the graded witt group kernel of biquadratic extensions in characteristic two baeza showed that when char f 2 if e f is the separable biquadratic extension e f 1 b1 1 b2 then ker wq f wq e wf 1 b1 wf 1 b2 here we give the analogous result for the graded witt group specifically we obtain an exact sequence f n 1 f n 1 h2n 1f h2n 1e from which the result for gwqf follows by the isomorphisms of kato applications to 2 algebras of exponent and index 4 are also given

guided image completion by confidence propagation this paper presents a new guided image completion method which fills any missing values by considering information from a guidance image we develop a confidence propagation scheme that allows the filling process to be carried out simultaneously without the need of deciding the filling order we conduct experiments in several applications where the problem can be formulated into a guided image completion problem such as interactive segmentation and colorization the experimental results show that our method provides good results and succeeds in situations where conventional methods fail in addition as all building blocks are parallel processes our method is much suitable for hardware acceleration highlightswe proposed an image completion method based on a new formulation filling process was carried out simultaneously without deciding the filling order good results were obtained in a variety of applications

nonlinear approximation based image recovery using adaptive sparse reconstructions and iterated denoising part ii adaptive algorithms we combine the main ideas introduced in part i with adaptive techniques to arrive at a powerful algorithm that estimates missing data in nonstationary signals the proposed approach operates automatically based on a chosen linear transform that is expected to provide sparse decompositions over missing regions such that a portion of the transform coefficients over missing regions are zero or close to zero unlike prevalent algorithms our method does not necessitate any complex preconditioning segmentation or edge detection steps and it can be written as a progression of denoising operations we show that constructing estimates based on nonlinear approximants is fundamentally a nonconvex problem and we propose a progressive algorithm that is designed to deal with this issue directly the algorithm is applied to images through an extensive set of simulation examples primarily on missing regions containing textures edges and other image features that are not readily handled by established estimation and recovery methods we discuss the properties required of good transforms and in conjunction show the types of regions over which well known transforms provide good predictors we further discuss extensions of the algorithm where the utilized transforms are also chosen adaptively where unpredictable signal components in the progressions are identified and not predicted and where the prediction scenario is more general

simultaneous structure and texture image inpainting an algorithm for the simultaneous filling in of texture and structure in regions of missing image information is presented in this paper the basic idea is to first decompose the image into the sum of two functions with different basic characteristics and then reconstruct each one of these functions separately with structure and texture filling in algorithms the first function used in the decomposition is of bounded variation representing the underlying image structure while the second function captures the texture and possible noise the region of missing information in the bounded variation image is reconstructed using image inpainting algorithms while the same region in the texture image is filled in with texture synthesis techniques the original image is then reconstructed adding back these two sub images the novel contribution of this paper is then in the combination of these three previously developed components image decomposition with inpainting and texture synthesis which permits the simultaneous use of filling in algorithms that are suited for different image characteristics examples on real images show the advantages of this proposed approach

a hybrid algorithm with artifact detection mechanism for region filling after object removal from a digital photograph this work aims to develop a novel function of the digital camera i e region filling after object removal from a digital photograph this problem is defined as how to guess the lacuna region after removal of an object by replicating a part from the remainder of the whole image with visually plausible quality we propose a hybrid region filling algorithm composed of a texture synthesis technique and an efficient interpolation method with a refinement approach 1 the subpatch texture synthesis technique can synthesize the lacuna region with significant accuracy 2 the weighted interpolation method is applied to reduce computation time and 3 the artifact detection mechanism integrates the kirsch edge detector and color ratio gradients to detect the artifact blocks in the filled region after the first pass of filling the lacuna region when the result may not be satisfactory this can lead to resynthesizing the artifact blocks without user intervention and can be compliant to the unsuccessful results of other algorithms in the procedure of region filling color texture distribution analysis is used to choose whether the subpatch texture synthesis technique or the weighted interpolation method should be applied in the subpatch texture synthesis technique the actual pixel values of the lacuna region are synthesized by adaptively sampling from the source region the experimental results show that our proposed algorithm can achieve a better performance than previous methods particularly the regular computation of our proposed algorithm is more suitable for implementation of the hardware in a digital camera

on the brauer group complex for a multiquadratic field extension abstract let f be a field of characteristic not 2 a 1 a n f m f a 1 a n let further g be the subgroup of f f 2 generated by a 1 a n for any i 1 n put a i i i a i a 1 consider the complex i k i k i 2 g f f 2 br 2 f res br 2 m n m e f e m m e 2 br 2 e where k i f a i are all the quadratic extensions of f containing in m w i i a i n k i f w i a i z a i z the homology group of this complex at i 1 th term from the left is denoted by h i m f independently of char f we give examples of these complexes with nontrivial h 3 m f and prescribed n 3 and a 1 a n 1 also similar examples concerning the group h 1 m f are constructed

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

on the dec group of finite abelian galois extensions over global fields abstract if k f is a finite abelian galois extension of global fields whose galois group has exponent t we prove that there exists a short exact sequence 0 dec k f br t k f q p r q z z 0 where r q q and p is a finite set of primes of f that is empty if t is square free in particular we obtain that if t is square free then dec k f br t k f which we use to show that prime exponent division algebras over henselian valued fields with global residue fields are isomorphic to a tensor product of cyclic algebras finally we construct a counterexample to the result for higher exponent division algebras

witt rings and brauer groups under multiquadratic extensions ii let f be a field of characteristic not 2 and suppose m is a multiquadratic extension of f that is m f is a finite abelian extension of exponent 2 so that m f for some finite subgroup g e f f where f 0 in studying brauer groups and products of quaternion algebras the second author was led to consider the homology groups n m f of a certain complex gm f associated to the extension m f this complex appears in 11 3 1 301 and in 1 1 below the purpose of the present work is to investigate the first homology group n m f and to exhibit its close connections with quadratic form theory the higher homology groups are examined in 11 301 the field f is said to have property pi n if n m f 1 for every multiquadratic extension m f with m f q 2 properties p l and p 2 always hold but there are examples 29 of fields f for which p 3 fails these examples are generalized in section 5

detection and inpainting of facial wrinkles using texture orientation fields and markov random field modeling facial retouching is widely used in media and entertainment industry professional software usually require a minimum level of user expertise to achieve the desirable results in this paper we present an algorithm to detect facial wrinkles imperfection we believe that any such algorithm would be amenable to facial retouching applications the detection of wrinkles imperfections can allow these skin features to be processed differently than the surrounding skin without much user interaction for detection gabor filter responses along with texture orientation field are used as image features a bimodal gaussian mixture model gmm represents distributions of gabor features of normal skin versus skin imperfections then a markov random field model is used to incorporate the spatial relationships among neighboring pixels for their gmm distributions and texture orientations an expectation maximization algorithm then classifies skin versus skin wrinkles imperfections once detected automatically wrinkles imperfections are removed completely instead of being blended or blurred we propose an exemplar based constrained texture synthesis algorithm to inpaint irregularly shaped gaps left by the removal of detected wrinkles imperfections we present results conducted on images downloaded from the internet to show the efficacy of our algorithms

coupled variational image decomposition and restoration model for blurred cartoon plus texture images with missing pixels in this paper we develop a decomposition model to restore blurred images with missing pixels our assumption is that the underlying image is the superposition of cartoon and texture components we use the total variation norm and its dual norm to regularize the cartoon and texture respectively we recommend an efficient numerical algorithm based on the splitting versions of augmented lagrangian method to solve the problem theoretically the existence of a minimizer to the energy function and the convergence of the algorithm are guaranteed in contrast to recently developed methods for deblurring images the proposed algorithm not only gives the restored image but also gives a decomposition of cartoon and texture parts these two parts can be further used in segmentation and inpainting problems numerical comparisons between this algorithm and some state of the art methods are also reported

cartoon texture image decomposition using blockwise low rank texture characterization using a novel characterization of texture we propose an image decomposition technique that can effectively decomposes an image into its cartoon and texture components the characterization rests on our observation that the texture component enjoys a blockwise low rank nature with possible overlap and shear because texture in general is globally dissimilar but locally well patterned more specifically one can observe that any local block of the texture component consists of only a few individual patterns based on this premise we first introduce a new convex prior named the block nuclear norm bnn leading to a suitable characterization of the texture component we then formulate a cartoon texture decomposition model as a convex optimization problem where the simultaneous estimation of the cartoon and texture components from a given image or degraded observation is executed by minimizing the total variation and bnn in addition patterns of texture extending in different directions are extracted separately which is a special feature of the proposed model and of benefit to texture analysis and other applications furthermore the model can handle various types of degradation occurring in image processing including blur missing pixels with several types of noise by rewriting the problem via variable splitting the so called alternating direction method of multipliers becomes applicable resulting in an efficient algorithmic solution to the problem numerical examples illustrate that the proposed model is very selective to patterns of texture which makes it produce better results than state of the art decomposition models

image inpainting by patch propagation using patch sparsity this paper introduces a novel examplar based inpainting algorithm through investigating the sparsity of natural image patches two novel concepts of sparsity at the patch level are proposed for modeling the patch priority and patch representation which are two crucial steps for patch propagation in the examplar based inpainting approach first patch structure sparsity is designed to measure the confidence of a patch located at the image structure e g the edge or corner by the sparseness of its nonzero similarities to the neighboring patches the patch with larger structure sparsity will be assigned higher priority for further inpainting second it is assumed that the patch to be filled can be represented by the sparse linear combination of candidate patches under the local patch consistency constraint in a framework of sparse representation compared with the traditional examplar based inpainting approach structure sparsity enables better discrimination of structure and texture and the patch sparse representation forces the newly inpainted regions to be sharp and consistent with the surrounding textures experiments on synthetic and natural images show the advantages of the proposed approach

interpolation of missing data in image sequences this paper presents a number of model based interpolation schemes tailored to the problem of interpolating missing regions in image sequences these missing regions may be of arbitrary size and of random but known location this problem occurs regularly with archived film material the film is abraded or obscured in patches giving rise to bright and dark flashes known as dirt and sparkle in the motion picture industry both 3 d autoregressive models and 3 d markov random fields are considered in the formulation of the different reconstruction processes the models act along motion directions estimated using a multiresolution block matching scheme it is possible to address this sort of impulsive noise suppression problem with median filters and comparisons with earlier work using multilevel median filters are performed these comparisons demonstrate the higher reconstruction fidelity of the new interpolators

an adaptive high order discontinuous galerkin method with error control for the hamilton jacobi equations part i the one dimensional steady state case we propose and study an adaptive version of the discontinuous galerkin method for hamilton jacobi equations it works as follows given the tolerance and the degree of the polynomial of the approximate solution the adaptive algorithm finds a mesh on which the approximate solution has an l 1 distance to the viscosity solution no bigger than the prescribed tolerance the algorithm uses three main tools the first is an iterative solver combining the explicit runge kutta discontinuous galerkin method and the implicit newton s method that enables us to solve the hamilton jacobi equations efficiently the second is a new a posteriori error estimate based on the approximate resolution of an approximate problem for the actual error the third is a method that allows us to find a new mesh as a function of the old mesh and the ratio of the a posteriori error estimate to the tolerance we display extensive numerical evidence that indicates that for any given polynomial degree the method achieves its goal with optimal complexity independently of the tolerance this is done in the framework of one dimensional steady state model problems with periodic boundary conditions

on the structure of pythagorean fields abstract in this paper we study in detail the relationship between fans and valuations first uncovered by brocker see 2 our techniques are somewhat different as our valuations are constructed by brute force from the properties of the fields involved this approach has the advantage in that the valuation theory it yields can be directly related to the structure theory for spaces of orderings as developed by murray marshall see 11 14 we also discuss several applications which include results in k theory

exemplar based inpainting technical review and new heuristics for better geometric reconstructions this paper proposes a technical review of exemplar based inpainting approaches with a particular focus on greedy methods several comparative and illustrative experiments are provided to deeply explore and enlighten these methods and to have a better understanding on the state of the art improvements of these approaches from this analysis three improvements over criminisi et al algorithm are then presented and detailed 1 a tensor based data term for a better selection of pixel candidates to fill in 2 a fast patch lookup strategy to ensure a better global coherence of the reconstruction and 3 a novel fast anisotropic spatial blending algorithm that reduces typical block artifacts using tensor models relevant comparisons with the state of the art inpainting methods are provided that exhibit the effectiveness of our contributions

rigid elements valuations and realization of witt rings to the theory over the residue class field of the valuation this theorem generalizes to any 2 henselian valuation cf kl sect 12 21 let v be the valuation let a e k f o 1 be such that v a is not divisible by two the key idea behind the proof is that the quadratic form 1 a only represents elements in u a such an element a is called

group based image decomposition using 3 d cartoon and texture priors we propose a novel image decomposition method to decompose an image into its cartoon and texture components to exploit the nonlocal self similarity of cartoon plus texture images we construct groups by stacking together similar image patches into 3 d arrays and consider group as the basic unit of decomposition we decompose each group via a convex optimization model consisting of 3 d cartoon and texture priors these priors characterize the local properties of the cartoon and texture components and the nonlocal similarity within each component in a unified and natural manner we develop the alternating direction method of multipliers admm to efficiently solve the proposed model for further improvement we investigate an adaptive rule for the estimation of the regularization parameter the proposed method is also extended to tackle noisy images numerical experiments confirm that the performance of the proposed method is competitive with some of the state of the art schemes

nonexcellence of multiquadratic field extensions abstract let k0 be a field chark0 2 n 2 a b 1 b n k 0 such that the elements a b 1 b n k 0 k 0 2 are linearly independent we show that there exists a field extension f k0 and an anisotropic 4 dimensional form over f such that d a the form f b 1 b n is isotropic and the form f b 1 b n an is not defined over f

a patchy dynamic programming scheme for a class of hamilton jacobi bellman equations in this paper we present a new algorithm for the solution of hamilton jacobi bellman equations related to optimal control problems the key idea is to divide the domain of computation into subdomains which are shaped by the optimal dynamics of the underlying control problem this can result in a rather complex geometrical subdivision but it has the advantage that every subdomain is invariant with respect to the optimal dynamics and then the solution can be computed independently in each subdomain the features of this dynamics dependent domain decomposition can be exploited to speed up the computation and for an efficient parallelization since the classical transmission conditions at the boundaries of the subdomains can be avoided for their properties the subdomains are patches in the sense introduced by ancona and bressan esaim control optim calc var 4 1999 pp 445 471 several examples in two and three dimensions illustrate the properties of the new method

a global approach for solving evolutive heat transfer for image denoising and inpainting this paper proposes an alternative to partial differential equations pdes for solving problems in computer vision based on evolutive heat transfer traditionally the method for solving such physics based problems is to discretize and solve a pde by a purely mathematical process instead of using the pde we propose to use the global heat principle and to decompose it into basic laws we show that some of these laws admit an exact global version since they arise from conservative principles we also show that the assumptions made about the other basic laws can be made wisely taking into account knowledge about the problem and the domain the numerical scheme is derived in a straightforward way from the modeled problem thus providing a physical explanation for each step in the solution the advantage of such an approach is that it minimizes the approximations made during the whole process and it modularizes it allowing changing the application to a great number of problems we apply the scheme to two applications image denoising and inpainting which are modeled with heat transfer for denoising we propose a new approximation for the conductivity coefficient and we add thin lines to the features in order to block diffusion

on the equivalence between jensen shannon divergence and michelson contrast this paper focuses on the link between a visible linear and local distortion in a pictorial scene and its cost in terms of information theory quantities in particular a formal relation between the michelson visual contrast and the jensen shannon divergence jsd will be provided a universal just noticeable threshold is also derived by maximizing jsd constrained to the greatest michelson contrast of an invisible distortion such a threshold is independent of both distortion parameters and the probability density function of the degraded image it is then able to measure the bits budget to be spent for leaving the distortion invisible some tests on both synthetic and real distorted images validate the theoretical findings they confirm that the proposed universal threshold is really able to get the lower bound of human perception and then it may be useful for many applications such as bit allocation in coding procedures and automatic parameters setting in restoration algorithms

a posteriori error estimates for general numerical methods for hamilton jacobi equations part i the steady state case a new upper bound is provided for the l norm of the difference between the viscosity solution of a model steady state hamilton jacobi equation u and any given approximation v this upper bound is independent of the method used to compute the approximation v it depends solely on the values that the residual takes on a subset of the domain which can be easily computed in terms of v numerical experiments investigating the sharpness of the a posteriori error estimate are given

nonlinear approximation based image recovery using adaptive sparse reconstructions and iterated denoising part i theory we study the robust estimation of missing regions in images and video using adaptive sparse reconstructions our primary application is on missing regions of pixels containing textures edges and other image features that are not readily handled by prevalent estimation and recovery algorithms we assume that we are given a linear transform that is expected to provide sparse decompositions over missing regions such that a portion of the transform coefficients over missing regions are zero or close to zero we adaptively determine these small magnitude coefficients through thresholding establish sparsity constraints and estimate missing regions in images using information surrounding these regions unlike prevalent algorithms our approach does not necessitate any complex preconditioning segmentation or edge detection steps and it can be written as a sequence of denoising operations we show that the region types we can effectively estimate in a mean squared error sense are those for which the given transform provides a close approximation using sparse nonlinear approximants we show the nature of the constructed estimators and how these estimators relate to the utilized transform and its sparsity over regions of interest the developed estimation framework is general and can readily be applied to other nonstationary signals with a suitable choice of linear transforms part i discusses fundamental issues and part ii is devoted to adaptive algorithms with extensive simulation examples that demonstrate the power of the proposed techniques

powers of the fundamental ideal in the witt ring abstract let k be a field of characteristic different from 2 in the algebraic theory of quadratic forms one studies the witt ring w k of equivalence classes of non degenerate quadratic forms the witt ring has a filtration given by the powers in k of the fundamental ideal i k of even dimensional forms the ideal in k is generated by the set pn k of n fold pfister forms a1 an ni 1 1 ai where ai k k 0 many questions about this filtration and its quotients have arisen in the study of w k the spectacular work of voevodsky together with his collaborative work with orlov and vishik allows one to answer many old questions the purpose of this paper is to indicate some of these solutions

local a posteriori error estimates for time dependent hamilton jacobi equations university of minnesota ph d dissertation may 2010 major mathematics advisor prof bernardo cockburn 1 computer file pdf viii 67 pages ill some col

context aware patch based image inpainting using markov random field modeling in this paper we first introduce a general approach for context aware patch based image inpainting where textural descriptors are used to guide and accelerate the search for well matching candidate patches a novel top down splitting procedure divides the image into variable size blocks according to their context constraining thereby the search for candidate patches to nonlocal image regions with matching context this approach can be employed to improve the speed and performance of virtually any patch based inpainting method we apply this approach to the so called global image inpainting with the markov random field mrf prior where mrf encodes a priori knowledge about consistency of neighboring image patches we solve the resulting optimization problem with an efficient low complexity inference method experimental results demonstrate the potential of the proposed approach in inpainting applications like scratch text and object removal improvement and significant acceleration of a related global mrf based inpainting method is also evident

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

a discontinuous galerkin finite element method for directly solving the hamilton jacobi equations in this paper we propose a new discontinuous galerkin finite element method to solve the hamilton jacobi equations unlike the discontinuous galerkin method of c hu c w shu a discontinuous galerkin finite element method for hamilton jacobi equations siam journal on scientific computing 21 1999 666 690 which applies the discontinuous galerkin framework on the conservation law system satisfied by the derivatives of the solution the method in this paper applies directly to the solution of the hamilton jacobi equations for the linear case this method is equivalent to the traditional discontinuous galerkin method for conservation laws with source terms thus stability and error estimates are straightforward for the nonlinear convex hamiltonians numerical experiments demonstrate that the method is stable and provides the optimal k 1 th order of accuracy for smooth solutions when using piecewise kth degree polynomials singularities in derivatives can also be resolved sharply if the entropy condition is not violated special treatment is needed for the entropy violating cases both one and two dimensional numerical results are provided to demonstrate the good qualities of the scheme

the transfer ideal of quadratic forms and a hasse norm theorem mod squares any finite degree field extension k f determines an ideal jk f of the witt ring wf of f called the transfer ideal which is the image of any nonzero transfer map wk wf the ideal 59k f is computed for certain field extensions concentrating on the case where k has the form f va a ai e f when f and k are global fields we investigate whether there is a local global principle for membership in tkifthis is shown to be equivalent to the existence of a hasse norm theorem mod squares i e a local global principle for the image of the norm map nk f k k 2 f f 2 it is shown that such a hasse norm theorem holds whenever k f aj va although it does not always hold for more general extensions of global fields even some galois extensions with group z 2z x z 4z

differential forms and bilinear forms under field extensions abstract let f be a field of characteristic p 0 let n f be the f vector space of n differentials of f over f p let k f g be the function field of an irreducible polynomial g in m 1 variables over f we derive an explicit description of the kernel of the restriction map n f n k as an application in the case p 2 we determine the kernel of the restriction map when passing from the witt ring resp graded witt ring of symmetric bilinear forms over f to that over such a function field extension k

exemplar based image inpainting using multiscale graph cuts we present a novel formulation of exemplar based inpainting as a global energy optimization problem written in terms of the offset map the proposed energy function combines a data attachment term that ensures the continuity of reconstruction at the boundary of the inpainting domain with a smoothness term that ensures a visually coherent reconstruction inside the hole this formulation is adapted to obtain a global minimum using the graph cuts algorithm to reduce the computational complexity we propose an efficient multiscale graph cuts algorithm to compensate the loss of information at low resolution levels we use a feature representation computed at the original image resolution this permits alleviation of the ambiguity induced by comparing only color information when the image is represented at low resolution levels our experiments show how well the proposed algorithm performs compared with other recent algorithms

edge based image restoration in this paper we propose a new image inpainting algorithm that relies on explicit edge information the edge information is used both for the reconstruction of a skeleton image structure in the missing areas as well as for guiding the interpolation that follows the structure reconstruction part exploits different properties of the edges such as the colors of the objects they separate an estimate of how well one edge continues into another one and the spatial order of the edges with respect to each other in order to preserve both sharp and smooth edges the areas delimited by the recovered structure are interpolated independently and the process is guided by the direction of the nearby edges the novelty of our approach lies primarily in exploiting explicitly the constraint enforced by the numerical interpretation of the sequential order of edges as well as in the pixel filling method which takes into account the proximity and direction of edges extensive experiments are carried out in order to validate and compare the algorithm both quantitatively and qualitatively they show the advantages of our algorithm and its readily application to real world cases

dual diversified dynamical gaussian process latent variable model for video repairing in this paper we propose a dual diversified dynamical gaussian process latent variable model text d 3 gplvm to tackle the video repairing issue for preservation purposes videos have to be conserved on media however storing on media such as films and hard disks can suffer from unexpected data loss for instance physical damage so repairing of missing or damaged pixels is essential for better video maintenance most methods seek to fill in missing holes by synthesizing similar textures from local patches the neighboring pixels consecutive frames or the whole video however these can introduce incorrect contexts especially when the missing hole or number of damaged frames is large furthermore simple texture synthesis can introduce artifacts in undamaged and recovered areas to address aforementioned problems we introduce two diversity encouraging priors to both of inducing points and latent variables for considering the variety in existing videos in text d 3 gplvm the inducing points constitute a smaller subset of observed data while latent variables are a low dimensional representation of observed data since they have a strong correlation with the observed data it is essential that both of them can capture distinct aspects of and fully represent the observed data the dual diversity encouraging priors ensure that the trained inducing points and latent variables are more diverse and resistant for context aware and artifacts free based video repairing the defined objective function in our proposed model is initially not analytically tractable and must be solved by variational inference finally experimental testing results illustrate the robustness and effectiveness of our method for damaged video repairing

a comprehensive framework for image inpainting inpainting is the art of modifying an image in a form that is not detectable by an ordinary observer there are numerous and very different approaches to tackle the inpainting problem though as explained in this paper the most successful algorithms are based upon one or two of the following three basic techniques copy and paste texture synthesis geometric partial differential equations pdes and coherence among neighboring pixels we combine these three building blocks in a variational model and provide a working algorithm for image inpainting trying to approximate the minimum of the proposed energy functional our experiments show that the combination of all three terms of the proposed energy works better than taking each term separately and the results obtained are within the state of the art

rapid image completion system using multiresolution patch based directional and nondirectional approaches this study presents a rapid image completion system comprising a training or analysis process and an image completion or synthesis process the proposed system adopts a multiresolution approach which not only improves the convergence rate of the synthesis process but also provides the ability to deal with large replaced regions in the training process a down sampling approach is applied to create a patch based texture eigenspace based on multiresolution background region information in the image completion process an up sampling approach is applied to synthesize the replaced foreground regions to ensure the continuity of the geometric texture structure between the original background scene regions and the replaced foreground regions directional and nondirectional image completion approaches are developed to reconstruct the global geometric structure and to enhance the local detailed features of the replaced foreground regions in the lower and higher resolution level images respectively moreover the synthesis priority order of the individual patches and the appropriate choice of completion scheme i e directional or nondirectional are both determined in accordance with a hessian matrix decision value hmdv parameter finally a texture refinement process is performed to optimize the resolution of the synthesized result

decomposable and indecomposable algebras of degree 8 and exponent 2 we study the decomposition of central simple algebras of exponent 2 into tensor products of quaternion algebras we consider in particular decompositions in which one of the quaternion algebras contains a given quadratic extension let b be a biquaternion algebra over f a with trivial corestriction a degree 3 cohomological invariant is defined and we show that it determines whether b has a descent to f this invariant is used to give examples of indecomposable algebras of degree 8 and exponent 2 over a field of 2 cohomological dimension 3 and over a field m t where the u invariant of m is 8 and t is an indeterminate the construction of these indecomposable algebras uses chow group computations provided by merkurjev in appendix

hybrid patching for a sequence of differently exposed images with moving objects it is very challenging to synthesize a high dynamic range hdr image from multiple differently exposed low dynamic range images when there are moving objects in the images this is due to the fact that the moving objects will cause ghosting artifacts to appear in the synthesized hdr image to prevent such artifacts a patching algorithm is required to correct motion regions such that all the moving objects are synchronized in the differently exposed images in this paper a new optimization problem is formulated to correct the motion regions of the multiple differently exposed images by considering both spatial and temporal consistencies the resultant scheme is a hybrid patching scheme composed of a correction method which is an intensity mapping function at pixel level and a hole filling method that uses block level template matching the proposed patching scheme is not only robust to large intensity changes in these input images but also at regions that are over or under exposed experimental results show that the proposed method is able to prevent ghosting artifacts from appearing in the final synthesized hdr image

a multiscale image segmentation method this paper presents a novel image segmentation framework that combines image segmentation and feature extraction into a unified model the proposed model consists of two parts the segmentation part and the multiscale decomposition part in the model the segmentation part relies on the image intensities in the regions of interest while the multiscale decomposition part depends on the features in different scales the multiscale decomposition facilitates the process of segmentation since the region of interest can be easily detected from a proper scale the total variation projection regularization tvpr is used to preserve geometric shape of the segmented regions according to the geometric significance of tvpr parameters an adaptive tvpr parameters selection method is presented and edges of different region can be well preserved the proposed method is able to deal with intensity inhomogeneities and mixed noises often occurred in real world images which present challenges in image segmentation numerical examples on synthetic and real images are given to demonstrate the effectiveness of the proposed method this paper proposes a novel image segmentation framework a multiscale image segmentation method is presented within our framework total variation projection regularization tvpr is used to the proposed model we present an adaptive tvpr parameters selection method for image segmentation the experimental results show the effectiveness of the proposed method

some properties of viscosity solutions of hamilton jacobi equations abstract recently m g crandall and p l lions introduced the notion of viscosity solutions of scalar nonlinear first order partial differential equations viscosity solutions need not be differentiable anywhere and thus are not sensitive to the classical problem of the crossing of characteristics the value of this concept is established by the fact that very general existence uniqueness and continuous dependence results hold for viscosity solutions of many problems arising in fields of application the notion of a viscosity solution admits several equivalent formulations here we look more closely at two of these equivalent criteria and exhibit their virtues by both proving several new facts and reproving various known results in a simpler manner moreover by forsaking technical generality we hereby provide a more congenial introduction to this subject than the original paper author

an adaptive method with rigorous error control for the hamilton jacobi equations part ii the two dimensional steady state case in this paper we devise and study an adaptive method for finding approximations to the viscosity solution of hamilton jacobi equations the method which is an extension to two space dimensions of a similar method previously proposed for one space dimension is studied in the framework of steady state hamilton jacobi equations with periodic boundary conditions it seeks numerical approximations whose l distance to the viscosity solution is no bigger than a prescribed tolerance a thorough numerical study is carried out which shows that a strict error control is achieved and that the method exhibits an optimal computational complexity which does not depend on the value of the tolerance or on the type of hamiltonian

detection of missing data in image sequences bright and dark flashes are typical artifacts in degraded motion picture material the distortion is referred to as dirt and sparkle in the motion picture industry this is caused either by dirt becoming attached to the frames of the film or by the film material being abraded the visual result is random patches of the frames having grey level values totally unrelated to the initial information at those sites to restore the film without causing distortion to areas of the frames that are not affected the locations of the blotches must be identified heuristic and model based methods for the detection of these missing data regions are presented in this paper and their action on simulated and real sequences is compared

graph laplace for occluded face completion and recognition this paper proposes a spectral graph based algorithm for face image repairing which can improve the recognition performance on occluded faces the face completion algorithm proposed in this paper includes three main procedures 1 sparse representation for partially occluded face classification 2 image based data mining and 3 graph laplace gl for face image completion the novel part of the proposed framework is gl as named from graphical models and the laplace equation and can achieve a high quality repairing of damaged or occluded faces the relationship between the gl and the traditional poisson equation is proven we apply our face repairing algorithm to produce completed faces and use face recognition to evaluate the performance of the algorithm experimental results verify the effectiveness of the gl method for occluded face completion

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