ideal spatial adaptation by wavelet shrinkage summary with ideal spatial adaptation an oracle furnishes information about how best to adapt a spatially variable estimator whether piecewise constant piecewise polynomial variable knot spline or variable bandwidth kernel to the unknown function estimation with the aid of an oracle offers dramatic advantages over traditional linear estimation by nonadaptive kernels however it is a priori unclear whether such performance can be obtained by a procedure relying on the data alone we describe a new principle for spatially adaptive estimation selective wavelet reconstruction we show that variable knot spline fits and piecewise polynomial fits when equipped with an oracle to select the knots are not dramatically more powerful than selective wavelet reconstruction with an oracle we develop a practical spatially adaptive method riskshrink which works by shrinkage of empirical wavelet coefficients riskshrink mimics the performance of an oracle for selective wavelet reconstruction as well as it is possible to do so a new inequality in multivariate normal decision theory which we call the oracle inequality shows that attained performance differs from ideal performance by at most a factor of approximately 2 log n where n is the sample size moreover no estimator can give a better guarantee than this within the class of spatially adaptive procedures riskshrink is essentially optimal relying only on the data it comes within a factor log 2 n of the performance of piecewise polynomial and variableknot spline methods equipped with an oracle in contrast it is unknown how or if piecewise polynomial methods could be made to function this well when denied access to an oracle and forced to rely on data alone

blur identification by the method of generalized cross validation the point spread function psf of a blurred image is often unknown a priori the blur must first be identified from the degraded image data before restoring the image generalized cross validation gcv is introduced to address the blur identification problem the gcv criterion identifies model parameters for the blur the image and the regularization parameter providing all the information necessary to restore the image experiments are presented which show that gvc is capable of yielding good identification results a comparison of the gcv criterion with maximum likelihood ml estimation shows the gcv often outperforms ml in identifying the blur and image model parameters

a new indirect anisotropic quadrilateral mesh generation scheme with enhanced local mesh smoothing procedures an enhanced version of indirect advancing front technique is proposed for the construction of full quadrilateral anisotropic meshes on 3d surfaces the final quadrilateral mesh is constructed from a background triangular mesh and the merging procedure is carried out in the parametric space the proposed method employed the systemic merging technique for the formation of quadrilaterals and the metric specifications for controlling the anisotropic characteristics of the elements in order to generate well graded anisotropic quadrilaterals the selection criteria of base segment for merging are carefully defined furthermore in order to improve the shape quality of the final mesh a set of new local smoothing algorithms for anisotropic quadrilateral mesh quality enhancement has been proposed and tested in this study numerical examples obtained indicate that the proposed enhanced local smoothing schemes can effectively improve the quality of the quadrilateral meshes produced and increase the robustness of the mesh generation scheme copyright 2003 john wiley sons ltd

a new mesh generation scheme for arbitrary planar domains this paper describes a new algorithm to generate interior nodes within any arbitrary multi connected regions the boundary nodes and the interior nodes are then linked up to form the best possible triangular elements by a completely revised technique in an efficient and stable manner owing to the generality of the central generation program the global domain is allowed to be divided into as many irregular subdomains as desired in order to model closely the actual physical situation moreover the boundaries of the sub domains are updated from time to time when necessary to include the possibilities of progressive refinement around a sharp corner generating radiating mesh from a prescribed node generating mesh between two circular arcs etc despite its flexibility and capabilities data for triangulation have been kept to a minimum by a logical input module no connectivity information between subregions is needed and common boundaries are defined once only all these features have contributed to a powerful method to generate 3 node or 6 node triangular element meshes of great variety within the most irregular heterogeneous regions

estimation of the mean of a multivariate normal distribution estimation of the means of independent normal random variables is considered using sum of squared errors as loss an unbiased estimate of risk is obtained for an arbitrary estimate and certain special classes of estimates are then discussed the results are applied to smoothing by use of moving averages and to trimmed analogs of the james stein estimate a suggestion is made for calculating approximate confidence sets for the mean vector centered at an arbitrary estimate

generalized 3 d paving an automated quadrilateral surface mesh generation algorithm this paper discusses the extension of the paving algorithm for all quadrilateral mesh generation to arbitrary three dimensional trimmed surfaces methods of calculating angles projecting elements and detecting collisions between paving boundaries for general surfaces are presented extensions of the smoothing algorithms for three dimensions are set forth advances in the use of scalar sizing functions are presented these functions can be used to better approximate internal mesh density from boundary densities and surface characteristics

h morph an indirect approach to advancing front hex meshing h morph is a new automatic algorithm for the generation of a hexahedral dominant finite element mesh for arbitrary volumes the h morph method starts with an initial tetrahedral mesh and systematically transforms and combines tetrahedral into hexahedra it uses an advancing front technique where the initial front consists of a set of prescribed quadrilateral surface facets fronts are individually processed by recovering each of the six quadrilateral faces of a hexahedron from the tetrahedral mesh recovery techniques similar to those used in boundary constrained delaunay mesh generation are used tetrahedral internal to the six hexahedral faces are then removed and a hexahedron is formed at any time during the h morph procedure a valid mixed hexahedral tetrahedral mesh is in existence within the volume the procedure continues until no tetrahedral remain within the volume or tetrahedral remain which cannot be transformed or combined into valid hexahedral elements any remaining tetrahedral are typically towards the interior of the volume generally a less critical region for analysis transition from tetrahedral to hexahedra in the final mesh is accomplished through pyramid shaped elements advantages of the proposed method include its ability to conform to an existing quadrilateral surface mesh its ability to mesh without the need to decompose or recognize special classes of geometry and its characteristic well aligned layers of elements parallel to the boundary example test cases are presented on a variety of models

an elementary proof of the polar factorization of vector valued functions we present an elementary proof of an important result of y brenier br1 br2 namely that vector fields in d satisfying a nondegeneracy condition admit the polar factorization u x s x where is a convex function and s is a measure preserving mapping brenier solves a minimization problem using monge kantorovich theory whereas we turn our attention to a dual problem whose euler lagrange equation turns out to be

automatic generation of anisotropic quadrilateral meshes on three dimensional surfaces using metric specifications a new algorithm for constructing full quadrilateral anisotropic meshes on 3d surfaces is proposed in this paper the proposed method is based on the advancing front and the systemic merging techniques full quadrilateral meshes are constructed by systemically converting triangular elements in the background meshes into quadrilateral elements by using the metric specifications to describe the element characteristics the proposed algorithm is applicable to convert both isotropic and anisotropic triangular meshes into full quadrilateral meshes special techniques for generating anisotropic quadrilaterals such as new selection criteria of base segment for merging new approaches for the modifications of the background mesh and construction of quadrilateral elements are investigated and proposed in this study since the final quadrilateral mesh is constructed from a background triangular mesh and the merging procedure is carried out in the parametric space the mesh generator is robust and no expensive geometrical computation that is commonly associated with direct quadrilateral mesh generation schemes is needed copyright 2002 john wiley sons ltd

blind deconvolution using a variational approach to parameter image and blur estimation following the hierarchical bayesian framework for blind deconvolution problems in this paper we propose the use of simultaneous autoregressions as prior distributions for both the image and blur and gamma distributions for the unknown parameters hyperparameters of the priors and the image formation noise we show how the gamma distributions on the unknown hyperparameters can be used to prevent the proposed blind deconvolution method from converging to undesirable image and blur estimates and also how these distributions can be inferred in realistic situations we apply variational methods to approximate the posterior probability of the unknown image blur and hyperparameters and propose two different approximations of the posterior distribution one of these approximations coincides with a classical blind deconvolution method the proposed algorithms are tested experimentally and compared with existing blind deconvolution methods

a new sure approach to image denoising interscale orthonormal wavelet thresholding this paper introduces a new approach to orthonormal wavelet image denoising instead of postulating a statistical model for the wavelet coefficients we directly parametrize the denoising process as a sum of elementary nonlinear processes with unknown weights we then minimize an estimate of the mean square error between the clean image and the denoised one the key point is that we have at our disposal a very accurate statistically unbiased mse estimate stein s unbiased risk estimate that depends on the noisy image alone not on the clean one like the mse this estimate is quadratic in the unknown weights and its minimization amounts to solving a linear system of equations the existence of this a priori estimate makes it unnecessary to devise a specific statistical model for the wavelet coefficients instead and contrary to the custom in the literature these coefficients are not considered random any more we describe an interscale orthonormal wavelet thresholding algorithm based on this new approach and show its near optimal performance both regarding quality and cpu requirement by comparing it with the results of three state of the art nonredundant denoising algorithms on a large set of test images an interesting fallout of this study is the development of a new group delay based parent child prediction in a wavelet dyadic tree

a nonlinear stein based estimator for multichannel image denoising the use of multicomponent images has become widespread with the improvement of multisensor systems having increased spatial and spectral resolutions however the observed images are often corrupted by an additive gaussian noise in this paper we are interested in multichannel image denoising based on a multiscale representation of the images a multivariate statistical approach is adopted to take into account both the spatial and the intercomponent correlations existing between the different wavelet subbands more precisely we propose a new parametric nonlinear estimator which generalizes many reported denoising methods the derivation of the optimal parameters is achieved by applying stein s principle in the multivariate case experiments performed on multispectral remote sensing images clearly indicate that our method outperforms conventional wavelet denoising techniques

the monge problem for supercritical mane potentials on compact manifolds abstract we prove the existence of optimal transport maps for the monge problem when the cost is a finsler distance on a compact manifold our point of view consists in considering the distance as a mane potential and to rely on recent developments in the theory of viscosity solutions of the hamilton jacobi equation

a soft double regularization approach to parametric blind image deconvolution this paper proposes a blind image deconvolution scheme based on soft integration of parametric blur structures conventional blind image deconvolution methods encounter a difficult dilemma of either imposing stringent and inflexible preconditions on the problem formulation or experiencing poor restoration results due to lack of information this paper attempts to address this issue by assessing the relevance of parametric blur information and incorporating the knowledge into the parametric double regularization pdr scheme the pdr method assumes that the actual blur satisfies up to a certain degree of parametric structure as there are many well known parametric blurs in practical applications further it can be tailored flexibly to include other blur types if some prior parametric knowledge of the blur is available a manifold soft parametric modeling technique is proposed to generate the blur manifolds and estimate the fuzzy blur structure the pdr scheme involves the development of the meaningful cost function the estimation of blur support and structure and the optimization of the cost function experimental results show that it is effective in restoring degraded images under different environments

the sure let approach to image denoising we propose a new approach to image denoising based on the image domain minimization of an estimate of the mean squared error stein s unbiased risk estimate sure unlike most existing denoising algorithms using the sure makes it needless to hypothesize a statistical model for the noiseless image a key point of our approach is that although the nonlinear processing is performed in a transformed domain typically an undecimated discrete wavelet transform but we also address nonorthonormal transforms this minimization is performed in the image domain indeed we demonstrate that when the transform is a ldquotightrdquo frame an undecimated wavelet transform using orthonormal filters separate subband minimization yields substantially worse results in order for our approach to be viable we add another principle that the denoising process can be expressed as a linear combination of elementary denoising processes linear expansion of thresholds let armed with the sure and let principles we show that a denoising algorithm merely amounts to solving a linear system of equations which is obviously fast and efficient quite remarkably the very competitive results obtained by performing a simple threshold image domain sure optimized on the undecimated haar wavelet coefficients show that the sure let principle has a huge potential

defocus map estimation from a single image based on two parameter defocus model defocus map estimation dme is highly important in many computer vision applications nearly all existing approaches for dme from a single image are based on a one parameter defocus model which does not allow for the variation of depth over edges in this paper a novel two parameter model of defocused edges is proposed for dme from a single image we can estimate the defocus amounts for each side of the edges through this proposed model and the confidence that the edge is a pattern edge where the depth remains the same over the edge can be generated then we modify the tv l1 algorithm for structure texture decomposition by taking advantage of this confidence to eliminate pattern edges while preserving structural ones finally the defocus amounts estimated at the edge positions are used as initial values and the structure component is employed as a guidance in the following laplacian matting procedure to avoid the influence of pattern edges on the final defocus map experiment results show that the proposed method can effectively eliminate the influence of pattern edges compared with the state of art method furthermore the estimated defocus map is feasible in applications of depth estimation and foreground background segmentation

blind deblurring and denoising of images corrupted by unidirectional object motion blur and sensor noise low light photography suffers from blur and noise in this paper we propose a novel method to recover a dense estimate of spatially varying blur kernel as well as a denoised and deblurred image from a single noisy and object motion blurred image a proposed method takes the advantage of the sparse representation of double discrete wavelet transform a generative model of image blur that simplifies the wavelet analysis of a blurred image and the bayesian perspective of modeling the prior distribution of the latent sharp wavelet coefficient and the likelihood function that makes the noise handling explicit we demonstrate the effectiveness of the proposed method on moderate noise and severely blurred images using simulated and real camera data

adaptive zoning for singular problems in two dimensions abstract winslow s method for the automatic generation of computation meshes is extended to adaptively vary the zone sizes and orthogonality of grid lines in the resulting mesh through simple analysis and numerical examples the adaptive mesh is shown to give significant increases in accuracy in the computation of singular problems

blind deconvolution of medical ultrasound images a parametric inverse filtering approach the problem of reconstruction of ultrasound images by means of blind deconvolution has long been recognized as one of the central problems in medical ultrasound imaging in this paper this problem is addressed via proposing a blind deconvolution method which is innovative in several ways in particular the method is based on parametric inverse filtering whose parameters are optimized using two stage processing at the first stage some partial information on the point spread function is recovered subsequently this information is used to explicitly constrain the spectral shape of the inverse filter from this perspective the proposed methodology can be viewed as a ldquohybridizationrdquo of two standard strategies in blind deconvolution which are based on either concurrent or successive estimation of the point spread function and the image of interest moreover evidence is provided that the ldquohybridrdquo approach can outperform the standard ones in a number of important practical cases additionally the present study introduces a different approach to parameterizing the inverse filter specifically we propose to model the inverse transfer function as a member of a principal shift invariant subspace it is shown that such a parameterization results in considerably more stable reconstructions as compared to standard parameterization methods finally it is shown how the inverse filters designed in this way can be used to deconvolve the images in a nonblind manner so as to further improve their quality the usefulness and practicability of all the introduced innovations are proven in a series of both in silico and in vivo experiments finally it is shown that the proposed deconvolution algorithms are capable of improving the resolution of ultrasound images by factors of 2 24 or 6 52 as judged by the autocorrelation criterion depending on the type of regularization method used

constructing optimal maps for monge s transport problem as a limit of strictly convex costs the monge kantorovich problem is to move one distribution of mass onto another as efficiently as possible where monge s original criterion for efficiency 19 was to minimize the average distance transported subsequently studied by many authors it was not until 1976 that sudakov showed solutions to be realized in the original sense of monge i e as mappings from rn to rn 23 a second proof of this existence result formed the subject of a recent monograph by evans and gangbo 7 who avoided sudakov s measure decomposition results by using a partial differential equations approach in the present manuscript we give a third existence proof for optimal mappings which has some advantages and disadvantages relative to existing approaches it requires no continuity or separation of the mass distributions yet our explicit construction yields more geometrical control than the abstract method of sudakov indeed this control turns out to be essential for addressing a gap which has recently surfaced in sudakov s approach to the problem in dimensions n 3 see the remarks at the end of this section it is also shorter and more flexible than either and can be adapted to handle transportation on riemannian manifolds or around obstacles as we plan to show in a subsequent work 13 the problem considered here is the classical one problem 1 monge fix a norm d x y llx yll on rn and two densities non negative borel functions f fe ll rn satisfying the mass balance condition

motion blur identification in noisy images using mathematical models and statistical measures motion blur is one of the most common blurs that degrades images restoration of such images is highly dependent on estimation of motion blur parameters since 1976 many researchers have developed algorithms to estimate linear motion blur parameters these algorithms are different in their performance time complexity precision and robustness in noisy environments in this paper we have presented a novel algorithm to estimate linear motion blur parameters such as direction and length we used radon transform to find direction and bispectrum modeling to find the length of motion our algorithm is based on the combination of spatial and frequency domain analysis the great benefit of our algorithm is its robustness and precision in noisy images we used statistical measures to prove goodness of our model our method was tested on 80 standard images that were degraded with different directions and motion lengths with additive gaussian noise the error tolerance average of the estimated parameters was 0 9 o in direction and 0 95 pixel in length and the standard deviations were 0 69 and 0 85 respectively

generalized sure for exponential families applications to regularization stein s unbiased risk estimate sure was proposed by stein for the independent identically distributed i i d gaussian model in order to derive estimates that dominate least squares ls recently the sure criterion has been employed in a variety of denoising problems for choosing regularization parameters that minimize an estimate of the mean squared error mse however its use has been limited to the i i d case which precludes many important applications in this paper we begin by deriving a sure counterpart for general not necessarily i i d distributions from the exponential family this enables extending the sure design technique to a much broader class of problems based on this generalization we suggest a new method for choosing regularization parameters in penalized ls estimators we then demonstrate its superior performance over the conventional generalized cross validation and discrepancy approaches in the context of image deblurring and deconvolution the sure technique can also be used to design estimates without predefining their structure however allowing for too many free parameters impairs the estimate s performance to address this inherent tradeoff we propose a regularized sure objective and demonstrate its use in the context of wavelet denoising

a novel sure based criterion for parametric psf estimation we propose an unbiased estimate of a filtered version of the mean squared error the blur sure stein s unbiased risk estimate as a novel criterion for estimating an unknown point spread function psf from the degraded image only the psf is obtained by minimizing this new objective functional over a family of wiener processings based on this estimated blur kernel we then perform nonblind deconvolution using our recently developed algorithm the sure based framework is exemplified with a number of parametric psf involving a scaling factor that controls the blur size a typical example of such parametrization is the gaussian kernel the experimental results demonstrate that minimizing the blur sure yields highly accurate estimates of the psf parameters which also result in a restoration quality that is very similar to the one obtained with the exact psf when plugged into our recent multi wiener sure let deconvolution algorithm the highly competitive results obtained outline the great potential of developing more powerful blind deconvolution algorithms based on sure like estimates

a sure approach for digital signal image deconvolution problems in this paper we are interested in the classical problem of restoring data degraded by a convolution and the addition of a white gaussian noise the originality of the proposed approach is twofold first we formulate the restoration problem as a nonlinear estimation problem leading to the minimization of a criterion derived from stein s unbiased quadratic risk estimate secondly the deconvolution procedure is performed using any analysis and synthesis frames that can be overcomplete or not new theoretical results concerning the calculation of the variance of the stein s risk estimate are also provided in this work simulations carried out on natural images show the good performance of our method with respect to conventional wavelet based restoration methods

blind image deconvolution using machine learning for three dimensional microscopy in this work we propose a novel method for the regularization of blind deconvolution algorithms the proposed method employs example based machine learning techniques for modeling the space of point spread functions during an iterative blind deconvolution process a prior term attracts the point spread function estimates to the learned point spread function space we demonstrate the usage of this regularizer within a bayesian blind deconvolution framework and also integrate into the latter a method for noise reduction thus creating a complete blind deconvolution method the application of the proposed algorithm is demonstrated on synthetic and real world three dimensional images acquired by a wide field fluorescence microscope where the need for blind deconvolution algorithms is indispensable yielding excellent results

parametric blur estimation for blind restoration of natural images linear motion and out of focus this paper presents a new method to estimate the parameters of two types of blurs linear uniform motion approximated by a line characterized by angle and length and out of focus modeled as a uniform disk characterized by its radius for blind restoration of natural images the method is based on the spectrum of the blurred images and is supported on a weak assumption which is valid for the most natural images the power spectrum is approximately isotropic and has a power law decay with the spatial frequency we introduce two modifications to the radon transform which allow the identification of the blur spectrum pattern of the two types of blurs above mentioned the blur parameters are identified by fitting an appropriate function that accounts separately for the natural image spectrum and the blur frequency response the accuracy of the proposed method is validated by simulations and the effectiveness of the proposed method is assessed by testing the algorithm on real natural blurred images and comparing it with state of the art blind deconvolution methods

direct blind deconvolution blind deconvolution seeks to deblur an image without knowing the cause of the blur iterative methods are commonly applied to that problem but the iterative process is slow uncertain and often ill behaved this paper considers a significant but limited class of blurs that can be expressed as convolutions of two dimensional symmetric levy stable probability density functions this class includes and generalizes gaussian and lorentzian distributions for such blurs methods are developed that can detect the point spread function from one dimensional fourier analysis of the blurred image a separate image deblurring technique uses this detected point spread function to deblur the image each of these two steps uses direct noniterative methods and requires interactive tuning of parameters as a result blind deblurring of 512 512 images can be accomplished in minutes of cpu time on current desktop workstations numerous blind experiments on synthetic data show that for a given blurred image several di

single image refocusing and defocusing in this paper we present a postprocessing method to tackle the single image refocusing and defocusing problem the proposed method can accomplish the tasks of focus map estimation and image refocusing and defocusing given an image with a mixture of focused and defocused objects we first detect the edges and then estimate the focus map based on the edge blurriness which is depicted explicitly by a parametric model the image refocusing problem is addressed in a blind deconvolution framework where the image prior is modeled by using both global and local constraints in particular we correct the defocused blurry edges to sharp ones with the aid of the parametric edge model and then render this cue as a local prior to ensure the sharpness of the refocused image experimental results demonstrate that the proposed method performs well in producing visually plausible images with different focus effects from a single input

existence of optimal transport maps for crystalline norms we show the existence of optimal transport maps in the case when the cost function is the distance induced by a crystalline norm in n assuming that the initial distribution of mass is absolutely continuous with respect to mathcal l n the proof is based on a careful decomposition of the space in transport rays induced by a secondary variational problem having the euclidean distance as cost function moreover improving a construction by larman we show the existence of a nikodym set in 3 having full measure in the unit cube intersecting each element of a family of pairwise disjoint open lines only in one point this example can be used to show that the regularity of the decomposition in transport rays plays an essential role in sudakov type arguments for proving the existence of optimal transport maps

linear and nonlinear image deblurring a documented study nonlinear image deblurring procedures based on probabilistic considerations are widely believed to outperform conventional linear methods this paper is exclusively concerned with nonsmooth images such as those that occur in biomedical imaging where reconstruction of high frequency detail is of prime interest and where avoidance of a priori smoothness constraints is a major concern the theoretical basis behind each of the following nonlinear procedures is examined the lucy richardson method the maximum likelihood e m algorithm the poisson maximum a posteriori method and the nunez llacer version of the maximum entropy method a linear iterative method vancittert s iteration is also studied it is shown that each of the first three methods as well as vancittert s method lack a necessary ingredient for successful solution of the ill posed deblurring problem while in the maximum entropy method the enforced smoothness may have adverse consequences in medical imaging a direct linear method the slow evolution from the continuation boundary secb method designed specifically for nonsmooth images is also considered that method is stabilized by constraining the blurring operator as well as the solution and does not require smoothness constraints it is shown that useful error estimates can be obtained in the secb method while this is impossible in tikhonov s method without a priori bounds on derivatives of the unknown solution reconstruction experiments on low noise synthetic mri data show that thousands of iterations are necessary to achieve sufficient resolution in the iterative procedures however the secb method provides higher resolution at considerable savings in computer time at high noise levels the iterative algorithms are shown to diverge at these same noise levels the secb method produces reconstructions comparable in quality to those that would be obtained in the iterative methods were one able to terminate the divergent algorithm at that iteration which best approximates the true solution in the l1 norm

multi wiener sure let deconvolution in this paper we propose a novel deconvolution algorithm based on the minimization of a regularized stein s unbiased risk estimate sure which is a good estimate of the mean squared error we linearly parametrize the deconvolution process by using multiple wiener filters as elementary functions followed by undecimated haar wavelet thresholding due to the quadratic nature of sure and the linear parametrization the deconvolution problem finally boils down to solving a linear system of equations which is very fast and exact the linear coefficients i e the solution of the linear system of equations constitute the best approximation of the optimal processing on the wiener haar threshold basis that we consider in addition the proposed multi wiener sure let approach is applicable for both periodic and symmetric boundary conditions and can thus be used in various practical scenarios the very competitive both in computation time and quality results show that the proposed algorithm which can be interpreted as a kind of nonlinear wiener processing can be used as a basic tool for building more sophisticated deconvolution algorithms

development of an automatic two dimensional finite element mesh generator using quadrilateral elements and bezier curve boundary definition this paper describes the development of an automatic two dimensional quadrilateral element mesh generator the methodology is based on the looping algorithm developed in part by dr m l c sluiter bezier curves are used to define the boundaries of the parts to be meshed the required interaction by the user is reduced to specifying the boundary geometry the preferred element size and the refinement coefficient transition elements are automatically generated between regions of varying element sizes the ability to offset specified boundary curves insures well conditioned elements along the boundary meshes for several sample geometries are presented to illustrate the versatility of the mesh generator

an empirical identification method of gaussian blur parameter for image deblurring in this paper we propose an empirical identification method of the gaussian blur parameter for image deblurring the parameter estimate is chosen from a collection of candidate parameters the blurred image is restored by these candidate parameters under the assumption that the candidate is equal to the true value the estimate is selected to be at the maximum point of the differential coefficients of restored image laplacian l1 norm curve experimental results are presented to demonstrate the performance of the proposed method

a new approach to the development of automatic quadrilateral mesh generation a methodology for the automatic mesh generation of quadrilateral elements is proposed the methodology is based on the facts that i a region can always be subdivided entirely into quadrilaterals if the polygon which forms the boundary of the region has an even number of sides ii a quadrilateral can be formed by two triangles which share a common side by taking advantage of the techniques developed in an existing automatic triangular mesh generator quadrilateral meshes can be generated according to the distribution of user specified element size over the domain of interest in particular an automatic quadrilateral mesh generator based on the advancing front technique for triangular mesh generation1 is described techniques to improve the quality of the generated quadrilateral meshes are introduced the robustness and versatility of the mesh generator are demonstrated by a variety of examples

recognition of images degraded by gaussian blur in this paper we propose a new theory of invariants to gaussian blur we introduce a notion of a primordial image as a canonical form of all gaussian blur equivalent images the primordial image is defined in spectral domain by means of projection operators we prove that the moments of the primordial image are invariant to gaussian blur and we derive recursive formulas for their direct computation without actually constructing the primordial image itself we show how to extend their invariance also to image rotation the application of these invariants is in blur invariant image comparison and recognition in the experimental part we perform an exhaustive comparison with two main competitors 1 the zhang distance and 2 the local phase quantization

monge s transport problem on a riemannian manifold monge s problem refers to the classical problem of optimally transporting mass given borel probability measures find the measurepreserving map s m m between them which minimizes the average distance transported set on a complete connected riemannian manifold m and assuming absolute continuity of an optimal map will be shown to exist aspects of its uniqueness are also established

blind deconvolution using generalized cross validation approach to regularization parameter estimation in this paper we propose and present an algorithm for total variation tv based blind deconvolution both the unknown image and blur can be estimated within an alternating minimization framework with the generalized cross validation gcv method the regularization parameters associated with the unknown image and blur can be updated in alternating minimization steps experimental results confirm that the performance of the proposed algorithm is better than variational bayesian blind deconvolution algorithms with student s t priors or a total variation prior

adaptive triangular quadrilateral mesh generation in this paper we begin by recalling an adaptive mesh generation method governed by isotropic and anisotropic discrete metric maps by means of the generation of a unit mesh with respect to a riemannian structure we propose then an automatic triangular to quadrilateral mesh conversion scheme which generalizes the standard case to the anisotropic context in addition we introduce an optimal vertex smoothing procedure application test examples in particular a cfd test are given to demonstrate the eciency of the proposed method 1998 john wiley sons ltd int j numer meth engng 41 915 934 1998

polar factorization and monotone rearrangement of vector valued functions given a probability space x p and a bounded domain r in rd equipped with the lebesgue measure 1 i normalized so that 10 i i it is shown under additional technical assumptions on x and q that for every vector valued function u e lp x p rd there is a unique polar factorization u v s where is a convex function defined on r and s is a measure preserving mapping from x p into q i i provided that u is nondegenerate in the sense that p u e 0 for each lebesgue negligible subset e of rd through this result the concepts of polar factorization of real matrices helmholtz decomposition of vector fields and nondecreasing rearrangements of real valued functions are unified the monge amgre equation is involved in the polar factorization and the proof relies on the study of an appropriate monge kantorovich problem

the geometry of optimal transportation introduction 113 1 summary of main results 120 2 background on optimal measures 126 part i strictly convex costs 133 3 existence and uniqueness of optimal maps 133 4 characterization of the optimal map 137 part ii costs which are strictly concave as a function of d i s t a n c e 141 5 the role of optimal maps 141 6 uniqueness of optimal solutions 144 part iii appendices 148 a legendre transforms and conjugate costs 148 b examples of c concave potentials 152 c regularity of c concave potentials 154 references 159