a group based image inpainting using patch refinement in mrf framework this paper presents a markov random field mrf based image inpainting algorithm using patch selection from groups of similar patches and optimal patch assignment through joint patch refinement in patch selection a novel group formation strategy based on subspace clustering is introduced to search the candidate patches in relevant source region only this improves patch searching in terms of both quality and time we also propose an efficient patch refinement scheme using higher order singular value decomposition to capture underlying pattern among the candidate patches this eliminates random variation and unwanted artifacts as well finally a weight term is computed based on the refined patches and is incorporated in the objective function of the mrf model to improve the optimal patch assignment experimental results on a large number of natural images and comparison with well known existing methods demonstrate the efficacy and superiority of the proposed method

euler s elastica and curvature based inpainting image inpainting is a special image restoration problem for which image prior models play a crucial role euler s elastica was first introduced to computer vision by mumford algebraic geometry and its applications springer verlag new york 1994 pp 491 506 as a curve prior model by functionalizing the elastica energy masnou and morel proceedings of the 5th ieee international conference image processing 3 1998 pp 259 263 proposed an elastica based variational inpainting model the current paper is intended to contribute to the development of its mathematical foundation and the study of its properties and connections to the earlier works of bertalmio sapiro caselles and ballester siggraph 2000 acm press new york 2000 and chan and shen j visual comm image rep 12 2001 pp 436 449 a computational scheme based on numerical pdes is presented which allows the automatic handling of topologically complex inpainting domains

a differential quadrature procedure for three dimensional buckling analysis of rectangular plates abstract this paper presents an application of the differential quadrature dq method for three dimensional buckling analysis of rectangular plates the governing equations of the plate model are first presented in terms of displacement stress displacement relationship and boundary conditions with three dimensional flexibility these equations are then normalised and discretised using the dq procedure example problems pertaining to the buckling of rectangular plates with generic boundary conditions are selected to illustrate the efficiency and simplicity of implementing the dq procedure the convergence characteristics of the method are first conducted based on numerical studies the dq solutions are then compared where possible with exact or approximate solutions it is found that the differential quadrature method yields accurate results for the plate problems under the current investigation in addition to the above some parametric studies are carried out by varying the plates aspect ratio boundary conditions and thickness to width ratio under axial and biaxial loading

three dimensional free vibrations of thick skewed cantilevered plates abstract the natural frequencies of skewed cantilevered thick plates are determined by using the ritz method the present work is the first known three dimensional study of the problem assumed displacement functions are in the form of algebraic polynomials which satisfy the fixed face conditions exactly and which are mathematically complete accurate natural frequencies are calculated for skewed thick plates having arbitrary degrees of skewness detailed numerical studies reveal interesting trends concerning the variation of frequencies with increasing skew angle results obtained by using the present method are compared with those obtained by using three dimensional finite elements

review of options for structural design sensitivity analysis part 1 linear systems the paper reviews options for structural design sensitivity analysis including global finite differences continuum derivatives discrete derivatives and computational or automated differentiation the objective is to put these different approaches to design sensitivity analysis in the context of accuracy and consistency computational cost and implementation options and effort linear static analysis and transient dynamic analysis are reviewed in a separate appendix special attention is paid to the semi analytical method a future paper will address design sensitivity analysis in nonlinear structural problems

design sensitivity analysis of coupled thermoviscoelastic systems abstract both the direct differentiation and adjoint variable methods for design sensitivity analysis of transient dynamic arbitrarily nonlinear thermoviscoelastic coupled systems are presented in this paper the approach is based on the thermodynamic description of simple materials due to coleman large strains as well as arbitrary material nonlinearities are accounted for in the derivations the domain parametrization or reference volume concept is used allowing a uniform treatment of both the shape and sizing design sensitivity analysis analytical examples demonstrating the use of the derived equations are given this approach provides a solid basis for discretization of the developed equations for subsequent use in numerical computations

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

vibration analysis of linear coupled thermoviscoelastic thin plates by a variational approach abstract according to the integral type constitutive relation of linear coupled thermoviscoelasticity a mathematical model of thin plates is set up by the introduction of structural functions and thermal functions in the sense of the kirchhoff s hypothesis the corresponding integral type variational formulations are presented by means of modern convolution bilinear forms as well as classical cartesian bilinear forms the ritz method in the spatial domain and the differentiating method in the temporal domain are used to approximate the mathematical model in a system of rectangular cartesian coordinates by properties of inequality and parabola the structure of dynamic solution to vibration of a thermoviscoelastic thin plate under a harmonic thermal load is studied in the space splayed by material parameter and loading parameter the influences of thermal excitation frequency mechanical relaxation time and thermal relaxation time on amplitude and phase difference of steady state vibration of a square plate are investigated by amplitude frequency analysis and phase frequency analysis double peak resonance vibration of thermoviscoelastic plates exists for given parameters

three dimensional elasticity solutions to some orthotropic plate problems abstract this paper presents a three dimensional analysis of rectangular orthotropic plates by employing the differential quadrature dq method the derivation of the governing equations from the governing equations and the stress strain relationship of the three dimensional elasticity model is detailed the constrained conditions of the orthotropic plate edges are given the governing equations and boundary conditions are first normalized and discretized according to the dq procedure example problems pertaining to the bending buckling and free vibration of orthotropic plates with generic boundary conditions are selected to illustrate the simplicity and applicability of the dq method the convergence characteristics of the dq method are first obtained based on numerical studies after which the dq solutions are compared where possible with exact solutions it is found that the dq method yields accurate results for the plate problems under investigation

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

hierarchical super resolution based inpainting this paper introduces a novel framework for examplar based inpainting it consists in performing first the inpainting on a coarse version of the input image a hierarchical super resolution algorithm is then used to recover details on the missing areas the advantage of this approach is that it is easier to inpaint low resolution pictures than high resolution ones the gain is both in terms of computational complexity and visual quality however to be less sensitive to the parameter setting of the inpainting method the low resolution input picture is inpainted several times with different configurations results are efficiently combined with a loopy belief propagation and details are recovered by a single image super resolution algorithm experimental results in a context of image editing and texture synthesis demonstrate the effectiveness of the proposed method results are compared to five state of the art inpainting methods

stochastic relaxation gibbs distributions and the bayesian restoration of images we make an analogy between images and statistical mechanics systems pixel gray levels and the presence and orientation of edges are viewed as states of atoms or molecules in a lattice like physical system the assignment of an energy function in the physical system determines its gibbs distribution because of the gibbs distribution markov random field mrf equivalence this assignment also determines an mrf image model the energy function is a more convenient and natural mechanism for embodying picture attributes than are the local characteristics of the mrf for a range of degradation mechanisms including blurring nonlinear deformations and multiplicative or additive noise the posterior distribution is an mrf with a structure akin to the image model by the analogy the posterior distribution defines another imaginary physical system gradual temperature reduction in the physical system isolates low energy states annealing or what is the same thing the most probable states under the gibbs distribution the analogous operation under the posterior distribution yields the maximum a posteriori map estimate of the image given the degraded observations the result is a highly parallel relaxation algorithm for map estimation we establish convergence properties of the algorithm and we experiment with some simple pictures for which good restorations are obtained at low signal to noise ratios

image inpainting through metric labeling via guided patch mixing in this paper we present a novel formulation of exemplar based image inpainting as a metric labeling problem and solve it through the simulated annealing algorithm due to their greedy nature exemplar based methods sometimes produce inpainted images which are visually inconsistent these methods are highly dependent upon the initialization to solve these problems we generate five images with a different initialization a suitable mixture of these five images produces a good inpainted image the cost function of the proposed metric labeling problem consists of three components namely neighbor cost total variation cost and structure cost a linear combination among these components is used to maintain better visual consistency in the inpainted region having smooth transition from the bordering regions of the source image we use a quality measure to this end our experiments on a wide variety of images demonstrate that the proposed technique produces better inpainting images as compared with some other state of the art techniques

simultaneous material load shape variations of thermoelastic structures a continuous approach is adopted in order to find the total variation of a general performance criterion the present analysis may find important physical applications in the simultaneous shape optimization and control of large space structures in time by applied thermal and or mechanical loads the adjoint variable method and the material derivative concept are used to find the sensitivity expressions

no reference image quality assessment in the spatial domain we propose a natural scene statistic based distortion generic blind no reference nr image quality assessment iqa model that operates in the spatial domain the new model dubbed blind referenceless image spatial quality evaluator brisque does not compute distortion specific features such as ringing blur or blocking but instead uses scene statistics of locally normalized luminance coefficients to quantify possible losses of naturalness in the image due to the presence of distortions thereby leading to a holistic measure of quality the underlying features used derive from the empirical distribution of locally normalized luminances and products of locally normalized luminances under a spatial natural scene statistic model no transformation to another coordinate frame dct wavelet etc is required distinguishing it from prior nr iqa approaches despite its simplicity we are able to show that brisque is statistically better than the full reference peak signal to noise ratio and the structural similarity index and is highly competitive with respect to all present day distortion generic nr iqa algorithms brisque has very low computational complexity making it well suited for real time applications brisque features may be used for distortion identification as well to illustrate a new practical application of brisque we describe how a nonblind image denoising algorithm can be augmented with brisque in order to perform blind image denoising results show that brisque augmentation leads to performance improvements over state of the art methods a software release of brisque is available online http live ece utexas edu research quality brisque release zip for public use and evaluation

on the three dimensional vibrations of the cantilevered rectangular parallelepiped a solution is presented for the three dimensional problem of determining the free vibration frequencies and mode shapes for a rectangular parallelepiped which is completely fixed on one face and free on the other five faces this problem apparently is previously unsolved in the published literature the ritz method is used with displacements assumed in the form of algebraic polynomials convergence is studied numerical results are given for the first five frequencies of each of the four symmetry classes of vibration for five thick parallelepiped configurations including the cube contour plots are exhibited for the modal displacements of the cube the effects of varying poisson s ratio are also observed

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

disocclusion a variational approach using level lines object recognition robot vision image and film restoration may require the ability to perform disocclusion we call disocclusion the recovery of occluded areas in a digital image by interpolation from their vicinity it is shown in this paper how disocclusion can be performed by means of the level lines structure which offers a reliable complete and contrast invariant representation of images level lines based disocclusion yields a solution that may have strong discontinuities the proposed method is compatible with kanizsa s 1979 amodal completion theory

sensitivity analysis for coupled thermoelastic systems abstract this paper presents an adjoint approach derived from the reciprocal theorem for the sensitivity analysis of linear dynamic thermoelastic systems the variation of a general response functional is expressed in explicit form with respect to variations of the design fields which consist of the material properties applied loads prescribed boundary initial conditions and the structural shape the functional is dependent on these design quantities as well as the following implicity defined response fields displacement temperature stress strain heat flux temperature gradient reaction forces and reaction surface flux the formulation incorporates the reciprocal relation between variations of the real system design and response fields and an adjoint state here convolution is employed in lieu of time mappings used in other transient adjoint sensitivity derivations specializations of the formulation to uncoupled combined quasi static uncoupled and steady state thermoelasticity are also presented the finite element method is used to demonstrate the application of the formulation to a problem in automobile engine design

convergence of an annealing algorithm the annealing algorithm is a stochastic optimization method which has attracted attention because of its success with certain difficult problems including np hard combinatorial problems such as the travelling salesman steiner trees and others there is an appealing physical analogy for its operation but a more formal model seems desirable in this paper we present such a model and prove that the algorithm converges with probability arbitrarily close to 1 we also show that there are cases where convergence takes exponentially long that is it is no better than a deterministic method we study how the convergence rate is affected by the form of the problem finally we describe a version of the algorithm that terminates in polynomial time and allows a good deal of practical confidence in the solution

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

three dimensional free vibration analysis of isotropic rectangular plates using the b spline ritz method abstract this paper presents three dimensional free vibration analysis of isotropic rectangular plates with any thicknesses and arbitrary boundary conditions using the b spline ritz method based on the theory of elasticity the proposed method is formulated by the ritz procedure with a triplicate series of b spline functions as amplitude displacement components the geometric boundary conditions are numerically satisfied by the method of artificial spring to demonstrate the convergence and accuracy of the present method several examples with various boundary conditions are solved and the results are compared with other published solutions by exact and other numerical methods based on the theory of elasticity and various plate theories rapid stable convergences as well as high accuracy are obtained by the present method the effects of geometric parameters on the vibrational behavior of cantilevered rectangular plates are also investigated the results reported here may serve as benchmark data for finite element solutions and future developments in numerical methods

free vibrations of a simply supported rectangular plate an exact elasticity solution abstract an exact three dimensional solution for the free vibrations of simply supported rectangular plates of arbitrary thickness within the linear theory of elastodynamics is given in this paper the solution obtained in a semi inverse fashion as was the solution of the elastostatic problem for such plates satisfies all of the boundary conditions of the problem in a pointwise manner it is found that there are two types of modes of oscillation possible which are consistent with the kinematic assumptions made to find the semi inverse solution other modes of oscillation may exist in the three dimensional theory of elastodynamics for such plates but our kinematic assumptions would not be consistent with such modes the two types of modes found are analogous to the flexural modes of classical plate theory and the thickness twist modes here called breathing modes of mindlin plate theory some numerical results are given which indicate that the predictions of mindlin plates are uncannily good approximations to the flexural frequencies given by the present three dimensional analysis even for very thick plates however the predictions of mindlin plate theory for the thickness twist or breathing frequencies are not nearly so good these discrepancies are discussed briefly in an appendix

approximation algorithms for classification problems with pairwise relationships metric labeling and markov random fields in a traditional classification problem we wish to assign one of k labels or classes to each of n objects in a way that is consistent with some observed data that we have about the problem an active line of research in this area is concerned with classification when one has information about pairwise relationships among the objects to be classified this issue is one of the principal motivations for the framework of markov random fields and it arises in areas such as image processing biometry and document analysis in its most basic form this style of analysis seeks to find a classification that optimizes a combinatorial function consisting of assignment costs based on the individual choice of label we make for each object and separation costs based on the pair of choices we make for two related objects we formulate a general classification problem of this type the metric labeling problem we show that it contains as special cases a number of standard classification frameworks including several arising from the theory of markov random fields from the perspective of combinatorial optimization our problem can be viewed as a substantial generalization of the multiway cut problem and equivalent to a type of uncapacitated quadratic assignment problem we provide the first nontrivial polynomial time approximation algorithms for a general family of classification problems of this type our main result is an o log k log log k approximation algorithm for the metric labeling problem with respect to an arbitrary metric on a set of k labels and an arbitrary weighted graph of relationships on a set of objects for the special case in which the labels are endowed with the uniform metric all distances are the same our methods provide a 2 approximation algorithm

on the three dimensional vibration analysis of simultaneously skewed and twisted cantilevered parallelepipeds the natural frequencies of simultaneously skewed and twisted cantilevered parallelepipeds are determined using the ritz method the present work is the first known three dimensional study of the problem assumed displacement functions are in the form of algebraic polynomials which satisfy the fixed face conditions exactly and which are mathematically complete reasonably accurate natural frequencies are calculated for low aspect ratio thick parallelepipeds having arbitrary degrees of twist and skewness detailed numerical studies show that a three dimensional analysis is essential in monitoring complicated coupled mode sensitivities in the variation of non dimensional natural frequencies with increasing skew and twist angles and thickness ratio results obtained using the present method are compared with those obtained in a detailed three dimensional finite element analysis where the suitability and limitations of s version solid element discretizations are clearly brought out

shape design sensitivity analysis of viscoplastic structures abstract design sensitivity analysis of nonlinear viscoplastic structures is developed in the continuum form starting from hamilton s principle constitutive models based on internal variable theory are incorporated in response analysis such models are described by a set of first order nonlinear differential equations with respect to time and some of them allow development of the yield surface the direct variation method is employed to obtain the sensitivity of the response discretization of the analysis and sensitivity equations and computer implementation aspects are discussed the discretized equations are implemented into a computer program and two numerical examples are solved to demonstrate the theory in the numerical examples only material nonlinearity under quasi static loading history is considered and the explicit integration method is employed to integrate the constitutive equations and their design variations the accuracy and efficiency of the developed sensitivity analysis are compared with the central finite difference method cyclic loading and loading rate effects are studied and discussed to show the general applicability of the developed sensitivity formulation

design sensitivity analysis in dynamic thermoviscoelasticity with implicit integration design sensitivity equations for coupled thermoviscoelastic systems are discretized via the finite element method the approach is developed for structural systems by using the total lagrangian approach and the reference domain concept the discretization is based on implicit integration schemes the implementation of finite element and design sensitivity analysis utilizes the christensen naghdi free energy function and the direct differentiation approach which is most suitable for the systems under consideration a relationship between the discretized sensitivity equations and the equations for the original analysis is shown use of the same discretization for analysis and sensitivity analysis is emphasized partial derivatives of the right hand side required for sensitivity calculations are implemented via the central difference method which provides greater flexibility without sacrificing accuracy examples of analysis and design sensitivity analysis for a thermoviscoelastic non linear truss and a plate with a hole are given the calculated sensitivity results are verified by comparison with overall finite difference calculations