radial solutions are found which extend known results for d 1 including barut girardello and perelomov coherent states i e vector coherent states which are shown to be related to eigenfunctions of the quadratic invariant by the transformation this transformation which leaves the ermakov equation invariant implements su 1 1 transformations on linear dynamical invariants coherent states are derived also for the time dependent linear potential exact solutions are found for hamiltonians with electromagnetic interactions in which the time dependent magnetic and electric fields are not necessarily spatially uniform as an example it is shown how to find exact solutions of the time dependent schrodinger equation for the dirac magnetic monopole in the presence of time dependent magnetic and electric fields of a specified form

a geometric model for active contours in image processing we propose a new model for active contours based on a geometric partial differential equation our model is intrinsec stable satisfies the maximum principle and permits a rigorous mathematical analysis it enables us to extract smooth shapes we cannot retrieve angles and it can be adapted to find several contours simultaneously moreover as a consequence of the stability we can design robust algorithms which can be engineed with no parameters in applications numerical experiments are presented

a non conforming piecewise quadratic finite element on triangles it is shown in this paper that non conforming finite elements on the triangle using second degree polynomials can be easily built and used indeed they appear as an enriched version of the standard piecewise quadratic six node element this work is divided into two parts in the first we present the basic properties of the element namely how it can be built and basic error estimates we also show that this element exhibits a very peculiar regularity property in the second part we apply our element to the approximation of viscous incompressible flows and more generally to the approximation of incompressible materials

snakes active contour models a snake is an energy minimizing spline guided by external constraint forces and influenced by image forces that pull it toward features such as lines and edges snakes are active contour models they lock onto nearby edges localizing them accurately scale space continuation can be used to enlarge the capture region surrounding a feature snakes provide a unified account of a number of visual problems including detection of edges lines and subjective contours motion tracking and stereo matching we have used snakes successfully for interactive interpretation in which user imposed constraint forces guide the snake near features of interest

a morphological scheme for mean curvature motion and applications to anisotropic diffusion and motion of level sets this paper introduces a discrete scheme for mean curvature motion using a morphological image processing approach an axiomatic approach of image processing and the mean curvature partial differential equation pde are briefly presented then the properties of the proposed scheme are studied in particular consistency and convergence are proved the applications of mean curvature motion in image denoising and form evolution are developed and experiences are presented

dynamical invariance algebra of the hartmann potential the accidental degeneracy occurring in the quantum mechanical treatment of the ring shaped potential v eta sigma 2r 1 1 2q eta 2 sigma 2 r sin theta 2 is explained by constructing an su 2 dynamical invariance algebra the schrodinger equation is solved in parabolic coordinates written in the framework of the kustaanheimo stiefel transformation and the hamilton jacobi equations are solved in ordinary parabolic coordinates all finite trajectories are found to be periodic

enhancement of morphological snake based segmentation by imparting image attachment through scale space continuity in this paper we propose a new multi scale morphological approach to curve evolution useful for object extraction through segmentation the homogenous image structures that characterize the segmentation process are edges and terminations normally the conventional morphological snake ms technique employs morphological binary level set operators for realizing forces these operations handle definite components of the pde partial differential equation used for modeling the dynamic system the proposed model can segment with reasonably high level of accuracy and efficiency while ensuring smooth segmentation at object boundaries with scale space continuity application of discrete image force in ms is a per pixel decision based on the sign of image force pde component in the continuous domain however the intensity of the image force pde component is the primary factor for snake evolution in our model we embed scale space continuity into the morphological operators dictated by ms in order to realize the image force both in intensity and direction thus our model confirms to the speed agility and robustness of morphological snakes with regard to segmentation while ensuring enhanced efficiency of segmentation under noise we have rated the performance both on qualitative and quantitative basis against benchmark results on a set of 2d gray scale real images both in absence and presence of noise a comparative study has also been carried among our method ms geodesic active contour gac and distance regularized level set evolution drlse highlightsmulti scale morphological approach to curve evolution is suggested for segmentation we embed scale space continuity in morphological snakes morphological operators ensure fast curve evolution scale space continuity ensures smoother segmentation near edges extraction improvement near noisy pixels is observed with scale space continuity

signal matching through scale space given a collection of similar signals that have been deformed with respect to each other the general signal matching problem is to recover the deformation we formulate the problem as the minimization of an energy measure that combines a smoothness term and a similarity term the minimization reduces to a dynamic system governed by a set of coupled first order differential equations the dynamic system finds an optimal solution at a coarse scale and then tracks it continuously to a fine scale among the major themes in recent work on visual signal matching have been the notions of matching as constrained optimization of variational surface reconstruction and of coarse to fine matching our solution captures these in a precise succinct and unified form results are presented for one dimensional signals a motion sequence and a stereo pair

bound state solutions of the dirac equation for the trigonometric and hyperbolic scarf grosche potentials using the nikiforov uvarov method the relativistic dirac equation with equal trigonometric and hyperbolic scarf grosche scalar and vector potentials in 3 1 and 1 1 space time dimension are solved by using the nikiforov uvarov method the exact energy equations and the spinor wave functions are obtained for these sets of potentials the bound states energy are calculated numerically also with appropriate transformations solutions of the fourth potential v4 can be deduced from the solutions of the third potential v3

a morphological approach to curvature based evolution of curves and surfaces we introduce new results connecting differential and morphological operators that provide a formal and theoretically grounded approach for stable and fast contour evolution contour evolution algorithms have been extensively used for boundary detection and tracking in computer vision the standard solution based on partial differential equations and level sets requires the use of numerical methods of integration that are costly computationally and may have stability issues we present a morphological approach to contour evolution based on a new curvature morphological operator valid for surfaces of any dimension we approximate the numerical solution of the curve evolution pde by the successive application of a set of morphological operators defined on a binary level set and with equivalent infinitesimal behavior these operators are very fast do not suffer numerical stability issues and do not degrade the level set function so there is no need to reinitialize it moreover their implementation is much easier since they do not require the use of sophisticated numerical algorithms we validate the approach providing a morphological implementation of the geodesic active contours the active contours without borders and turbopixels in the experiments conducted the morphological implementations converge to solutions equivalent to those achieved by traditional numerical solutions but with significant gains in simplicity speed and stability

exact solutions of the schrodinger equation with non central potential by the nikiforov uvarov method the general solutions of the schrodinger equation for a non central potential are obtained by using the nikiforov uvarov method the schrodinger equation with general non central potential is separated into radial and angular parts and energy eigenvalues and eigenfunctions are derived analytically by making special selections the non central potential is reduced to coulomb and hartmann ring shaped potentials and the obtained results are compared with the solutions of coulomb and hartmann potentials given in the literature

nonconforming multigrid method for nonsymmetric and indefinite problems abstract the convergence of w cycle multigrid algorithms applied to nonsymmetric and indefinite elliptic boundary value problems using p 1 nonconforming finite elements is proved

two level additive schwarz preconditioners for p1 nonconforming finite elements for nonsymmetric and indefinite problems two level additive schwarz preconditioners are developed for p1 nonconforming finite element approximation of second order nonsymmetric and indefinite elliptic problems the convergence factor is shown to be independent of the number of subspaces when this preconditioner is used with gmres method

fast geodesic active contours we use an unconditionally stable numerical scheme to implement a fast version of the geodesic active contour model the proposed scheme is useful for object segmentation in images like tracking moving objects in a sequence of images the method is based on the weickert romeney viergever additive operator splitting aos scheme it is applied at small regions motivated by the adalsteinsson sethian level set narrow band approach and uses sethian s 1996 fast marching method for re initialization experimental results demonstrate the power of the new method for tracking in color movies

a topology preserving level set method for geometric deformable models active contour and surface models also known as deformable models are powerful image segmentation techniques geometric deformable models implemented using level set methods have advantages over parametric models due to their intrinsic behavior parameterization independence and ease of implementation however a long claimed advantage of geometric deformable models the ability to automatically handle topology changes turns out to be a liability in applications where the object to be segmented has a known topology that must be preserved we present a new class of geometric deformable models designed using a novel topology preserving level set method which achieves topology preservation by applying the simple point concept from digital topology these new models maintain the other advantages of standard geometric deformable models including subpixel accuracy and production of nonintersecting curves or surfaces moreover since the topology preserving constraint is enforced efficiently through local computations the resulting algorithm incurs only nominal computational overhead over standard geometric deformable models several experiments on simulated and real data are provided to demonstrate the performance of this new deformable model algorithm

a new ring shaped potential and its dynamical invariance algebra a new ring shaped potential obtained by replacing the coulomb part of the hartmann potential by a harmonic oscillator term is investigated the schrodinger equation is solved in spherical circular cylindrical prolate and oblate spheroidal coordinates as in the case of the hartmann potential the accidental degeneracies occurring in the spectrum are shown to be due to an su 2 dynamical invariance algebra this establishes a close connection between both ring shaped potentials

a class of exactly solvable rationally extended non central potentials in two and three dimensions we start from a seven parameter six continuous and one discrete family of non central exactly solvable potentials in three dimensions and construct a wide class of ten parameters six continuous and four discrete family of rationally extended exactly solvable non central real as well as pt symmetric complex potentials the energy eigenvalues and the eigenfunctions of these extended non central potentials are obtained explicitly and it is shown that the wave eigenfunctions of these potentials are either associated with the exceptional orthogonal polynomials or some type of new polynomials which can be further re expressed in terms of the corresponding classical orthogonal polynomials similarly we also construct a wide class of rationally extended exactly solvable non central real as well as complex pt invariant potentials in two dimensions we start from a seven parameter six continuous and one discrete family of non central exactly solvable potentials in three dimensions and construct a wide class of ten parameters six continuous and four discrete family of rationally extended exactly solvable non central real as well as pt symmetric complex potentials the energy eigenvalues and the eigenfunctions of these extended non central potentials are obtained explicitly and it is shown that the wave eigenfunctions of these potentials are either associated with the exceptional orthogonal polynomials or some type of new polynomials which can be further re expressed in terms of the corresponding classical orthogonal polynomials similarly we also construct a wide class of rationally extended exactly solvable non central real as well as complex pt invariant potentials in two dimensions

erratum distance regularized level set evolution and its application to image segmentation ieee transactions on image processingvol 2010 19 12 3243 3254

an optimal order multigrid method for p1 nonconforming finite elements etude d une methode multigrille d ordre optimal pour la resolution des problemes aux limites elliptiques du second ordre a l aide d elements finis non conformes

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

a comparison of two multilevel iterative methods for nonsymmetric and indefinite elliptic finite element equations we describe and analyze two multilevel iterative procedures for solving linear systems arising from certain finite element discretizations of nonself adjoint and indefinite elliptic partial differential equations we prove convergence and optimal work estimate for both schemes

a new convergence proof for the multigrid method including the v cycle for a positive definite finite element equation we describe a multigrid iteration and prove convergence under natural assumptions on the discretization and the elliptic problem hitherto existing convergence proofs require a sufficiently large number of smoothing iterations and exclude the v cycle the presented proof applies to procedures with any number of smoothing iterations and to the v cycle

an optimal order process for solving finite element equations a k level iterative procedure for solving the algebraic equations which arise from the finite element approximation of elliptic boundary value problems is presented and analyzed the work estimate for this procedure is proportional to the number of unknowns an optimal order result general geometry is permitted for the underlying domain but the shape plays a role in the rate of convergence through elliptic regularity finally a short discussion of the use of this method for parabolic problems is presented

the analysis of multigrid algorithms for nonsymmetric and indefinite elliptic problems we prove some new estimates for the convergence of multigrid algorithms applied to nonsymmetric and indefinite elliptic boundary value problems we provide results for the so called symmetric multigrid schemes we show that for the variable v script cycle and the w script cycle schemes multigrid algorithms with any amount of smoothing on the finest grid converge at a rate that is independent of the number of levels or unknowns provided that the initial grid is sufficiently fine we show that the v script cycle algorithm also converges under appropriate assumptions on the coarsest grid but at a rate which may deteriorate as the number of levels increases this deterioration for the v script cycle may occur even in the case of full elliptic regularity finally the results of numerical experiments are given which illustrate the convergence behavior suggested by the theory

distance regularized level set evolution and its application to image segmentation level set methods have been widely used in image processing and computer vision in conventional level set formulations the level set function typically develops irregularities during its evolution which may cause numerical errors and eventually destroy the stability of the evolution therefore a numerical remedy called reinitialization is typically applied to periodically replace the degraded level set function with a signed distance function however the practice of reinitialization not only raises serious problems as when and how it should be performed but also affects numerical accuracy in an undesirable way this paper proposes a new variational level set formulation in which the regularity of the level set function is intrinsically maintained during the level set evolution the level set evolution is derived as the gradient flow that minimizes an energy functional with a distance regularization term and an external energy that drives the motion of the zero level set toward desired locations the distance regularization term is defined with a potential function such that the derived level set evolution has a unique forward and backward fab diffusion effect which is able to maintain a desired shape of the level set function particularly a signed distance profile near the zero level set this yields a new type of level set evolution called distance regularized level set evolution drlse the distance regularization effect eliminates the need for reinitialization and thereby avoids its induced numerical errors in contrast to complicated implementations of conventional level set formulations a simpler and more efficient finite difference scheme can be used to implement the drlse formulation drlse also allows the use of more general and efficient initialization of the level set function in its numerical implementation relatively large time steps can be used in the finite difference scheme to reduce the number of iterations while ensuring sufficient numerical accuracy to demonstrate the effectiveness of the drlse formulation we apply it to an edge based active contour model for image segmentation and provide a simple narrowband implementation to greatly reduce computational cost

multigrid methods for nonconforming finite element methods the present paper analyzes a multigrid algorithm for the crouzeix raviart discretization of the poisson and stokes equations in two and three dimensions the central point is the construction of easily computable l 2 projections based on suitable quadrature rules for the transfer from coarse to fine grids and vice versa