a green s function approach to shape from shading we present a new algorithm for shape from shading inspired on the recently introduced disparity based approach to photometric stereo dbps assuming that the single input image will be matched to a second image through a uniform disparity field we construct an irradiance conservation equation and solve it for the matching image via green s function when a linear expansion of the reflectance map is considered this leads to a closed form approximate expression for the surface function whose parameters can be estimated via a structure from motion approach already used for dbps

three dimensional face shape by local fitting to a single reference model the authors present a simple method to estimate the three dimensional shape of a face from an input image using a single reference model based on least squares between the output of the linear nonlinear ln neuronal model applied to blocks from an intensity image and blocks from a depth reference model the authors present the results obtained by varying the ln model parameters and estimate their best values which provide an acceptable reconstruction of each subject s depth the authors show that increasing the light source angle over the horizontal plane in the input image produces slight increases in reconstruction error but increasing the ambient light proportion produces greater increases in reconstruction error the authors applied the method to predict each subject s unknown depth using different individual reference models and an average reference model which provides the best results as a noise reduction technique the authors perform a point by point weighted averaging with the average reference model with weights equal to the fractions of the squares of the laplacian of a gaussian applied to the prediction and to the reference depth over the sum of both finally the authors present acceptable visual results obtained from external images of faces under arbitrary illumination having performed an illumination estimation previously

evaluating kube and pentland s fractal imaging model the paper assesses the validity of a model proposed by kube and pentland 1988 that relates a rough surface to its image texture simulation was used to assess whether a linear approximation is appropriate and whether the optimal linear filter agrees with the predictions of kube and pentland s model the predictions of the model about the image directionality were also assessed on real images it was found that a linear model is capable of modeling the imaging process for surfaces of moderate roughness and lambertian reflectance and that subject to a small modification kube and pentland s model accurately predicts the relationship between surface and image spectra

the timoshenko system with history and cattaneo law in this paper we study a fully hyperbolic thermoelastic timoshenko system with past history where the thermal effects are given by cattaneo s law we obtain exponential stability of solutions if and only if a new condition on the wave speed of propagation is verified otherwise when that condition fails we obtain polynomial stability of solutions in this case optimal rates of decay are established

unsupervised variational image segmentation classification using a weibull observation model studies have shown that the weibull distribution can model accurately a wide variety of images its parameters index a family of distributions which includes the exponential and approximations of the gaussian and the raleigh models widely used in image segmentation this study investigates the weibull distribution in unsupervised image segmentation and classification by a variational method the data term of the segmentation functional measures the conformity of the image intensity in each region to a weibull distribution whose parameters are determined jointly with the segmentation minimization of the functional is implemented by active curves via level sets and consists of iterations of two consecutive steps curve evolution via euler lagrange descent equations and evaluation of the weibull distribution parameters experiments with synthetic and real images are described which verify the validity of method and its implementation

energy decay for timoshenko systems of memory type abstract linear systems of timoshenko type equations for beams including a memory term are studied the exponential decay is proved for exponential kernels while polynomial kernels are shown to lead to a polynomial decay the optimality of the results is also investigated

rates of decay to non homogeneous timoshenko model with tip body abstract we consider the uniform stabilization of a hybrid elastic model consisting of a timoshenko beam and a tip load at the free end of the beam our main result proves that the semigroup e a t associated to this model is not exponentially stable moreover we prove that the semigroup decays polynomially to zero as t 1 2 when the damping mechanism is effective only on the boundary of the rotational angle the solution also decays polynomially as t 1 2 provided the wave speeds are equal otherwise it decays as t 1 4 for any initial data taken in d a

the eikonal equation some results applicable to computer vision in this paper we investigate certain first order partial differential equations which formulate the relationship between the light reflected from a surface and its shape particular emphasis is given to eikonal equations two results are presented first we prove that a special type of eikonal equation has only one convex and positive c2 solution in some neighborhood of a singular point using this result we show that a restricted form of this equation has exactly two solutions these results have application in scanning electron microscopy

asymptotic stability of abstract dissipative systems with infinite memory we consider in this paper the problem of asymptotic behavior of solutions to an abstract linear dissipative integrodifferential equation with infinite memory past history modeling linear viscoelasticity we show that the stability of the system holds for a much larger class of the convolution kernels than the one considered in the literature and we provide a relation between the decay rate of the solutions and the growth of the kernel at infinity some applications are also given

boundary control of the timoshenko beam it is shown that the timoshenko beam can be uniformly stabilized by means of a boundary control a numerical study on the spectrum is also presented

direct shape from shading with improved rate of convergence in this paper new direct shape from shading algorithms with improved rate of convergence for inclined and perpendicular light source are presented the algorithms are mainly based on optimal dynamic system control with dynamic programming unlike the previous shading algorithms which first estimate the gradient of surface instead of depth using variational approaches our algorithms provide a direct relative depth perception here the maximum uphill principle for inclined and perpendicular light source is derived instead of using the existing minimum downhill criteria in order to perceive the normal shape of the object also the convergence conditions for the algorithms are derived and proven under zero initial condition we show that the learning rate is linearly proportional to the minimum value of the input image in the discrete case furthermore in order to increase the rate of convergence the momentum factor is introduced

a general decay result for a memory type timoshenko thermoelasticity system with second sound abstract in this paper we consider a system of timoshenko thermoelasticity with second sound in the presence of an infinite history term we prove under suitable conditions on the coefficients and the relaxation function a general decay result from which the exponential and polynomial decay estimates are only special cases we also establish a lack of exponential decay result and discuss the optimality for some situation

recovering intrinsic images from a single image interpreting real world images requires the ability distinguish the different characteristics of the scene that lead to its final appearance two of the most important of these characteristics are the shading and reflectance of each point in the scene we present an algorithm that uses multiple cues to recover shading and reflectance intrinsic images from a single image using both color information and a classifier trained to recognize gray scale patterns given the lighting direction each image derivative is classified as being caused by shading or a change in the surface s reflectance the classifiers gather local evidence about the surface s form and color which is then propagated using the generalized belief propagation algorithm the propagation step disambiguates areas of the image where the correct classification is not clear from local evidence we use real world images to demonstrate results and show how each component of the system affects the results

on timoshenko type systems with type iii thermoelasticity asymptotic behavior abstract in this study we consider a thermoelastic beam system where the oscillations are defined by the timoshenko model and heat conduction is given by the green and naghdi theories we provide an explicit characterization of the decay rate which can be exponential or polynomial depending on the relationship between the coefficients of the wave propagation speed

point light source estimation from two images and its limits in this paper the performance of parameter estimation of a single static distant point light source from two video images is analyzed in terms of estimation theory the illumination parameters are the intensity and direction of the light source in the first part of this paper estimators from the literature are reviewed most recent estimators evaluate as input data two video images as well as the 3d shape and the 3d motion of the visible moving objects in the second part of the paper the performance of these recent methods is analyzed the input data to estimation as well as the inherent input data errors are described by a stochastic observation model based on this model the performance is analyzed regarding the cramer rao theoretical lower bound of estimation error variances the bound is derived for a variety of cases of scene illumination object motion and errors in input data for simplification purpose the bound is valid only for object motions with the rotation axis lying in the image plane the analysis shows in which cases which estimation accuracy can be expected with current methods finally a comparison of the bound with one of the recent estimators shows that recent estimators are suboptimal in case of errors in the 3d shape of the objects in future work the stochastic observation model presented in this paper can be used to improve illumination estimation

statistical approach to shape from shading reconstruction of three dimensional face surfaces from single two dimensional images the human visual system is proficient in perceiving three dimensional shape from the shading patterns in a two dimensional image how it does this is not well understood and continues to be a question of fundamental and practical interest in this paper we present a new quantitative approach to shape from shading that may provide some answers we suggest that the brain through evolution or prior experience has discovered that objects can be classified into lower dimensional object classes as to their shape extraction of shape from shading is then equivalent to the much simpler problem of parameter estimation in a low dimensional space we carry out this proposal for an important class of three dimensional 3d objects human heads from an ensemble of several hundred laser scanned 3d heads we use principal component analysis to derive a low dimensional parameterization of head shape space an algorithm for solving shape from shading using this representation is presented it works well even on real images where it is able to recover the 3d surface for a given person maintaining facial detail and identity from a single 2d image of his face this algorithm has applications in face recognition and animation

free vibration analysis of orthotropic elliptical plates resting on arbitrarily distributed point supports the free vibration of point supported elliptical plates is studied analytically with consideration of rectangular orthotropy apparently this problem has been previously unsolved in the literature an analytical method used is an accurate variational approach the ritz lagrange multiplier method which constitutes an extension of the classical ritz method in numerical examples elliptical plates on some symmetric point supports are considered and it is shown that the method is straightforwardly applicable to determination of frequencies for elliptical plates resting on various support configurations

transverse vibrations of circular plates and membranes with intermediate supports the present paper deals with an approximate solution of the title problem in the case of a a concentric circular support and b a secant support fundamental frequency coefficients are determined by means of the rayleigh minimization procedure the modal shapes been approximated by simple polynomial co ordinate functions in the case of a circular plate with a secant support an independent solution is obtained by means of a finite element code and very good agreement is shown to exist

where and why local shading analysis works an apparent contradiction in the shape from shading literature is examined although practical experience suggests that shape can be inferred from the local analysis of shading mathematical analyses support the opposite a criterion for exact surface recovery is derived and it is shown that as a result of surface geometry elliptic hyperbolic and doubly curved surfaces could be recovered to reasonable accuracy provided that surface curvature and or foreshortening were limited in other words by relaxing the requirement that surfaces be recovered exactly it is found that local analysis of shading can provide useful descriptions of shape as evidenced by the results presented

a comparison theorem for a piecewise lipschitz continuous hamiltonian and application to shape from shading problems the reconstruction from a shaded image of a lambertian and not self shadowing surface illuminated by a single distant pointwise light source may be written as a first order hamilton jacobi equation in this paper we continue the investigation begun in e rouy and a tourin into the uniqueness of the solution of this equation the approach is based on the viscosity solutions theory and the dynamic programming principle more precisely we concentrate here on the uniqueness of the viscosity solution of this equation in case the measured luminous intensity reflected by the surface is discontinuous along a smooth curve we prove a general comparison result for a piecewise lipschitz continuous hamiltonian and illustrate it by numerical experiments

exponential stability for a timoshenko type system with history in this paper we consider hyperbolic timoshenko type vibrating systems that are coupled to a heat equation modeling an expectedly dissipative effect through heat conduction we use the semigroup method to prove the exponential stability result with assumptions on past history relaxation function g exponentially decaying for the equal wave speed case

the lack of exponential stability of the hybrid bresse system abstract in this paper we consider the dissipative bresse system with an attached hollow tip body that contains granular material the resulting model being called hybrid system our main result is to show that the corresponding model is not exponentially stable moreover we show that the solution decays polynomially to zero as 1 t 1 2 when t

the design and use of steerable filters the authors present an efficient architecture to synthesize filters of arbitrary orientations from linear combinations of basis filters allowing one to adaptively steer a filter to any orientation and to determine analytically the filter output as a function of orientation steerable filters may be designed in quadrature pairs to allow adaptive control over phase as well as orientation the authors show how to design and steer the filters and present examples of their use in the analysis of orientation and phase angularly adaptive filtering edge detection and shape from shading one can also build a self similar steerable pyramid representation the same concepts can be generalized to the design of 3 d steerable filters

mildly dissipative nonlinear timoshenko systems global existence and exponential stability we consider nonlinear systems of timoshenko type in a one dimensional bounded domain the system has a dissipative mechanism being present only in the equation for the rotation angle it is a damping effect through heat conduction the global existence of small smooth solutions as well as the exponential stability are investigated

direct analytical methods for solving poisson equations in computer vision problems direct analytical methods are discussed for solving poisson equations of the general form delta u f on a rectangular domain some embedding techniques that may be useful when boundary conditions obtained from stereo and occluding boundary are defined on arbitrary contours are described the suggested algorithms are computationally efficient owing to the use of fast orthogonal transforms applications to shape from shading lightness and optical flow problems are also discussed a proof for the existence and convergence of the flow estimates is given experiments using synthetic images indicate that results comparable to those using multigrid can be obtained in a very small number of iterations

geotensity combining motion and lighting for 3d surface reconstruction this paper is about automatically reconstructing the full 3d surface of an object observed in motion by a single static camera based on the two paradigms structure from motion and linear intensity subspaces we introduce the geotensity constraint that governs the relationship between four or more images of a moving object we show that it is possible in theory to solve for 3d lambertian surface structure for the case of a single point light source and propose that a solution exists for an arbitrary number point light sources the surface may or may not be textured we then give an example of automatic surface reconstruction of a face under a point light source using arbitrary unknown object motion and a single fixed camera

some remarks on the shape from shading problem in computer vision the shape from shading problem in computer vision see horn 11 deals with the reconstruction of the shape of an object from a two dimensional image we consider an object illuminated by a point source the reflected light being recorded on a photographic plate at a fixed position the intensity of the reflected light is a function of the position of the source the position of the plate and the normal to the surface of the object if the surface is given as u u x jj this leads see horn i to a first order partial differential equation of the form

shape from shading level set propagation and viscosity solutions we present a new implementation of an algorithm aimed at recovering a 3d shape from its 2d gray level picture in order to reconstruct the shape of the object an almost arbitrarily initialized 3d function is propagated on a rectangular grid so that a level set of this function tracks the height contours of the shape the method imports techniques from differential geometry fluid dynamics and numerical analysis and provides an accurate shape from shading algorithm the method solves some topological problems and gracefully handles cases of non smooth surfaces that give rise to shocks in the propagating contours real and synthetic images of 3d profiles were submitted to the algorithm and the reconstructed surfaces are presented demonstrating the effectiveness of the proposed method

uniform decay in a timoshenko type system with past history abstract fernandez sare and rivera h d fernandez sare j e munoz rivera stability of timoshenko systems with past history j math anal appl 339 1 2008 482 502 considered the following timoshenko type system 1 t t k x x 0 2 t t b x x 0 g t x x t s d s k x 0 where g is a positive differentiable exponentially decaying function they established an exponential decay result in the case of equal wave speed propagation and a polynomial decay result in the case of nonequal wave speed propagation in this paper we study the same system for g decaying polynomially and prove polynomial stability results for the equal and nonequal wave speed propagation our results are established under conditions on the relaxation function weaker than those in h d fernandez sare j e munoz rivera stability of timoshenko systems with past history j math anal appl 339 1 2008 482 502

maximum likelihood estimation of depth maps using photometric stereo photometric stereo and depth map estimation provide a way to construct a depth map from images of an object under one viewpoint but with varying illumination directions while estimating surface normals using the lambertian model of reflectance is well established depth map estimation is an ongoing field of research and dealing with image noise is an active topic using the zero mean gaussian model of image noise this paper introduces a method for maximum likelihood depth map estimation that accounts for the propagation of noise through all steps of the estimation process solving for maximum likelihood depth map estimates involves an independent sequence of nonlinear regression estimates one for each pixel followed by a single large and sparse linear regression estimate the linear system employs anisotropic weights which arise naturally and differ in value to related work the new depth map estimation method remains efficient and fast making it practical for realistic image sizes experiments using synthetic images demonstrate the method s ability to robustly estimate depth maps under the noise model practical benefits of the method on challenging imaging scenarios are illustrated by experiments using the extended yale face database b and an extensive data set of 500 reflected light microscopy image sequences

a method for enforcing integrability in shape from shading algorithms an approach for enforcing integrability a particular implementation of the approach an example of its application to extending an existing shape from shading algorithm and experimental results showing the improvement that results from enforcing integrability are presented a possibly nonintegrable estimate of surface slopes is represented by a finite set of basis functions and integrability is enforced by calculating the orthogonal projection onto a vector subspace spanning the set of integrable slopes the integrability projection constraint was applied to extending an iterative shape from shading algorithm of m j brooks and b k p horn 1985 experimental results show that the extended algorithm converges faster and with less error than the original version good surface reconstructions were obtained with and without known boundary conditions and for fairly complicated surfaces

a theory of photometric stereo for a class of diffuse non lambertian surfaces a theory of photometric stereo is proposed for a large class of non lambertian reflectance maps the authors review the different reflectance maps proposed in the literature for modeling reflection from real world surfaces from this they obtain a mathematical class of reflectance maps to which the maps belong they show that three lights can be sufficient for a unique inversion of the photometric stereo equation for the entire class of reflectance maps they also obtain a constraint on the positions of light sources for obtaining this solution they investigate the sufficiency of three light sources to estimate the surface normal and the illuminant strength the issue of completeness of reconstruction is addressed they show that if k lights are sufficient for a unique inversion 2k lights are necessary for a complete inversion

on the stability of damped timoshenko systems cattaneo versus fourier law we consider hyperbolic timoshenko type vibrating systems that are coupled to a heat equation modeling an expectedly dissipative effect through heat conduction while exponential stability under the fourier law of heat conduction holds it turns out that the coupling via the cattaneo law does not yield an exponentially stable system this seems to be the first example that a removal of the paradox of infinite propagation speed inherent in fourier s law by changing to the cattaneo law causes a loss of the exponential stability property actually for systems with history the fourier law keeps the exponential stability known for the pure timoshenko system without heat conduction but introducing the cattaneo coupling even destroys this property

direct methods for recovering motion we have developed direct methods for recovering the motion of an observer in a static environment in the case of pure rotation pure translation and arbitrary motion when the rotation is known some of these methods are based on the minimization of the difference between the observed time derivative of brightness and that predicted from the spatial brightness gradient given the estimated motion we minimize the square of the integral of this difference taken over the image region of interest other methods presented here exploit the fact that surfaces have to be in front of the observer in order to be seen

height and gradient from shading the method described here for recovering the shape of a surface from a shaded image can deal with complex wrinkled surfaces integrability can be enforced easily because both surface height and gradient are represented the robustness of the method stems in part from linearization of the reflectance map about the current estimate of the surface orientation at each picture cell the new scheme can find an exact solution of a given shape from shading problem even though a regularizing term is included this is a reflection of the fact that shape from shading problems are it not ill posed when boundary conditions are available or when the image contains singular points

a graph spectral approach to shape from shading in this paper we explore how graph spectral methods can be used to develop a new shape from shading algorithm we characterize the field of surface normals using a weight matrix whose elements are computed from the sectional curvature between different image locations and penalize large changes in surface normal direction modeling the blocks of the weight matrix as distinct surface patches we use a graph seriation method to find a surface integration path that maximizes the sum of curvature dependent weights and that can be used for the purposes of height reconstruction to smooth the reconstructed surface we fit quadrics to the height data for each patch the smoothed surface normal directions are updated ensuring compliance with lambert s law the processes of height recovery and surface normal adjustment are interleaved and iterated until a stable surface is obtained we provide results on synthetic and real world imagery

global well posedness and polynomial decay for a nonlinear timoshenko cattaneo system under minimal sobolev regularity abstract we consider the nonlinear stability of the timoshenko cattaneo system in the one dimensional whole space the timoshenko system consists of two coupled wave equations with non symmetric relaxation and describes vibrations of the beam with shear deformation and rotational inertia effect generally if the relaxation is not symmetric the dissipation is produced through the complicated interaction of the components of the system and their decay estimates and the energy estimates are of regularity loss type in this paper we introduce the mathematical method to control such a weak dissipativity by investigating the timoshenko system with cattaneo s law which is the first order approximation of fourier s law with its time delay effect racke said houari 2012 showed the global existence and the decay estimate of solutions by assuming high regularity h 8 l 1 on the small initial data to control their weak dissipativity in contrast we prove the global existence in h 2 by energy methods without any negative weights our regularity assumption is the same as that needed to show the local existence that is we do not need to assume the extra higher regularity on the initial data besides the optimal decay estimate in h 2 l 1 is shown by using the time decay inequality of l p l q l r type

vibration of eccentric ring and line supported circular plates carrying concentrated masses abstract the vibration of circular plates supported by combinations of ring and line supports and which are carrying concentrated masses is investigated for the first time to the author s knowledge by using the newly developed pb 2 rayleigh ritz method a set of ritz functions consisting of the product of the boundary expressions is used as the admissible displacement function this set of pb 2 ritz functions can accurately approximate the mode shapes of these circular plates with any prescribed boundary conditions and interior supports such as eccentric annular and or line supports to validate the present method numerical calculations have been carried out for several simplified plate problems and these are compared with those results available in the literature excellent agreement is achieved in all cases

recovering three dimensional shape from a single image of curved objects an algorithm to recover three dimensional shape i e surface orientation and relative depth from a single segmented image is presented it is assumed that the scene is composed of opaque regular solid objects bounded by piecewise smooth surfaces with no markings or textures it is also assumed that the reflectance map r n is known for the canonical case of lambertian surfaces illuminated by a point light source this implies knowing the light source direction a variational formulation of line drawing and shading constraints in a common framework is developed the global constraints are partitioned into constraint sets corresponding to the faces edges and vertices in the scene for a face the constraints are given by horn s image irradiance equation a variational formulation of the constraints at an edge both from the known direction of the image curve corresponding to the edge and shading is developed at a vertex the constraints are modeled by a system of nonlinear equations an algorithm is presented to solve this system of constraints

a stability result of a timoshenko system with a delay term in the internal feedback abstract in this paper we consider a timoshenko system with a delay term in the feedback and prove a stability result the beam is clamped at the endpoints and has in addition to an internal damping a feedback with a delay under an appropriate assumption on the weights of the two feedbacks we prove the well posedness of the system and establish an exponential decay result for the case of equal speed wave propagation

treatments of over restrained boundaries for doubly connected plates of arbitrary shape in vibration analysis abstract the problem of the free flexural vibrations of plates of doubly connected arbitrary shape is investigated a hybrid energy approach which combines both the advantages of the rayleigh ritz method and the lagrange multiplier method is developed for analysing the aforementioned plate problems the rayleigh ritz method with a set of pb 2 shape functions is used to formulate the plates with classical boundary conditions as a single continuum element while the lagrange multipliers are imposed at discrete points in the inner plate boundaries for instance when the overrestrained boundary has occurred the admissible pb 2 shape function consists of the product of a two dimensional polynomial and a basic function the basic function is defined by the product of the equations of the prescribed piecewise continuous boundary shape each raised to the power of 0 1 or 2 corresponding respectively to a free simply supported or clamped edge this set of functions automatically satisfies all the kinematic boundary conditions of the plate at the outset numerical results for several examples of doubly connected plates of arbitrary shape are presented to demonstrate the applicability and accuracy of the present method

photometric motion the author compares the photometric effects of motion which is defined as the variation of a point s imaged intensity as a consequence of motion and the geometric effects of motion which is defined as the variation in projected surface geometry as a consequence of motion it is shown that photometric motion provides a cue to surface shape that is potentially as useful as that provided by geometric motion a simple technique for using this photometric motion information to extract both surface shape and reflectance is developed and a biological implementation is proposed how this photometric motion mechanism can be integrated with and used to enhance existing structure motion algorithms is discussed intensity information is sometimes even more important than geometric distortion when estimating the shape of a single continuous surface that is rotating relative to the observer s frame of reference

free vibration of a solid plate of arbitrary shape lying on an arbitrarily shaped ring support this paper is concerned with a method for solving problems of vibrating plates of arbitrary shape lying on arbitrarily shaped inner ring supports to treat the inner ring support the reaction force of the support is assumed to be an external unknown force the exact solution of the equation of motion in polar co ordinates is applied the boundary conditions along the edge and the support are satisfied directly by means of the fourier expansion collocation method which has bee developed in the author s previous reports numerical calculations have been carried out for a solid polygonal plate on an annular ring support and a solid circular plate on a elliptical ring support

application of two dimensional orthogonal plate function to flexural vibration of skew plates abstract a set of two dimensional orthogonal plate functions is used as an admissible deflection function for the study of the flexural vibration of skew plates by the rayleigh ritz method from a prescribed starting function satisfying the boundary conditions the higher terms in the two dimensional orthogonal plate functions are generated by using the gram schmidt orthogonalization process the method is applied to obtain results for a few particular rhombic plates with different support conditions at various skew angles where possible the numerical results presented are compared with the values obtained by other numerical methods in the literature the results should be of considerable value and practical significance in design applications

on the imaging of fractal surfaces an analysis is presented of the imaging of surfaces modeled by fractal brownian elevation functions of the sort used in computer graphics it is shown that if lambertian reflectance modest surface slopes and the absence of occlusions and self shadowing are assumed a fractal surface with fourier power spectrum proportional to f sup beta produces an image with power spectrum proportional to f sup 2 beta here f is the spatial frequency and beta is related to the fractional dimension value this allows one to use the spectral falloff of the images to predict the fractal dimension of the surface

the element free kp ritz method for free vibration analysis of conical shell panels in this paper the free vibration of conical panels is analyzed by the mesh free kp ritz method both 1 d and 2 d versions of the kp ritz approach are formulated for conical panels for conical panels with two simply supported straight edges the 1 d kp ritz version is used where the kernel particle estimation is employed in hybridized form with harmonic functions to approximate the 2 d displacement field for conical panels having arbitrary boundary conditions the displacement field is approximated by the 2 d kp ritz version with 2 d form of kernel particle functions employed the classical thin shell theory based on love s hypothesis is employed in the present analyses and based on the kernel particle concept and ritz technique the eigenequations of the frequencies of the conical panels are obtained to validate the accuracy of stability of the present method convergence studies were carried out based on the influences of the support size and the number of nodes comparisons were also made with existing results available in the open literature this study also examines in detail the effects of variation in the semi vertex angle and boundary conditions on the frequency characteristics of conical panels

on the rate of decay in interacting continua with memory abstract this paper is concerning the linear theory of isothermal interacting continua with memory we consider anti plane shear deformations in a mixture of two elastic solids where the dissipation mechanisms can be the viscosity in one of the components and the viscosity with respect to the relative displacement we have seen that when the only dissipation mechanism applies on the relative displacement we cannot expect the exponential decay for the solutions we have also analyzed the case when the viscosity mechanism applies on a constituent we have seen that generically the decay is of exponential type however if the coupling constitutive parameter vanishes the decay is slow

general energy decay in a timoshenko type system of thermoelasticity of type iii with a viscoelastic damping in this paper we consider a one dimensional linear thermoelastic system of timoshenko type where the heat conduction is given by green and naghdi theories we prove a general decay result from which the exponential and polynomial decays are only special cases

incorporating illumination constraints in deformable models for shape from shading and light direction estimation we present a method for the integration of nonlinear holonomic constraints in deformable models and its application to the problems of shape and illuminant direction estimation from shading experimental results demonstrate that our method performs better than previous shape from shading algorithms applied to images of lambertian objects under known illumination it is also more general as it can be applied to non lambertian surfaces and it does not require knowledge of the illuminant direction in this paper 1 we first develop a theory for the numerically robust integration of nonlinear holonomic constraints within a deformable model framework in this formulation we use lagrange multipliers and a baumgarte stabilization approach 1972 2 we also describe a fast new method for the computation of constraint based forces in the case of high numbers of local parameters 3 we demonstrate how any type of illumination constraint from the simple lambertian model to more complex highly nonlinear models can be incorporated in a deformable model framework 4 we extend our method to work when the direction of the light source is not known we couple our shape estimation method with a method for light estimation in an iterative process where improved shape estimation results in improved light estimation and vice versa 5 we perform a series of experiments

local shading analysis local analysis of image shading in the absence of prior knowledge about the viewed scene may be used to provide information about the scene the following has been proved every image point has the same image intensity and first and second derivatives as the image of some point on a lambertian surface with principal curvatures of equal magnitude further if the principal curvatures are assumed to be equal there is a unique combination of image formation parameters up to a mirror reversal that will produce a particular set of image intensity and first and second derivatives a solution for the unique combination of surface orientation etc is presented this solution has been extended to natural imagery by using general position and regional constraints to obtain estimates of the following surface orientation at each image point the qualitative type of the surface i e whether the surface is planar cylindrical convex concave or saddle the illuminant direction within a region algorithms to recover illuminant direction and estimate surface orientation have been evaluated on both natural and synthesized images and have been found to produce useful information about the scene

linear shape from shading in many situations the reflectance function of a surface is approximately linear and there is an effielent closed form solution to the shape from shading problem when boundary conditions e g edges singular points are not available good estimates of shape may still be extracted by using the assumption of general viewing position an improved method for estimating the illuminant direction is also presented

some well posedness and general stability results in timoshenko systems with infinite memory and distributed time delay in this paper we consider a timoshenko system in one dimensional bounded domain with infinite memory and distributed time delay both acting on the equation of the rotation angle without any restriction on the speeds of wave propagation and under appropriate assumptions on the infinite memory and distributed time delay convolution kernels we prove first the well posedness and second the stability of the system where we present some decay estimates depending on the equal speed propagation case and the opposite one the obtained decay rates depend on the growths of the memory and delay kernels at infinity in the nonequal speed case the decay rate depends also on the regularity of initial data our stability results show that the only dissipation resulting from the infinite memory guarantees the asymptotic stability of the system regardless to the speeds of wave propagation and in spite of the presence of a distributed time delay applications of our approach to specific coupled timoshenko heat and timoshenko wave systems as well as the discrete time delay case are also presented

on the stabilization of timoshenko systems with memory and different speeds of wave propagation in this work we consider a one dimensional timoshenko system with different speeds of wave propagation and with only one control given by a viscoelastic term on the angular rotation equation for a wide class of relaxation functions and for sufficiently regular initial data we establish a general decay result for the energy of solution unlike the past history and internal feedback cases the second energy is not necessarily decreasing to overcome this difficulty a precise estimate of the second energy in terms of the initial data and the relaxation function is proved

estimation of illuminant direction albedo and shape from shading a robust approach to the recovery of shape from shading information is presented assuming uniform albedo and lambertian surface for the imaging model two methods for estimating the azimuth of the illuminant are presented one is based on local estimates on smooth patches and the other method uses shading information along image contours the elevation of the illuminant and surface albedo are estimated from image statistics taking into consideration the effect of self shadowing with the estimated reflectance map parameters the authors then compute the surface shape using a procedure that implements the smoothness constraint by requiring the gradients of reconstructed density to be close to the gradients of the input image the algorithm is data driven stable updates the surface slope and height maps simultaneously and significantly reduces the residual errors in irradiance and integrability terms a hierarchical implementation of the algorithm is presented typical results on synthetic and images are given to illustrate the usefulness of the approach

global existence and decay property of the timoshenko system in thermoelasticity with second sound abstract our main focus in the present paper is to study the asymptotic behavior of a nonlinear version of the timoshenko system in thermoelasticity with second sound as it has been already proved in said houari and kasimov 2012 29 the linear version of this system is of regularity loss type it is well known hosono and kawashima 2006 34 ide and kawashima 2008 27 kubo and kawashima 2009 41 that the regularity loss property of the linear problem creates difficulties when dealing with the nonlinear problem in fact the dissipative property of the problem becomes very weak in the high frequency region and as a result the classical energy method fails to overcome this difficulty and following ide and kawashima 2008 27 and ikehata 2002 30 we use an energy method with negative weights to create an artificial damping which allows us to control the nonlinearity we prove that for 0 k s 2 2 with s 8 the solution of our problem is global in time and decays as x k u t 2 c 1 t 1 4 k 2 provided that the initial datum u 0 h s r l 1 r

stability of timoshenko systems with past history we consider vibrating systems of timoshenko type with past history acting only in one equation we show that the dissipation given by the history term is strong enough to produce exponential stability if and only if the equations have the same wave speeds otherwise the corresponding system does not decay exponentially as time goes to infinity in the case that the wave speeds of the equations are different which is more realistic from the physical point of view we show that the solution decays polynomially to zero with rates that can be improved depending on the regularity of the initial data

a six stimulus theory for stochastic texture we report a six stimulus basis for stochastic texture perception fragmentation of the scene by a chaotic process causes the spatial scene statistics to conform to a weibull distribution the parameters of the weibull distribution characterize the spatial structure of uniform stochastic textures of many different origins completely in this paper we report the perceptual significance of the weibull parameters we demonstrate the parameters to be sensitive to orthogonal variations in the imaging conditions specifically to the illumination conditions camera magnification and resolving power and the texture orientation apparently the weibull parameters form a six stimulus basis for stochastic texture description the results indicate that texture perception can be approached like the experimental science of colorimetry

shape from shading viscosity solutions and edges this article deals with the so called shape from shading problem which arises when recovering a shape from a single image the general case of a distribution of light sources illuminating a lambertian surface is considered this involves original definitions of three types of edges mainly the apparent contours the grazing light edges and the shadow edges the elevation of the shape is expressed in terms of viscosity solution of a first order hamilton jacobi equation with various boundary conditions on these edges various existence and uniqueness results are presented