modified curvature motion for image smoothing and enhancement we formulate a general modified mean curvature based equation for image smoothing and enhancement the key idea is to consider the image as a graph in some r sup 72 and apply a mean curvature type motion to the graph we consider some special cases relevant to grey scale and color images

rotationally symmetric p harmonic maps from d2 to s2 we consider rotationally symmetric p harmonic maps from the unit disk d2 r2 to the unit sphere s2 r3 subject to dirichlet boundary conditions and with 1 p we show that the associated energy functional admits a unique minimizer which is of class c in the interior and c1 up to the boundary we also show that there exist infinitely many global solutions to the associated euler lagrange equation and we completely characterize them

image enhancement by entropy maximization and quantization resolution upconversion this article introduces a new contrast enhancement algorithm of tone preserving entropy maximization its design objective is to present the maximal amount of information content in the enhanced image or being optimal in an information theoretical sense while preventing the loss of tone continuity the resulting optimization problem can be graph theoretically modeled as the construction of the k edges maximum weight path and it can be solved efficiently by dynamic programming moreover the proposed algorithm is made more effective by being combined with a preprocess of image restoration that aims to correct quantization errors caused by the analog to digital conversion of image signals empirical evidences are provided to demonstrate the superior visual quality obtained by the new image enhancement algorithm

a new numerical scheme for discrete constrained total variation flows and its convergence in this paper we propose a new numerical scheme for a spatially discrete model of total variation flows whose values are constrained to a riemannian manifold the difficulty of this problem is that the underlying function space is not convex hence it is hard to calculate a minimizer of the functional with the manifold constraint even if it exists we overcome this difficulty by localization technique using the exponential map and prove a finite time error estimate finally we show a few numerical results for the target manifolds s 2 and so 3

scale space and edge detection using anisotropic diffusion a new definition of scale space is suggested and a class of algorithms used to realize a diffusion process is introduced the diffusion coefficient is chosen to vary spatially in such a way as to encourage intraregion smoothing rather than interregion smoothing it is shown that the no new maxima should be generated at coarse scales property of conventional scale space is preserved as the region boundaries in the approach remain sharp a high quality edge detector which successfully exploits global information is obtained experimental results are shown on a number of images parallel hardware implementations are made feasible because the algorithm involves elementary local operations replicated over the image

generalized spatio chromatic diffusion a framework for diffusion of color images is presented the method is based on the theory of thermodynamics of irreversible transformations which provides a suitable basis for designing correlations between the different color channels more precisely we derive an equation for color evolution which comprises a purely spatial diffusive term and a nonlinear term that depends on the interactions among color channels over space we apply the proposed equation to images represented in several color spaces such as rgb cielab opponent colors and ihs

finite element approximations of harmonic map heat flows and wave maps into spheres of nonconstant radii we prove the existence of weak solutions to the harmonic map heat flow and wave maps into spheres of nonconstant radii weak solutions are constructed as proper limits of iterates from a fully practical scheme based on lowest order conforming finite elements where discrete lagrange multipliers are employed to exactly meet the sphere constraint at mesh points computational studies are included to motivate interesting dynamics in two and three spatial dimensions

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

pde based image restoration a hybrid model and color image denoising the paper is concerned with pde based image restoration a new model is introduced by hybridizing a nonconvex variant of the total variation minimization tvm and the motion by mean curvature mmc in order to deal with the mixture of the impulse and gaussian noises reliably we suggest the essentially nondissipative enod difference schemes for the mmc component to eliminate the impulse noise with a minimum ideally no introduction of dissipation the mmc tvm hybrid model and the enod schemes are applied for both gray scale and color images for color image denoising we consider the chromaticity brightness decomposition with the chromaticity formulated in the angle domain an incomplete crank nicolson alternating direction implicit time stepping procedure is adopted to solve those differential equations efficiently numerical experiments have shown that the new hybrid model and the numerical schemes can remove the mixture of the impulse and gaussian noises efficiently and reliably preserving edges quite satisfactorily

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

on the boundary integral formulation of the plane theory of elasticity with applications analytical aspects abstract a formulation of the plane strain problem of the theory of elasticity in stresses for simply connected domains is carried out in terms of real functions within the frame of what is known as the boundary integral method special attention is devoted to the problem of determination of the arbitrary constants appearing in the solution in view of work in progress where numerical techniques are used relying on some mathematical results formulated in the appendix simple applications concerning the first and the second fundamental problems for the circle and for the ellipse are given which show the correctness of the formulation and the necessity of recurring to numerical techniques once the geometry of the problem or the type of boundary conditions deviates from being simple following parts of the present work are devoted to the numerical treatment of the obtained system of equations as well as to the theories of thermoelasticity and thermo electromagneto elasticity

curvilinear crosscuts of subdivision for a domain decomposition method in numerical conformal mapping abstract let q z 1 z 2 z 3 z 4 be a quadrilateral consisting of a jordan domain and four points z 1 z 2 z 3 z 4 in counterclockwise order on we consider a domain decomposition method for computing approximations to the conformal module m q of q in cases where q is long or equivalently m q is large this method is based on decomposing the original quadrilateral q into two or more component quadrilaterals q1 q2 and then approximating m q by the sum j m q j of the modules of the component quadrilaterals the purpose of this paper is to consider ways for determining appropriate crosscuts of subdivision so that the sum j m q j does indeed give a good approximation to m q and in particular to show that there are cases where the use of curved crosscuts is much more appropriate than the straight line crosscuts that have been used so far

synthesis of distillation trains with heat integration by a combined fuzzy and graphical approach abstract after passing some results of fuzzy synthesis of heat exchanger networks in review the application of this approach to the synthesis of distillation trains for the separation of multicomponent mixtures is demonstrated the available heuristic rules are transformed into fuzzy implications dependent on different criteria and that competing rule which is to be applied is selected by the fuzzy algorithm the theoretically possible amount of heat recovery within the networks generated in this way is estimated by a graphical method and included in the final cost evaluation regarding operating parameters like column pressure and reflux ratio according to the mathematical effort at least qualitative statements can be made in result of the estimation of possible heat recovery as already in the case of heat exchanger networks a following learning algorithm can serve to overcome the disadvantages of this sequential approach representing at the same time the first step of a further evolutionary improvement of the initial distillation train

an axiomatic approach to image interpolation we discuss possible algorithms for interpolating data given in a set of curves and or points in the plane we propose a set of basic assumptions to be satisfied by the interpolation algorithms which lead to a set of models in terms of possibly degenerate elliptic partial differential equations the absolute minimal lipschitz extension model amle is singled out and studied in more detail we show experiments suggesting a possible application the restoration of images with poor dynamic range

a variant of trefftz s method by boundary fourier expansion for solving regular and singular plane boundary value problems the main objective of the present work is to introduce a variant of trefftz s method for finding approximate solutions to regular or singular two dimensional boundary value problems for laplace s equation after expressing the solution as a finite linear combination of trial functions the method foresees the enforcement of the boundary condition by using a boundary fourier expansion technique instead of the usual pointwise approach the procedure ultimately produces a rectangular set of linear algebraic equations the method is used to find approximate solutions to five prototype problems mainly in rectangular regions using polar harmonics as trial functions more complicated cases could be envisaged the results are discussed and compared with those obtained by the boundary collocation method for the same set of trial functions it appears that the proposed method yields better results in the case of a singular behaviour of the solution at the boundary for which the singularity could be isolated we have compared the results obtained by the proposed method with isolation and without isolation of the singularity the proposed method may be easily extended to deal with other boundary value problems involving more complicated differential operators boundary geometries and boundary conditions in two or in three dimensions

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

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

behavioral analysis of anisotropic diffusion in image processing in this paper we analyze the behavior of the anisotropic diffusion model of perona and malik 1990 the main idea is to express the anisotropic diffusion equation as coming from a certain optimization problem so its behavior can be analyzed based on the shape of the corresponding energy surface we show that anisotropic diffusion is the steepest descent method for solving an energy minimization problem it is demonstrated that an anisotropic diffusion is well posed when there exists a unique global minimum for the energy functional and that the ill posedness of a certain anisotropic diffusion is caused by the fact that its energy functional has an infinite number of global minima that are dense in the image space we give a sufficient condition for an anisotropic diffusion to be well posed and a sufficient and necessary condition for it to be ill posed due to the dense global minima the mechanism of smoothing and edge enhancement of anisotropic diffusion is illustrated through a particular orthogonal decomposition of the diffusion operator into two parts one that diffuses tangentially to the edges and therefore acts as an anisotropic smoothing operator and the other that flows normally to the edges and thus acts as an enhancement operator

an efficient tvl1 algorithm for deblurring multichannel images corrupted by impulsive noise we extend the alternating minimization algorithm recently proposed in y wang j yang w yin and y zhang siam j imag sci 1 2008 pp 248 272 j yang w yin y zhang and y wang siam j imag sci 2 2009 pp 569 592 to the case of recovering blurry multichannel color images corrupted by impulsive rather than gaussian noise the algorithm minimizes the sum of a multichannel extension of total variation and a data fidelity term measured in the ell 1 norm and is applicable to both salt and pepper and random valued impulsive noise we derive the algorithm by applying the well known quadratic penalty function technique and prove attractive convergence properties including finite convergence for some variables and q linear convergence rate under periodic boundary conditions the main computational requirements of the algorithm are fast fourier transforms and a low complexity gaussian elimination procedure numerical results on images with different blurs and impulsive noise are presented to demonstrate the efficiency of the algorithm in addition it is numerically compared to the least absolute deviation method h y fu m k ng m nikolova and j l barlow siam j sci comput 27 2006 pp 1881 1902 and the two phase method j f cai r chan and m nikolova aims j inverse problems and imaging 2 2008 pp 187 204 for recovering grayscale images we also present results of recovering multichannel images

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

synthesis of engineering objects by recursive fuzzy valuation of crisp combinations abstract different types of fuzzy information in the cybernetical system of engineering synthesis are analysed a family of relational algebrae is introduced for the representation of possible variants fuzzy valuated relational algebrae are defined for the formalization of informational transfer accompanying the composition and decomposition of combinations a recursive algorithm comprising the selection of an appropriate maximum combination the evaluation of the selected object and the consecutive valuation of the containing minimum elements is constructed

the 1 harmonic flow with values into a smooth planar curve abstract we introduce a notion of solution to the 1 harmonic flow i e the formal gradient flow of the total variation with respect to the l 2 distance from a domain of r m into a connected subset of the image of a smooth jordan curve for such notion we establish existence and uniqueness of solutions to the homogeneous neumann problem we also discuss a consistent notion of solution when the target space is a smooth n 1 dimensional manifold whose geodesics are unique presenting conjectures and open questions related to it

anisotropic diffusion of multivalued images with applications to color filtering a general framework for anisotropic diffusion of multivalued images is presented we propose an evolution equation where at each point in time the directions and magnitudes of the maximal and minimal rate of change in the vector image are first evaluated these are given by eigenvectors and eigenvalues of the first fundamental form in the given image metric then the image diffuses via a system of coupled differential equations in the direction of minimal change the diffusion strength is controlled by a function that measures the degree of dissimilarity between the eigenvalues we apply the proposed framework to the filtering of color images represented in cie l a b space

color image segmentation by the vector valued allen cahn phase field model a multigrid solution we present an efficient numerical solution of a pde driven model for color image segmentation and give numerical examples of the results the method combines the vector valued allen cahn phase field equation with initial data fitting terms with prescribed interface width and fidelity constants efficient numerical solution is achieved using a multigrid splitting of a finite element space thereby producing an efficient and robust method for the segmentation of large images we also present the use of adaptive mesh refinement to further speed up the segmentation process

a convergent and constraint preserving finite element method for the p harmonic flow into spheres an explicit fully discrete finite element method which satisfies the nonconvex side constraint at every node is developed for approximating the p harmonic flow for p in 1 infty convergence of the method is established under certain conditions on the domain and mesh computational examples are presented to demonstrate finite time blow ups and qualitative geometric changes of weak solutions of the p harmonic flow

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

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

trefftz method fitting boundary conditions the paper presents various ways of fitting the boundary conditions in the t complete functions method the authors point out the distinct advantages of the orthogonal collocation in comparison to the equidistant collocation and the integral fit the convergence of the collatz error measures and the conditioning of the solution matrices are investigated in detail

solving variational problems and partial differential equations that map between manifolds via the closest point method abstract maps from a source manifold m to a target manifold n appear in liquid crystals color image enhancement texture mapping brain mapping and many other areas a numerical framework to solve variational problems and partial differential equations pdes that map between manifolds is introduced within this paper our approach the closest point method for manifold mapping reduces the problem of solving a constrained pde between manifolds m and n to the simpler problems of solving a pde on m and projecting to the closest points on n in our approach an embedding pde is formulated in the embedding space using closest point representations of m and n this enables the use of standard cartesian numerics for general manifolds that are open or closed with or without orientation and of any codimension an algorithm is presented for the important example of harmonic maps and generalized to a broader class of pdes which includes p harmonic maps improved efficiency and robustness are observed in convergence studies relative to the level set embedding methods harmonic and p harmonic maps are computed for a variety of numerical examples in these examples we denoise texture maps diffuse random maps between general manifolds and enhance color images

fuzzy sets as a basis for a theory of possibility the theory of possibility described in this paper is related to the theory of fuzzy sets by defining the concept of a possibility distribution as a fuzzy restriction which acts as an elastic constraint on the values that may be assigned to a variable more specifically if f is a fuzzy subset of a universe of discourse u u which is characterized by its membership function f then a proposition of the form x is f where x is a variable taking values in u induces a possibility distribution tx which equates the possibility of x taking the value u to f u the compatibility of u with f in this way x becomes a fuzzy variable which is associated with the possibility distribution tx in much the same way as a random variable is associated with a probability distribution in general a variable may be associated both with a possibility distribution and a probability distribution with the weak connection between the two expressed as the possibility probability consistency principle a thesis advanced in this paper is that the imprecision that is intrinsic in natural languages is in the main possibilistic rather than probabilistic in nature thus by employing the concept of a possibility distribution a proposition p in a natural language may be translated into a procedure which computes the probability distribution of a set of attributes which are implied by p several types of conditional translation rules are discussed and in particular a translation rule for propositions of the form x is f is possible where is a number in the interval 0 1 is formulated and illustrated by examples

reduction for the nonlinear problem of fluid waves to a system of integro differential equations with an oceangraphical application a numerical procedure for the solution of the nonlinear problem of irrotational wave propagation inside a finite or an infinite homogeneous fluid mass is proposed this procedure is applied to calculate the fluid gravity waves resulting from certain prescribed varying pressure applied to the free surface of an infinite fluid mass with finite or infinite depth these waves also are calculated analytically within the frame of the linear theory of motion the variation of the fluid s constant depth for this application is found to have no influence on the resulting flow a slight agreement between the numerical solution of the nonlinear problem and the analytical solution of the corresponding linearized problem is noticed in a narrow interval of time following the start of the motion in the course of time a significant divergence between the two theories is found and the nonlinear theory is therefore indispensable for the theoretical prediction of this phenomenon the proposed procedure can be applied to problems with more complicated geometry

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

numerical methods for minimization problems constrained to s 1 and s 2 in this paper we propose numerical methods for minimization problems constrained to s1 and s2 by our technique based on the angle formulation standard numerical difficulties are easily overcome applications to computations of harmonic maps denoising of directional data and of color images are presented in two and three dimensions

a new class of chromatic filters for color image processing theory and applications this paper advances a new framework for chromatic filtering of color images the chromatic content of a color image is encoded in the cie u v chromaticity coordinates whereas the achromatic content is encoded as cie y tristimulus value within the u v chromaticity diagram colors are added according to the well known center of gravity law of additive color mixtures which is generalized here into a nonlinear filtering scheme for processing the two chromatic signals u and v the achromatic channel y can be processed with traditional filtering schemes either linear or nonlinear depending on the specific task at hand the most interesting characteristics of the new filtering scheme are 1 the elimination of color smearing effects along edges between bright and dark areas 2 the possibility of processing chromatic components in a noniterative fashion through linear convolution operations and 3 the consequent amenability to computationally efficient implementations with fast fourier transform the paper includes several examples with both synthetic and real images where the performance of the new filtering method is compared with that of other color image processing algorithms

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

numerical conformal mapping onto a rectangle with applications to the solution of laplacian problems abstract let f be the function which maps conformally a simply connected domain onto a rectangle r so that four specified points on are mapped respectively onto the four vertices of r in this paper we consider the problem of approximating the conformal map f and present a survey of the available numerical methods we also illustrate the practical significance of the conformal map by presenting a number of applications involving the solution of laplacian boundary value problems

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

a quaternion framework for color image smoothing and segmentation in this paper we present feature detail preserving models for color image smoothing and segmentation using the hamiltonian quaternion framework first we introduce a novel quaternionic gabor filter qgf which can combine the color channels and the orientations in the image plane we show that these filters are optimally localized both in the spatial and frequency domains and provide a good approximation to quaternionic quadrature filters using the qgfs we extract the local orientation information in the color images second in order to model this derived orientation information we propose continuous mixtures of appropriate exponential basis functions and derive analytic expressions for these models these analytic expressions take the form of spatially varying kernels which when convolved with a color image or the signed distance function of an evolving contour placed in the color image yield a detail preserving smoothing and segmentation respectively several examples on widely used image databases are shown to depict the performance of our algorithms

backstepping observer based output feedback control for a class of coupled parabolic pdes with different diffusions abstract this paper aims to design a backstepping observer based output feedback controller for a class of coupled parabolic partial differential equations pdes with different diffusions the considered system is endowed with a sensor at the left boundary and an actuation at the right boundary firstly a backstepping observer is designed secondly compared to the existing literature a weaker condition is deduced to guarantee the stability of the plant system by means of a controller thirdly using the separation principle an observer based output feedback controller is set up based on the designed observer and controller finally the efficiency of the proposed method is shown by taking a simplified model of chemical tubular reactor

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

edge preserving image denoising via optimal color space projection denoising of color images can be done on each color component independently recent work has shown that exploiting strong correlation between high frequency content of different color components can improve the denoising performance we show that for typical color images high correlation also means similarity and propose to exploit this strong intercolor dependency using an optimal luminance color difference space projection experimental results confirm that performing denoising on the projected color components yields superior denoising performance both in peak signal to noise ratio and visual quality sense compared to that of existing solutions we also develop a novel approach to estimate directly from the noisy image data the image and noise statistics which are required to determine the optimal projection

sure let multichannel image denoising interscale orthonormal wavelet thresholding we propose a vector matrix extension of our denoising algorithm initially developed for grayscale images in order to efficiently process multichannel e g color images this work follows our recently published sure let approach where the denoising algorithm is parameterized as a linear expansion of thresholds let and optimized using stein s unbiased risk estimate sure the proposed wavelet thresholding function is pointwise and depends on the coefficients of same location in the other channels as well as on their parents in the coarser wavelet subband a nonredundant orthonormal wavelet transform is first applied to the noisy data followed by the subband dependent vector valued thresholding of individual multichannel wavelet coefficients which are finally brought back to the image domain by inverse wavelet transform extensive comparisons with the state of the art multiresolution image denoising algorithms indicate that despite being nonredundant our algorithm matches the quality of the best redundant approaches while maintaining a high computational efficiency and a low cpu memory consumption an online java demo illustrates these assertions

implementation of trefftz method for the solution of some elliptic boundary value problems the purpose of this paper is to implement the well known trefftz method for the approximate solution of some elliptic boundary value problems for the two dimensional laplace s and the biharmonic operators through the use of polar harmonics as trial functions four applications treating four different situations are presented the dirichlet problem for the steady state temperature distribution in an infinite elliptic cylinder giving rise to poisson s or laplace s equations with discontinuous boundary function for the complete and the truncated ellipses cases 1 2 and the first and the second fundamental problems of the plane strain theory of elastostatics for an infinite cylinder with rectangular normal cross section cases 3 4 for two of the examples cases 1 3 the results could be checked against known exact solutions to show in particular that the method can sometimes give the exact solution while for the other two cases 2 4 the method has provided solutions for new problems it is shown that the use of polar harmonics possibly together with other harmonics belonging to different coordinate systems can handle many situations in an efficient way i e by using few trial functions

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