a variational method in image recovery this paper is concerned with a classical denoising and deblurring problem in image recovery our approach is based on a variational method by using the legendre fenchel transform we show how the nonquadratic criterion to be minimized can be split into a sequence of half quadratic problems easier to solve numerically first we prove an existence and uniqueness result and then we describe the algorithm for computing the solution and we give a proof of convergence finally we present some experimental results for synthetic and real images

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

convergence of an iterative method for total variation denoising in total variation denoising one attempts to remove noise from a signal or image by solving a nonlinear minimization problem involving a total variation criterion several approaches based on this idea have recently been shown to be very effective particularly for denoising functions with discontinuities this paper analyzes the convergence of an iterative method for solving such problems the iterative method involves a lagged diffusivity approach in which a sequence of linear diffusion problems are solved global convergence in a finite dimensional setting is established and local convergence properties including rates and their dependence on various parameters are examined

computing optical flow via variational techniques defined as the apparent motion in a sequence of images the optical flow is very important in the computer vision community where its accurate estimation is necessary for many applications it is o

recovery algorithms for vector valued data with joint sparsity constraints vector valued data appearing in concrete applications often possess sparse expansions with respect to a preassigned frame for each vector component individually additionally different components may also exhibit common sparsity patterns recently there were introduced sparsity measures that take into account such joint sparsity patterns promoting coupling of nonvanishing components these measures are typically constructed as weighted ell 1 norms of componentwise ell q norms of frame coefficients we show how to compute solutions of linear inverse problems with such joint sparsity regularization constraints by fast thresholded landweber algorithms next we discuss the adaptive choice of suitable weights appearing in the definition of sparsity measures the weights are interpreted as indicators of the sparsity pattern and are iteratively updated after each new application of the thresholded landweber algorithm the resulting two step algorithm is interpreted as a double minimization scheme for a suitable target functional we show its ell 2 norm convergence an implementable version of the algorithm is also formulated and its norm convergence is proven numerical experiments in color image restoration are presented

on superregular matrices and mdp convolutional codes superregular matrices are a type of lower triangular toeplitz matrix that arises in the context of constructing convolutional codes having a maximum distance profile these matrices are characterized by the property that the only submatrices having a zero determinant are those whose determinants are trivially zero due to the lower triangular structure in this paper we discuss how superregular matrices may be used to construct codes having a maximum distance profile we also present an upper bound on the minimum size a finite field must have in order that a superregular matrix of a given size can exist over that field this in turn gives an upper bound on the smallest field size over which an mdp n k convolutional code can exist

l 2 discretization error bounds for maps into riemannian manifolds we study the approximation of functions that map a euclidean domain omega subset mathbb r d into an n dimensional riemannian manifold m g minimizing an elliptic semilinear energy in a function set h subset w 1 2 omega m the approximation is given by a restriction of the energy minimization problem to a family of conforming finite dimensional approximations s h subset h we provide a set of conditions on s h such that we can prove a priori w 1 2 and l 2 approximation error estimates comparable to standard euclidean finite elements this is done in an intrinsic framework independently of embeddings of the manifold or the choice of coordinates

a general framework for low level vision we introduce a new geometrical framework based on which natural flows for image scale space and enhancement are presented we consider intensity images as surfaces in the x i space the image is thereby a two dimensional 2 d surface in three dimensional 3 d space for gray level images and 2 d surfaces in five dimensions for color images the new formulation unifies many classical schemes and algorithms via a simple scaling of the intensity contrast and results in new and efficient schemes extensions to multidimensional signals become natural and lead to powerful denoising and scale space algorithms

control of a 3d piezo actuating table by using an adaptive sliding mode controller for a drilling process recently the micropositioner has become an important developing target for achieving the requirements of precision machinery the piezo actuating device plays a very important role in this application area in this paper a model free adaptive sliding mode controller is proposed for a 3d piezo actuating system because of the system s hysteresis nonlinearity and time varying characteristics this control strategy employs the functional approximation technique to establish the unknown function for releasing the model based requirements of the sliding mode control the update laws for the coefficients of the fourier series function parameters are derived from a lyapunov function to guarantee the control system stability to verify the effectiveness of the proposed controller drilling process control using the designed controller is investigated in this paper

a new algorithm for computing liquid crystal stable configurations the harmonic mapping case in this article we propose a new algorithm for minimizing the energy of a nematic liquid crystal based on the equal elastic constants oseen frank model the problem reduces to finding harmonic minimizing maps that take values into the unit sphere of bbb r 3 the convergence of this algorithm is proved in a continuous setting then numerous numerical results that show its efficiency are given

harmonic maps with defects two problems concerning maps with point singularities from a domain c 3 tos2 are solved the first is to determine the minimum energy of when the location and topological degree of the singularities are prescribed in the second problem is the unit ball and g is given on we show that the only cases in whichg x x minimizes the energy isg const org x rx withr a rotation extensions of these problems are also solved e g points are replaced by holes 3 s2 is replaced by n sn 1 or by n pn 1 the latter being appropriate for the theory of liquid crystals

implicit brain imaging we describe how implicit surface representations can be used to solve fundamental problems in brain imaging this kind of representation is not only natural following the state of the art segmentation algorithms reported in the literature to extract the different brain tissues but it is also as shown in this paper the most appropriate one from the computational point of view examples are provided for finding constrained special curves on the cortex such as sulcal beds regularizing surface based measures such as cortical thickness and for computing warping fields between surfaces such as the brain cortex all these result from efficiently solving partial differential equations pdes and variational problems on surfaces represented in implicit form the implicit framework avoids the need to construct intermediate mappings between 3 d anatomical surfaces and parametric objects such planes or spheres a complex step that introduces errors and is required by many other cortical processing approaches

fast image and video colorization using chrominance blending colorization the task of coloring a grayscale image or video involves assigning from the single dimension of intensity or luminance a quantity that varies in three dimensions such as red green and blue channels mapping between intensity and color is therefore not unique and colorization is ambiguous in nature and requires some amount of human interaction or external information a computationally simple yet effective approach of colorization is presented in this paper the method is fast and it can be conveniently used on the fly permitting the user to interactively get the desired results promptly after providing a reduced set of chrominance scribbles based on the concepts of luminance weighted chrominance blending and fast intrinsic distance computations high quality colorization results for still images and video are obtained at a fraction of the complexity and computational cost of previously reported techniques possible extensions of the algorithm introduced here included the capability of changing the colors of an existing color image or video as well as changing the underlying luminance and many other special effects demonstrated here

restoration of color images by vector valued bv functions and variational calculus we analyze a variational problem for the recovery of vector valued functions and compute its numerical solution the data of the problem are a small set of complete samples of the vector valued function and some significant incomplete information where the former are missing the incomplete information is assumed as the result of a distortion with values in a lower dimen sional manifold for the recovery of the function we minimize a functional which is formed by the discrepancy with respect to the data and total variation regularization constraints we show the existence of minimizers in the space of vector valued bounded variation functions for the computa tion of minimizers we provide a stable and efficient method first we approximate the functional by coercive functionals on w 1 2 in terms of convergence then we realize approximations of minimiz ers of the latter functionals by an iterative procedure to solve the pde system of the corresponding euler lagrange equations the numerical implementation comes naturally by finite element dis cretization we apply the algorithm to the restoration of color images from limited color information and gray levels where the colors are missing the numerical experiments show that this scheme is very fast and robust the reconstruction capabilities of the model are shown also from very limited randomly distributed color data several examples are included from the real restoration problem of a mantegna s art frescoes in italy

variational restoration of nonflat image features models and algorithms we develop both mathematical models and computational algorithms for variational denoising and restoration of nonflat image features nonflat image features are those that live on riemannian manifolds instead of on the euclidean spaces familiar examples include the orientation feature from optical flows or gradient flows that lives on the unit circle s1 the alignment feature from fingerprint waves or certain texture images that lives on the real projective line mathbb rp 1 and the chromaticity feature from color images that lives on the unit sphere s2 in this paper we apply the variational method to denoise and restore general nonflat image features mathematical models for both continuous image domains and discrete domains or graphs are constructed riemannian objects such as metric distance and levi civita connection play important roles in the models computational algorithms are also developed for the resulting nonlinear equations the mathematical framework can be applied to res

asymptotic synchronization of the colpitts oscillator in this paper we deal with the observer based asymptotic synchronization problem for a class of chaotic oscillators some results based on a differential algebraic approach are used in order to determine the algebraic observability of unknown variables the strategy consists of proposing a slave system observer which tends to follow asymptotically the master system the methodology is tested in the real time asymptotic synchronization of the colpitts oscillator by means of a proportional reduced order observer proo of free model type

orientation diffusions diffusions are useful for image processing and computer vision because they provide a convenient way of smoothing noisy data analyzing images at multiple scales and enhancing discontinuities a number of diffusions of image brightness have been defined and studied so far they may be applied to scalar and vector valued quantities that are naturally associated with intervals of either the real line or other flat manifolds some quantities of interest in computer vision and other areas of engineering that deal with images are defined on curved manifolds typical examples are orientation and hue that are defined on the circle generalizing brightness diffusions to orientation is not straightforward especially in the case where a discrete implementation is sought an example of what may go wrong is presented a method is proposed to define diffusions of orientation like quantities first a definition in the continuum is discussed then a discrete orientation diffusion is proposed the behavior of such diffusions is explored both analytically and experimentally it is shown how such orientation diffusions contain a nonlinearity that is reminiscent of edge process and anisotropic diffusion a number of open questions are proposed

noise removal using fourth order partial differential equation with applications to medical magnetic resonance images in space and time we introduce a new method for image smoothing based on a fourth order pde model the method is tested on a broad range of real medical magnetic resonance images both in space and time as well as on nonmedical synthesized test images our algorithm demonstrates good noise suppression without destruction of important anatomical or functional detail even at poor signal to noise ratio we have also compared our method with related pde models

a class of one dimensional mds convolutional codes a class of one dimensional convolutional codes will be presented they are all mds codes i e have the largest distance among all one dimensional codes of the same length n and overall constraint length furthermore their extended row distances are computed and they increase with slope at least n in certain cases of the algebraic parameters we will also derive parity check matrices of vandermonde type for these codes finally cyclicity in the convolutional sense of 8 will be discussed for our class of codes it will turn out that they are cyclic if and only if the field element used in the generator matrix has order n this can be regarded as a generalization of the block code case

design and implementation of fuzzy sliding mode controllers for generalized projective synchronization of chaos horizontal platform systems this paper presents robust chattering free fuzzy sliding mode control fsmc as a way to achieve generalized projective synchronization gps of two horizontal chaos platform vibration systems with system uncertainty and external disturbance an appropriate sliding surface is acquired through an smc design such that the error state trajectories of a master slave system will reach such a sliding surface and approaches to the origin based on the lyapunov stability theory we address the design schemes of integration fuzzy sliding mode control where the reaching law is proposed by a set of linguistic rules and the control input is chattering free as a consequence the system is simulated and experimented to demonstrate that the error state tends to be stabilized and the chattering problem can be thus resolved implying that the slave horizontal platform system hps is gps with the master hps

existence and partial regularity results for the heat flow for harmonic maps on considere le probleme d evolution t u m u n u 0 dans m r u 0 u 0 sur m ou m et n sont des varietes de riemann lisses compactes et u 0 l application harmonique de m dans n on demontre l existence d une solution globale faible

solving variational problems and partial differential equations mapping into general target manifolds a framework for solving variational problems and partial differential equations that define maps onto a given generic manifold is introduced in this paper we discuss the framework for arbitrary target manifolds while the domain manifold problem was addressed in j comput phys 174 2 2001 759 the key idea is to implicitly represent the target manifold as the level set of a higher dimensional function and then implement the equations in the cartesian coordinate system where this embedding function is defined in the case of variational problems we restrict the search of the minimizing map to the class of maps whose target is the level set of interest in the case of partial differential equations we re write all the equation s geometric characteristics with respect to the embedding function we then obtain a set of equations that while defined on the whole euclidean space are intrinsic to the implicitly defined target manifold and map into it this permits the use of classical numerical techniques in cartesian grids regardless of the geometry of the target manifold the extension to open surfaces and submanifolds is addressed in this paper as well in the latter case the submanifold is defined as the intersection of two higher dimensional hypersurfaces and all the computations are restricted to this intersection examples of the applications of the framework here described include harmonic maps in liquid crystals where the target manifold is a hypersphere probability maps where the target manifold is a hyperplane chroma enhancement texture mapping and general geometric mapping between high dimensional manifolds

sliding mode synchronization of an uncertain fractional order chaotic system synchronization of chaotic and uncertain duffing holmes system has been done using the sliding mode control strategy regarding the synchronization task as a control problem fractional order mathematics is used to express the system and sliding mode for synchronization it has been shown that not only the performance of the proposed method is satisfying with an acceptable level of control signal but also a rather simple stability analysis is performed the latter is usually a complicated task for uncertain nonlinear chaotic systems

relaxation methods for liquid crystal problems a point relaxation method for the liquid crystal problem is proposed and analyzed the liquid crystal problem is a minimization problem with a nonconvex local constraint it is proved that the energy of successive iterates is nonincreasing for the point relaxation method with relaxation parameter omega satisfying 0 omega 2 for a class of material constants it is also shown that the difference between successive iterates converges to zero and that limit points of the iteration sequence are minima with respect to perturbations which are supported at a point and which satisfy the constraint numerical results are given which demonstrate the improved rate of convergence for overrelaxation

fourth order partial differential equations for noise removal a class of fourth order partial differential equations pdes are proposed to optimize the trade off between noise removal and edge preservation the time evolution of these pdes seeks to minimize a cost functional which is an increasing function of the absolute value of the laplacian of the image intensity function since the laplacian of an image at a pixel is zero if the image is planar in its neighborhood these pdes attempt to remove noise and preserve edges by approximating an observed image with a piecewise planar image piecewise planar images look more natural than step images which anisotropic diffusion second order pdes uses to approximate an observed image so the proposed pdes are able to avoid the blocky effects widely seen in images processed by anisotropic diffusion while achieving the degree of noise removal and edge preservation comparable to anisotropic diffusion although both approaches seem to be comparable in removing speckles in the observed images speckles are more visible in images processed by the proposed pdes because piecewise planar images are less likely to mask speckles than step images and anisotropic diffusion tends to generate multiple false edges speckles can be easily removed by simple algorithms such as the one presented in this paper

anti synchronization of uncertain unified chaotic systems with dead zone nonlinearity abstract this paper addresses chaos anti synchronization of uncertain unified chaotic systems with dead zone input nonlinearity using the sliding mode control technique and lyapunov stability theory a proportional integral pi switching surface is proposed to ensure the stability of the closed loop error system in sliding mode then a sliding mode controller smc is proposed to guarantee the hitting of the switching surface even with uncertainties and the control input containing dead zone nonlinearity some simulation results are included to demonstrate the effectiveness and feasibility of the proposed synchronization scheme

stabilization of uncertain fuzzy control systems via a new descriptor system approach this paper addresses stabilizing a class of fuzzy control systems with a guaranteed h control performance via a new descriptor system approach based on the sector nonlinearity concept of tanaka and wang 2001 1 the uncertain nonlinear system can be exactly represented by t s fuzzy models then we propose using the composite state and output feedback csaof fuzzy control for the control design a new descriptor fuzzy system will be represented in this paper based on the lyapunov stability theorem and the linear matrix inequality lmi tool we solve the controller gain matrices some positive constants and some common positive definite matrices then we derive two sufficient conditions to stabilize the uncertain fuzzy control systems with guaranteed h control performance moreover the developed h criterion guarantees that the influence of external disturbance is as small as possible a practical system is given to illustrate the validity of the proposed scheme

diffusion of general data on non flat manifolds viaharmonic maps theory the direction diffusion case in a number of disciplines directional data provides a fundamental source of information a novel framework for isotropic and anisotropic diffusion of directions is presented in this paper the framework can be applied both to denoise directional data and to obtain multiscale representations of it the basic idea is to apply and extend results from the theory of harmonic maps and in particular harmonic maps in liquid crystals this theory deals with the regularization of vectorial data while satisfying the intrinsic unit norm constraint of directional data we show the corresponding variational and partial differential equations formulations for isotropic diffusion obtained from an l 2 norm and edge preserving diffusion obtained from an l norm in general and an l 1 norm in particular in contrast with previous approaches the framework is valid for directions in any dimensions supports non smooth data and gives both isotropic and anisotropic formulations in addition the framework of harmonic maps here described can be used to diffuse and analyze general image data defined on general non flat manifolds that is functions between two general manifolds we present a number of theoretical results open questions and examples for gradient vectors optical flow and color images

variable universe stable adaptive fuzzy control of a nonlinear system abstract a kind of stable adaptive fuzzy control of a nonlinear system is implemented based on the variable universe method proposed first in 1 first of all the basic structure of variable universe adaptive fuzzy controllers is briefly introduced then the contraction expansion factor which is a key tool of the variable universe method is defined by means of the integral regulation idea and then a kind of adaptive fuzzy controller is designed by using such a contraction expansion factor the simulation on the first order nonlinear system is done and as a result its simulation effect is quite good in comparison with the corresponding result in 2 3 second it is proved that the variable universe adaptive fuzzy control is asymptotically stable by use of liapunov theory the simulation on a second order nonlinear system shows that its simulation effect is also quite good in comparison with the corresponding result in 2 besides a useful tool called symbolic factor is proposed which may be of universal significance it can greatly reduce the setting time and enhance the robustness of the system

color image enhancement via chromaticity diffusion a novel approach for color image denoising is proposed in this paper the algorithm is based on separating the color data into chromaticity and brightness and then processing each one of these components with partial differential equations or diffusion flows in the proposed algorithm each color pixel is considered as an n dimensional vector the vectors direction a unit vector gives the chromaticity while the magnitude represents the pixel brightness the chromaticity is processed with a system of coupled diffusion equations adapted from the theory of harmonic maps in liquid crystals this theory deals with the regularization of vectorial data while satisfying the intrinsic unit norm constraint of directional data such as chromaticity both isotropic and anisotropic diffusion flows are presented for this n dimensional chromaticity diffusion flow the brightness is processed by a scalar median filter or any of the popular and well established anisotropic diffusion flows for scalar image enhancement we present the underlying theory a number of examples and briefly compare with the current literature

numerical methods for p harmonic flows and applications to image processing we propose in this paper an alternative approach for computing p harmonic maps and flows instead of solving a constrained minimization problem on sn 1 we solve an unconstrained minimization problem on the entire space of functions this is possible using the projection on the sphere of any arbitrary function then we show how this formulation can be used in practice for problems with both isotropic and anisotropic diffusion with applications to image processing using a new finite difference scheme

a finite time synergetic control scheme for robot manipulators a finite time synergetic control ftsc scheme which is synthesized with synergetic theory and a terminal attractor technique is proposed for controlling robot manipulators unlike conventional synergetic control sc or conventional sliding mode control smc the proposed control scheme has the characteristics of finite time convergence and chattering free phenomena the lyapunov stability method is adopted here to verify the stability of the controlled system the proposed controller is then applied in the control of n link robot manipulators all the simulation results demonstrate the effectiveness and feasibility of the proposed control method

orientation matching minimization for image denoising and inpainting in this paper we propose an orientation matching functional minimization for image denoising and image inpainting following the two step tv stokes algorithm rahman et al in scale space and variational methods in computer vision pp 473 482 springer heidelberg 2007 tai et al in image processing based on partial differential equations pp 3 22 springer heidelberg 2006 bertalmio et al in proc conf comp vision pattern rec pp 355 362 2001 a regularized tangential vector field with zero divergence condition is first obtained then a novel approach to reconstruct the image is proposed instead of finding an image that fits the regularized normal direction from the first step we propose to minimize an orientation matching cost measuring the alignment between the image gradient and the regularized normal direction this functional yields a new nonlinear partial differential equation pde for reconstructing denoised and inpainted images the equation has an adaptive diffusivity depending on the orientation of the regularized normal vector field providing reconstructed images which have sharp edges and smooth regions the additive operator splitting aos scheme is used for discretizing euler lagrange equations we present the results of various numerical experiments that illustrate the improvements obtained with the new functional

nonlinear analysis and control of the uncertain micro electro mechanical system by using a fuzzy sliding mode control design this study analyzes the chaotic behavior of a micromechanical resonator with electrostatic forces on both sides and investigates the control of chaos a phase portrait maximum lyapunov exponent and bifurcation diagram are used to find the chaotic dynamics of this micro electro mechanical system mems to suppress chaotic motion a robust fuzzy sliding mode controller fsmc is designed to turn the chaotic motion into a periodic motion even when the mems has system uncertainties

design of a fuzzy sliding mode synchronization controller for two different chaos systems this investigation presents a fuzzy sliding mode technology for synchronizing two chaotic systems a method of designing a fuzzy sliding mode control fsmc is presented which utilizes a variable normalization factor fsmc is designed to guarantee the global asymptotic synchronization of state trajectories of two different chaotic systems the chaotic systems are numerically simulated to demonstrate the validity and feasibility of the proposed control structure

a feasible method for optimization with orthogonality constraints minimization with orthogonality constraints e g x top x i and or spherical constraints e g vert x vert 2 1 has wide applications in polynomial optimization combinatorial optimization eigenvalue problems sparse pca p harmonic flows 1 bit compressive sensing matrix rank minimization etc these problems are difficult because the constraints are not only non convex but numerically expensive to preserve during iterations to deal with these difficulties we apply the cayley transform a crank nicolson like update scheme to preserve the constraints and based on it develop curvilinear search algorithms with lower flops compared to those based on projections and geodesics the efficiency of the proposed algorithms is demonstrated on a variety of test problems in particular for the maxcut problem it exactly solves a decomposition formulation for the sdp relaxation for polynomial optimization nearest correlation matrix estimation and extreme eigenvalue problems the proposed algorithms run very fast and return solutions no worse than those from their state of the art algorithms for the quadratic assignment problem a gap 0 842 to the best known solution on the largest problem tai256c in qaplib can be reached in 5 min on a typical laptop

filling in by joint interpolation of vector fields and gray levels a variational approach for filling in regions of missing data in digital images is introduced the approach is based on joint interpolation of the image gray levels and gradient isophotes directions smoothly extending in an automatic fashion the isophote lines into the holes of missing data this interpolation is computed by solving the variational problem via its gradient descent flow which leads to a set of coupled second order partial differential equations one for the gray levels and one for the gradient orientations the process underlying this approach can be considered as an interpretation of the gestaltist s principle of good continuation no limitations are imposed on the topology of the holes and all regions of missing data can be simultaneously processed even if they are surrounded by completely different structures applications of this technique include the restoration of old photographs and removal of superimposed text like dates subtitles or publicity examples of these applications are given we conclude the paper with a number of theoretical results on the proposed variational approach and its corresponding gradient descent flow

variational problems and partial differential equations on implicit surfaces a novel framework for solving variational problems and partial differential equations for scalar and vector valued data defined on surfaces is introduced in this paper the key idea is to implicitly represent the surface as the level set of a higher dimensional function and to solve the surface equations in a fixed cartesian coordinate system using this new embedding function the equations are then both intrinsic to the surface and defined in the embedding space this approach thereby eliminates the need for performing complicated and inaccurate computations on triangulated surfaces as is commonly done in the literature we describe the framework and present examples in computer graphics and image processing applications including texture synthesis flow field visualization and image and vector field intrinsic regularization for data defined on 3d surfaces

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

numerical methods for the landau lifshitz equation we discuss numerical schemes for various forms of the landau lifshitz equation a new simple projection method is introduced and is shown to be unconditionally stable the advantages over other schemes are also demonstrated numerically

constructions of mds convolutional codes maximum distance separable mds convolutional codes are characterized through the property that the free distance attains the generalized singleton bound the existence of mds convolutional codes was established by two of the authors by using methods from algebraic geometry this correspondence provides an elementary construction of mds convolutional codes for each rate k n and each degree spl delta the construction is based on a well known connection between quasi cyclic codes and convolutional codes

on behaviors and convolutional codes it is well known that a convolutional code is essentially a linear system defined over a finite field in this paper we elaborate on this connection we define a convolutional code as the dual of a complete linear behavior in the sense of willems 1979 using ideas from systems theory we describe a set of generalized first order descriptions for convolutional codes as an application of these ideas we present a new algebraic construction for convolutional codes

a two step model for image denoising using a duality strategy and surface fitting in order to alleviate the staircase effect or the edge blurring in the course of the image denoising we propose a two step model based on the duality strategy in fact this strategy follows the observation that the dual variable of the restored image can be looked at as the normal vector so we first obtain the dual variable and then reconstruct the image by fitting the dual variable following the augmented lagrangian strategy we propose a projection gradient method for solving this two step model we also give some convergence analyses of the proposed projection gradient method several numerical experiments are tested to compare our proposed model with the rof model and the llt model

generalized multichannel image filtering structures recent works in multispectral image processing advocate the employment of vector approaches for this class of signals vector processing operators that involve the minimization of a suitable error criterion have been proposed and shown appropriate for this task in this framework two main classes of vector processing filters have been reported in the literature astola et al 1990 introduce the well known class of vector median filters vmf which are derived as maximum likelihood ml estimates from exponential distributions trahanias et al see ibid vol 2 no 4 p 528 34 1993 and vol 5 no 6 p 868 80 1996 study the processing of color image data using directional information considering the class of vector directional filters vdf we introduce a new filter structure the directional distance filters ddf which combine both vdf and vmf in a novel way we show that ddf are robust signal estimators under various noise distributions they have the property of chromaticity preservation and finally compare favorably to other multichannel image processing filters

sensorless stator field orientation controlled induction motor drive with a fuzzy speed controller a sensorless stator field oriented control induction motor drive with a fuzzy logic speed controller is presented first a current and voltage parallel model stator flux estimator is established using measured phase currents and voltages of the induction motor then the estimated rotor shaft position is obtained from the magnitude and position of the estimated stator flux the speed controller is developed by utilizing fuzzy logic control techniques the control algorithms are realized by a dsp 6713 and using a dsp f2812 to generate pwm signals to the power stage drive the motor to experimentally validate the proposed approach

a modified tv stokes model for image processing we introduce and investigate the modified total variation tv stokes model for two classical image processing tasks i e image restoration and image inpainting the modified tv stokes model is a two step model based on a tv minimization in each step and the use of geometric information of the image in the first step a smoothed and divergence free tangential field of the given image is recovered and in the second step the image is reconstructed from the corresponding normals the existence and the uniqueness of the solution to the minimization problems are established for both steps of the model numerical examples and comparisons are presented to illustrate the effectiveness of the model

on the algebraic parameters of convolutional codes with cyclic structure in this paper convolutional codes with cyclic structure will be investigated these codes can be understood as left principal ideals in a suitable skew polynomial ring it has been shown in 4 that only certain combinations of the algebraic parameters field size length dimension and forney indices can occur for such cyclic codes we will investigate whether all these combinations can indeed be realized by a suitable cyclic code and if so how to construct such a code a complete characterization and construction will be given for minimal cyclic codes it is derived from a detailed investigation of the units in the skew polynomial ring

directional processing of color images theory and experimental results the processing of color image data using directional information is studied the class of vector directional filters vdf which was introduced by the authors in a previous work is further considered the analogy of vdf to the spherical median is shown and their relation to the spatial median is examined moreover their statistical and deterministic properties are studied which demonstrate their appropriateness in image processing vdf result in optimal estimates of the image vectors in the directional sense this is very important in the case of color images where the vectors direction signifies the chromaticity of a given color issues regarding the practical implementation of vdf are also considered in addition efficient filtering schemes based on vdf are proposed which include adaptive and or double window structures experimental and comparative results in image filtering show very good performance measures when the error is measured in the l a b space l a b is known as a space where equal color differences result in equal distances and therefore it is very close to the human perception of colors moreover an indication of the chromaticity error is obtained by measuring the error on the maxwell triangle the results demonstrate that vdf are very accurate chromaticity estimators

adaptive neural network based tracking control for electrically driven flexible joint robots without velocity measurements this paper addresses the motion tracking control for a class of flexible joint robotic manipulators actuated by brushed direct current motors this class of electrically driven flexible joint robots is perturbed by plant uncertainties and external disturbances adaptive neural network systems are employed to approximate the behaviors of uncertain mechanical and electrical dynamics a reduced order observer is constructed to estimate the velocity signals only the measurements of link position and armature current are required for feedback consequently an adaptive neural network based dynamic feedback tracking controller without velocity measurements is developed such that all the states and signals of the closed loop system are bounded and the trajectory tracking errors can be made as small as possible finally simulation results are presented to demonstrate the effectiveness of the proposed control algorithms

convolutional goppa codes in this correspondence we define convolutional goppa codes over algebraic curves and construct their corresponding dual codes examples over the projective line and over elliptic curves are described obtaining in particular some maximum distance separable mds convolutional codes

entropy solutions for a fourth order nonlinear degenerate problem for noise removal abstract in this paper we establish the existence and uniqueness of entropy solutions for a fourth order nonlinear degenerate parabolic problem for noise removal in dimension 1 d 4

variational models for image colorization via chromaticity and brightness decomposition colorization refers to an image processing task which recovers color in grayscale images when only small regions with color are given we propose a couple of variational models using chromaticity color components to colorize black and white images we first consider total variation minimizing tv colorization which is an extension from tv inpainting to color using chromaticity model second we further modify our model to weighted harmonic maps for colorization this model adds edge information from the brightness data while it reconstructs smooth color values for each homogeneous region we introduce penalized versions of the variational models we analyze their convergence properties and we present numerical results including extension to texture colorization

noise removal using smoothed normals and surface fitting in this work we use partial differential equation techniques to remove noise from digital images the removal is done in two steps we first use a total variation filter to smooth the normal vectors of the level curves of a noise image after this we try to find a surface to fit the smoothed normal vectors for each of these two stages the problem is reduced to a nonlinear partial differential equation finite difference schemes are used to solve these equations a broad range of numerical examples are given in the paper

high order total variation based image restoration the total variation tv denoising method is a pde based technique that preserves edges well but has the sometimes undesirable staircase effect namely the transformation of smooth regions ramps into piecewise constant regions stairs in this paper we present an improved model constructed by adding a nonlinear fourth order diffusive term to the euler lagrange equations of the variational tv model our technique substantially reduces the staircase effect while preserving sharp jump discontinuities edges we show numerical evidence of the power of resolution of this novel model with respect to the tv model in some 1d and 2d numerical examples

edge forming methods for color image zooming this paper introduces edge forming schemes for image zooming of color images by general magnification factors in order to remove reduce artifacts arising in image interpolation such as image blur and the checkerboard effect an edge forming method is suggested to be applied as a postprocess of standard interpolation methods the method is based on nonconvex nonlinear partial differential equations the equations are carefully discretized incorporating numerical schemes of anisotropic diffusion to be able to form reliable edges satisfactorily the alternating direction implicit adi method is employed for an efficient simulation of the model it has been numerically verified that the resulting algorithm can form clear edges in 2 to 3 adi iterations various results are given to show th effectiveness and reliability of the algorithm

mathematical models for local nontexture inpaintings dedicated to stanley osher on the occasion of his 60th birthday abstract inspired by the recent work of bertalmio et al on digital inpaintings siggraph 2000 we develop general mathematical models for local inpaintings of nontexture images on smooth regions inpaintings are connected to the harmonic and biharmonic extensions and inpainting orders are analyzed for inpaintings involving the recovery of edges we study a variational model that is closely connected to the classical total variation tv denoising model of rudin osher and fatemi phys d 60 1992 pp 259 268 other models are also discussed based on the mumford shah regularity comm pure appl math xlii 1989 pp 577 685 and curvature driven diffusions cdd of chan and shen j visual comm image rep 12 2001 the broad applications of the inpainting models are demonstrated through restoring scratched old photos disocclusion in vision analysis text removal digital zooming and edge based image coding

boundary regularity and the dirichlet problem for harmonic maps in a previous paper 10 we developed an interior regularity theory for energy minimizing harmonic maps into riemannian manifolds in the first two sections of this paper we prove boundary regularity for energy minimizing maps with prescribed dirichlet boundary condition we show that such maps are regular in a full neighborhood of the boundary assuming appropriate regularity on the manifolds the boundary and the data the reader may refer to theorem 2 7 for a statement of the precise result it is not surprising that the boundary regularity is actually stronger than the partial regularity we obtained for the interior this is due to the fact that there are no nontrivial smooth harmonic maps from hemispheres s which map the boundary s 9s to a point i j n 2 and is analogous to the fact that in certain cases we were able to obtain complete regularity in the interior many authors have worked on boundary regularity for this general type of problem we mention hildebrandt and widman 5 and hamilton 4 as having obtained important results specifically for harmonic maps morrey had obtained the boundary regularity for domain dimension n 2 in conjunction with his investigation of the plateau problem in riemannian manifolds 8 in 3 of this paper we observe that the direct method gives solvability of the dirichlet problem under reasonable hypotheses on the manifolds we give as an application an amusing proof of a theorem of sacks and uhlenbeck 9 on the existence of minimal 2 spheres representing the second homotopy group of a manifold the same method gives smooth harmonic representations for k n for a certain class of manifolds n these are characterized by the nonexistence of lower dimensional harmonic spheres whose homogeneous extensions are minimal see proposition 3 4 in the last section of the paper we discuss approximation of l maps by smooth maps we give a simple example of an l map from the three dimensional ball to the two sphere which is not an l limit of continuous maps we