3 d shape from a shaded and textural surface image a new 3d texture model is developed by considering the scene image as the superposition of a random texture image on a smooth shaded image the whole image is analyzed using a patch by patch process each patch is assumed to be a tilted and slanted texture plane a modified reflectance map function is applied to describe the deterministic part and the fractional differencing periodic model is chosen to describe the random texture because of its good performance in texture synthesis and its ability to represent the coarseness and the pattern of the surface at the same time an orthographical projection technique is developed to deal with this particular random model which has a nonisotropically distributed texture pattern for estimating the parameter a hybrid method that uses both the least square and the maximum likelihood estimates is applied directly to the given intensity function by using these parameters the synthesized image is obtained and used to reconstruct the original image

recovering surface shape and orientation from texture texture provides an important source of information about the three dimensional structure of visible surfaces particularly for stationary monocular views to recover 3d structure the distorting effects of projection must be distinguished from properties of the texture on which the distortion acts this requires that assumptions must be made about the texture yet the unpredictability of natural textures precludes the use of highly restrictive assumptions the recovery method reported in this paper exploits the minimal assumption that textures do not mimic projective effects this assumption determines the strategy of attributing as much as possible of the variation observed in the image to projection equivalently the interpretation is chosen for which the texture prior to projection is made as uniform as possible this strategy was implemented using statistical methods first for the restricted case of planar surfaces and then by extension for curved surfaces the technique was applied successfully to natural images

shape from recognition a novel approach for 3 d face shape recovery in this paper we develop a novel framework for robust recovery of three dimensional 3 d surfaces of faces from single images the underlying principle is shape from recognition i e the idea that pre recognizing face parts can constrain the space of possible solutions to the image irradiance equation thus allowing robust recovery of the 3 d structure of a specific part parts of faces like nose lips and eyes are recognized and localized using robust expansion matching filter templates under varying pose and illumination specialized backpropagation based neural networks are then employed to recover the 3 d shape of particular face parts representation using principal components allows to efficiently encode classes of objects such as nose lips etc the specialized networks are designed and trained to map the principal component coefficients of the part images to another set of principal component coefficients that represent the corresponding 3 d surface shapes to achieve robustness to viewing conditions the network is trained with a wide range of illumination and viewing directions a method for merging recovered 3 d surface regions by minimizing the sum squared error in overlapping areas is also derived quantitative analysis of the reconstruction of the surface parts in varying illumination and pose show relatively small errors indicating that the method is robust and accurate several examples showing recovery of the complete face also illustrate the efficacy of the approach

adaptive segmentation of noisy and textured images abstract an image segmentation algorithm is described which is based on the integration of signal model parameter estimates and maximum a posteriori labelling the parameter estimation is based on either a maximum likelihood based method for a quadric signal model or a maximum pseudo likelihood based method for a gauss markov signal model the first case is applicable to standard grey level image segmentation as well as segmentation of shaded 3d surfaces while the second case is applicable to texture segmentation a key aspect of the algorithm is the incorporation of a coarse to fine processing strategy which limits the search for the optimum labelling at any one resolution to a subset of labellings which are consistent with the optimum labelling at the previous coarser resolution consistency is in terms of a prior label model which specifies the conditional probability of a given label in terms of the labelling at the previous level of resolution it is shown how such an approach leads to a simple relaxation procedure based on local pyramid node computations an extension of the algorithm is also described which performs accurate inter region boundary placement using a step wise refinement procedure based on a simple adaptive filter the problem of automatic determination of the number of regions is also addressed it is shown how a simple agglomerative clustering idea again based on pyramid node computations can effectively solve this problem

improved methods of estimating shape from shading using the light source coordinate system abstract this paper develops improved methods of estimating local surface orientation from shading information with the aid of a coordinate system having one axis in the assumed direction of the light source in this system the surface tilt is related to the direction of the gray level gradient at the given point an alternative formulation of the surface slant probability density is developed that takes the discrete nature of digital images into account and that yields a better estimate of the light source direction

surface topography using shape from shading abstract this paper demonstrates how a recently reported shape from shading scheme can be used to extract topographic information from 2d intensity imagery worthington and hancock ieee trans pattern anal mach intell 21 1999 1250 1267 the shape from shading scheme has two important features which enhance the recovered surface description firstly it uses a geometric update procedure which allows the image irradiance equation to be satisfied as a hard constraint this not only improves the data closeness of the recovered needle map but also removes the necessity for extensive parameter tuning secondly we use curvature information to impose topographic constraints on the recovered needle map the topographic information is captured using the shape index of koenderink and van doorn image vision comput 10 1992 557 565 and consistency is imposed using a robust error function we show that the new shape from shading scheme leads to a meaningful topographic labelling of 3d surface structures moreover the resulting topographic information proves to be useful in a simple histogram based object recognition scheme

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

multiple illuminant direction detection with application to image synthesis pentland observed 1982 1984 that the human eye is sensitive to the change of intensities on an image of a smooth surface the change of intensities is maximal whenever the illuminant direction is perpendicular to the normal of the surface this motivates us to introduce the concept of critical points where the surface normal is perpendicular to some light source direction apparently the illuminant direction has a simple geometric relationship with the corresponding critical points in this paper for simplicity reasons we restrict our discussions to the shading of a lambertian sphere of known size in a multiple distant light source environment a novel global representation of the intensity function is derived based on this intensity characterization the least squares and iteration techniques are used to determine critical points and thus the light source directions and their intensities if certain conditions are satisfied the performance of this new approach is evaluated using both synthetic images and real images as an application we use it as a tool to determine light sources in real image synthesis the experimental results show that this technique can be used to superimpose synthetic objects with a real scene

a multiresolution approach for shape from shading coupling deterministic and stochastic optimization shape from shading is an ill posed inverse problem for which there is no completely satisfactory solution in the existing literature in this paper we address shape from shading as an energy minimization problem we first show that the deterministic approach provides efficient algorithms in terms of cpu time but reaches its limits since the energy associated with shape from shading can contain multiple deep local minima we derive an alternative stochastic approach using simulated annealing the obtained results strongly outperform the results of the deterministic approach the shortcoming is an extreme slowness of the optimization therefore we propose a hybrid approach which combines the deterministic and stochastic approaches in a multiresolution framework

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

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

stress intensity factors of a rectangular crack meeting a bimaterial interface using the hypersingular integral equation method based on body force method a planar crack meeting the interface in a three dimensional dissimilar materials is analyzed the singularity of the singular stress field around the crack front terminating at the interface is analyzed by the main part analytical method of hypersingular integral equations then the numerical method of the hypersingular integral equation for a rectangular crack subjected to normal load is proposed by the body force method which the crack opening dislocation is approximated by the product of basic density functions and polynomials numerical solutions of the stress intensity factors of some examples are given

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

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

determining orientation location and size of primitive surfaces by a modified hough transformation technique abstract this paper proposes a new computational approach to determining parameters that represent the orientation location and size of primitive surfaces the method which is motivated from the hough transformation method estimates these parameters by transforming the image s needle maps into the parameter space of the surfaces in order to reduce the great computational expense of the hough transform method we firstly divide the parameter space into three subspaces on the basis of the relationships between the image s needle maps and the parameters then the hough transformation method is iteratively used and the parameters are derived sequentially by clustering in each subspace this procedure has been successfully applied to a number of real images two of which we present in the paper

exploiting the generic viewpoint assumption the generic viewpoint assumption states that an observer is not in a special position relative to the scene it is commonly used to disqualify scene interpretations that assume special viewpoints following a binary decision that the viewpoint was either generic or accidental in this paper we apply bayesian statistics to quantify the probability of a view and so derive a useful tool to estimate scene parameters generic variables can include viewpoint object orientation and lighting position by considering the image as a differentiable function of these variables we derive the probability that a set of scene parameters created a given image this scene probability equation has three terms the fidelity of the scene interpretation to the image data the prior probability of the scene interpretation and a new genericity term which favors scenes likely to produce the observed image the genericity term favors image interpretations for which the image is stable with respect to changes in the generic variables it results from integration over the generic variables using a low noise approximation common in bayesian statistics this approach may increase the scope and accuracy of scene estimates it applies to a range of vision problems we show shape from shading examples where we rank shapes or reflectance functions in cases where these are otherwise unknown the rankings agree with the perceived values

shape from fractal geometry abstract a novel method for the recovery of a planar surface orientation from its image using fractal measures is presented a fractal related feature the average holder constant is defined in the two dimensional topological space it is proven that the average holder constant is scale sensitive and the distance ratio from any two points on the fractal surface to the viewer can be calculated from their average holder constants by incorporating the distance ratio into the surface vanishing line formula in the geometric model a method for inferring planar surface shape is derived the novelty of this method is that the fractal related feature is used as a direct input in the shape recovery process experimental results showing the validity of applying this method to artificially rotated textured images and images of naturally textured surfaces are presented

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

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

new constraints on data closeness and needle map consistency for shape from shading this paper makes two contributions to the problem of needle map recovery using shape from shading first we provide a geometric update procedure which allows the image irradiance equation to be satisfied as a hard constraint this not only improves the data closeness of the recovered needle map but also removes the necessity for extensive parameter tuning second we exploit the improved ease of control of the new shape from shading process to investigate various types of needle map consistency constraint the first set of constraints are based on needle map smoothness the second avenue of investigation is to use curvature information to impose topographic constraints third we explore ways in which the needle map is recovered so as to be consistent with the image gradient field in each case we explore a variety of robust error measures and consistency weighting schemes that can be used to impose the desired constraints on the recovered needle map we provide an experimental assessment of the new shape from shading framework on both real world images and synthetic images with known ground truth surface normals the main conclusion drawn from our analysis is that the data closeness constraint improves the efficiency of shape from shading and that both the topographic and gradient consistency constraints improve the fidelity of the recovered needle map

shape from shading under perspective projection shape from shading sfs is a fundamental problem in computer vision a very common assumption in this field is that image projection is orthographic this paper re examines the basis of sfs the image irradiance equation under a perspective projection assumption the resultant equation does not depend on the depth function directly but rather on its natural logarithm as such it is invariant to scale changes of the depth function a reconstruction method based on the perspective formula is then suggested it is a modification of the fast marching method of kimmel and sethian following that a comparison of the orthographic fast marching perspective fast marching and the perspective algorithm of prados and faugeras on synthetic images is presented the two perspective methods show better reconstruction results than the orthographic the algorithm of prados and faugeras equates with the perspective fast marching following that a comparison of the orthographic and perspective versions of the fast marching method on endoscopic images is introduced the perspective algorithm outperformed the orthographic one these findings suggest that the more realistic set of assumptions of perspective sfs improves reconstruction significantly with respect to orthographic sfs the findings also provide evidence that perspective sfs can be used for real life applications in fields such as endoscopy

recovery of shgcs from a single intensity view generalized cylinders are a flexible loosely defined class of parametric shapes capable of modeling many real world objects straight homogeneous generalized cylinders are an important subclass of generalized cylinders whose cross sections are scaled versions of a reference curve although there has been considerable research into recovering the shape of shgcs from their contour this work has almost exclusively involved methods that couple contour and heuristic constraints a rigorous approach to the problem of recovering solid parametric shape from a single intensity view should involve at least two stages 1 deriving the contour constraints and 2 determining if additional image constraints e g intensity can be used to uniquely determine the 3d object shape in this paper the authors follow the approach just described this methodology is also important for the recovery of object classes like tubes where contour and heuristic constraints are shown to be insufficient for shape recovery first the authors prove that shgc contours generated under orthography have exactly two degrees of freedom next the authors show that the remaining free parameters can be resolved using reflectance based constraints without knowledge of the number of light sources their positions intensities the amount of ambient light or the surface albedo finally the reflectance based recovery algorithm is demonstrated on both synthetic and real shgc images

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

numerical shape from shading and occluding boundaries an iterative method for computing shape from shading using occluding boundary information is proposed some applications of this method are shown we employ the stereographic plane to express the orientations of surface patches rather than the more commonly used gradient space use of the stereographic plane makes it possible to incorporate occluding boundary information but forces us to employ a smoothness constraint different from the one previously proposed the new constraint follows directly from a particular definition of surface smoothness we solve the set of equations arising from the smoothness constraints and the image irradiance equation iteratively using occluding boundary information to supply boundary conditions good initial values are found at certain points to help reduce the number of iterations required to reach a reasonable solution numerical experiments show that the method is effective and robust finally we analyze scanning electron microscope sem pictures using this method other applications are also proposed

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

parametric shape from shading by radial basis functions we present a new method of shape from shading by using radial basis functions to parameterize the object depth the radial basis functions are deformed by adjusting their centers widths and weights such that the intensity errors are minimized the initial centers and widths are arranged hierarchically to speed up convergence and to stabilize the solution although the smoothness constraint is used it can be eventually dropped out without causing instabilities in the solution an important feature of our parametric shape from shading method is that it offers a unified framework for integration of multiple sensory information we show that knowledge about surface depth and or surface normals anywhere in the image can be easily incorporated into the shape from shading process it is further demonstrated that even qualitative knowledge can be used in shape from shading to improve 3d reconstruction experimental comparisons of our method with several existing ones are made by using both synthetic and real images results show that our solution is more accurate than the others

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

application of a conservative generalized multiscale finite element method to flow models in this paper we propose a method for the construction of locally conservative flux fields from generalized multiscale finite element method gmsfem pressure solutions the flux values are obtained from an element based postprocessing procedure in which an independent set of 4x4 linear systems need to be solved to test the performance of the method we consider two heterogeneous permeability coefficients and couple the resulting fluxes to a two phase flow model the increase in accuracy associated with the computation of the gmsfem pressure solutions is inherited by the postprocessed flux fields and saturation solutions and is closely correlated to the size of the reduced order systems in particular the addition of more basis functions to the enriched coarse space yields solutions that more accurately capture the behavior of the fine scale model a number of numerical examples are offered to validate the performance of the method

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

a shape from shading analysis for a single perspective image of a polyhedron a shape from shading analysis for a single perspective image of a polyhedron is presented given a single perspective image of a polyhedron the depth of any point of the polyhedron from the camera the direction of the light source illuminating the polyhedron and the albedo of the polyhedron a system of algebraic equations are derived which when combined with edge information quantitatively describes the shape of the polyhedron this analysis is best possible in the sense that if any component of what the author has assumed is omitted no similar analysis can provide the same results

image based rendering using parameterized image varieties this paper addresses the problem of characterizing the set of all images of a rigid set of m points and n lines observed by a weak perspective or paraperspective camera by taking explicitly into account the euclidean constraints associated with calibrated cameras we show that the corresponding image space can be represented by a six dimensional variety embedded in cal r 2 m n and parameterized by the image positions of three reference points the coefficients defining this parameterized image variety or piv for short can be estimated from a sample of images of a scene via linear and non linear least squares the piv provides an integrated framework for using both point and line features to synthesize new images from a set of pre recorded pictures image based rendering the proposed technique does not perform any explicit three dimensional scene reconstruction but it supports hidden surface elimination texture mapping and interactive image synthesis at frame rate on ordinary pcs it has been implemented and extensively tested on real data sets

illumination control as a means of enhancing image features in active vision systems in this paper illumination control has been studied as a means of enhancing image features such features are points edges and shading patterns which provide important cues for the interpretation of an image of a scene and the recognition of objects present in it based on approximate expressions for the reflectance map of lambertian and general surfaces a rigorous discussion on how intensity gradients are dependent on the direction of the light is presented subsequently three criteria for the illumination of convex shaped cylindrical surfaces are given two of these the contrast equalization criterion and the max min equalization criterion are developed for optimal illumination of convex polyhedrons the third denoted shading enhancement is applicable for the illumination of convex curved objects examples illustrate the merit of the criteria presented

shape from a single view using matching method abstract a proposed method for estimating shape of an object using only one image of it is introduced this method depends on matching each point in object image with another point in a standard object image the image formation system should be the same for both the standard object and the unknown object also the surface reflectance properties should be the same for the two objects the surface of the standard object should have all types of surface orientations the validity of the method is tested using synthetic images the experimental results are also discussed

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

model based recognition and positioning of polyhedra using intensity guided range sensing and interpretation in 3 d space abstract this paper presents a design of 3 d multi sensory visual and ranging system capable of identifying and locating polyhedral objects in six degrees of spatial freedom due to differences in sensor characteristics e g the fast data acquisition in intensity domain and the abundance of information inherent in range domain sensors should operate in a cooperative manner to increase system efficiency and to yield information otherwise unavailable or hard to obtain from any single sensor the adopted strategy of intensity guided range sensing firstly extracts features e g the line drawing and the control points from intensity images and then uses them as a guide to selectively sense ranges through the interfusion of both types of information 3 d object description in terms of a relational graph structure is thus constructed for recognition and positioning purposes to identify the object interpretation tree search in 3 d space is applied to the matching between the constructed relational graph and those stored in database since high level primitives such as faces derived from intensity and range informations are utilized for interpretation or matching the search space can be significantly reduced finally a non iterative method based on the quaternion technique is adopted to solve the transformation between sensor and model coordinates for further robotic applications

shape from shading with a linear triangular element surface model the authors propose to combine a triangular element surface model with a linearized reflectance map to formulate the shape from shading problem the main idea is to approximate a smooth surface by the union of triangular surface patches called triangular elements and express the approximating surface as a linear combination of a set of nodal basis functions since the surface normal of a triangular element is uniquely determined by the heights of its three vertices or nodes image brightness can be directly related to nodal heights using the linearized reflectance map the surface height can then be determined by minimizing a quadratic cost functional corresponding to the squares of brightness errors and solved effectively with the multigrid computational technique the proposed method does not require any integrability constraint or artificial assumptions on boundary conditions simulation results for synthetic and real images are presented to illustrate the performance and efficiency of the method

shape from shading using probability functions and belief propagation shape from shading sfs aims to reconstruct the three dimensional shape of an object from a single shaded image this article proposes an improved framework based on belief propagation for computing sfs the implementation of the well known brightness integrability and smoothness constraints inside this framework is shown we implement the constraints as probability density functions for example the brightness constraint is a two dimensional probability density function that relates all possible surface gradients at a pixel to their probability given the pixel intensity a straightforward extension of the framework to photometric stereo is presented where multiple images of the same scene taken under different lighting conditions are available the results are promising especially since the solution is obtained by iteratively applying simple operations on a regular grid of points the presented framework therefore can be implemented in parallel and is a reasonably likely biological scheme

learning shape from shading by a multilayer network the multilayer feedforward network has often been used for learning a nonlinear mapping based on a set of examples of the input output data in this paper we present a novel use of the network in which the example data are not explicitly given we consider the problem of shape from shading in computer vision where the input image coordinates and the output surface depth satisfy only a known differential equation we use the feedforward network as a parametric representation of the object surface and reformulate the shape from shading problem as the minimization of an error function over the network weights the stochastic gradient and conjugate gradient methods are used for the minimization boundary conditions for either surface depth or surface normal or both can be imposed by adjusting the same network at different levels it is further shown that the light source direction can be estimated based on an initial guess by integrating the source estimation with the surface estimation extensions of the method to a wider class of problems are discussed the efficiency of the method is verified by examples of both synthetic and real images

texture boundary detection based on the long correlation model the problem of detecting texture boundaries without assuming any knowledge on the number of regions or the types of textures is considered texture boundaries are often regarded as better features than intensity edges because a large class of images can be considered a composite of several different texture regions an algorithm is developed that detects texture boundaries at reasonably high resolution without assuming any prior knowledge on the texture composition of the image the algorithm utilizes the long correlation texture model with a small number of parameters to characterize textures the parameters of the model are estimated by a least squares method in the frequency domain the existence and the location of texture boundary is estimated by the maximum likelihood method the algorithm is applied to several different images and its performance is shown by examples experimental results show that the algorithm successfully detects texture boundaries without knowing the number of types of textures in the image

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