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

fast surface interpolation using hierarchical basis functions an alternative to multigrid relaxation that is much easier to implement and more generally applicable is presented conjugate gradient descent is used in conjunction with a hierarchical multiresolution set of basis functions the resultant algorithm uses a pyramid to smooth the residual vector before the direction is computed simulation results showing the speed of convergence and its dependence on the choice of interpolator the number of smoothing levels and other factors are presented the relationship of this approach to other multiresolution relaxation and representation schemes is also discussed

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

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

toward a symbolic representation of intensity changes in images the symbolic representation of gray value variations is studied with emphasis on the gradient of the image function the goal is to relate the results of this analysis to the structure of the picture which is determined by the physics of the image generation process candidates for contour points are the maximal magnitudes of the gray value gradient for different scales in the direction of the gradient based on the output of such a bank of gradient filters a procedure is proposed to select automatically a suitable scale and with that the size of the right convolution kernel the application of poorly adapted filters which make the exact localization of gray value corners or t x and y junctions more difficult is thus avoided possible gaps at such junctions are discussed for images of real scenes and possibilities for the closure of some of these gaps are demonstrated when the extrema of the magnitudes of the gray value gradients are used

the computation of visible surface representations a computational theory of visible surface representations is developed the visible surface reconstruction process that computes these quantitative representations unifies formal solutions to the key problems of 1 integrating multiscale constraints on surface depth and orientation from multiple visual sources 2 interpolating dense piecewise smooth surfaces from these constraints 3 detecting surface depth and orientation discontinuities to apply boundary conditions on interpolation and 4 structuring large scale distributed surface representations to achieve computational efficiency visible surface reconstruction is an inverse problem a well posed variational formulation results from the use of a controlled continuity surface model discontinuity detection amounts to the identification of this generic model s distributed parameters from the data finite element shape primitives yield a local discretization of the variational principle the result is an efficient algorithm for visible surface reconstruction

additivity obstructions for integral matrices and pyramids in discrete tomography there are two related notions of interest h uniqueness and h additivity of finite subsets of n m which are defined for certain finite sets h of linear subspaces of r m one knows complete sets of obstructions for h uniqueness bad h configurations and for h additivity weakly bad h configurations the classical case when h is the set of coordinate axes in r 2 is well known let h m denote the set of the m coordinate hyperplanes of r m the following question was raised in p c fishburn j c lagarias j a reeds l a shepp sets uniquely determined by projections on axes ii discrete case discrete math 91 1991 149 159 is there an upper bound on the weights of the bad h m configurations one needs to consider to determine h m uniqueness m 3 of an arbitrary set in n m this question can be asked for other sets h of linear subspaces and also for h additivity the answer to this question in the case of uniqueness is known when h is a set of lines in this paper we answer this question for uniqueness and additivity in the case of h 3 we show that there is no upper bound on the weights of the bad configurations resp weakly bad configurations one needs to consider to determine h 3 uniqueness resp h 3 additivity

an interfacially cracked orthotropic rectangular bi material subjected to antiplane shear loading abstract an interfacially cracked rectangular bi material composed of two dissimilar orthotropic elastic media is analyzed the crack is parallel to or perpendicular to the boundary surfaces under the action of antiplane shear loading the problem is reduced to a singular integral equation of the first kind by employing the fourier series method for four types of boundary conditions including the f f type c c type f c type and c f type numerical results of stress intensity factors are obtained by using the lobatto chebyshev method the results show that in addition to the geometric factor stress intensity factors are dependent on the material properties the influences of the material properties on stress intensity factors are examined and compared under different boundary conditions

the constraints on images of rectangular polyhedra this paper discusses how polyhedron interpretation techniques are simplified if the objects are rectangular trihedral polyhedra this restriction enables one to compute the spatial orientation of a given corner and its motion from its image in terms of polar coordinates eulerian angles and quaternions one can also interpret the shape and the face adjacency from local information only the necessary constraints are listed and some examples are given to compare the presented scheme to existing ones the possible nonuniqueness of the interpretation is also discussed

on the general treatment of an oblique crack near a bimaterial interface under antiplane loading this article provides a comprehensive theoretical treatment of the interaction between an arbitrarily located and oriented crack and a bimaterial interface under antiplane loading the analysis is based upon the use of an integral transform method and a self consistent iterative sci technique the resulting singular integral equations are solved using chebyshev polynomials to provide closed form expressions for the stress distribution along the interface and the stress intensity factor at the crack typical examples are provided to show the effect of the location and orientation of the crack and the material combination upon the interfacial stress distribution and the stress intensity factor of the crack the presented method can be extended to treat more complex interaction problems

variation of cost functions in integer programming we study the problem of minimizingc x subject toa x b x 0 andx integral for a fixed matrixa two cost functionsc andc are considered equivalent if they give the same optimal solutions for eachb we construct a polytopest a whose normal cones are the equivalence classes explicit inequality presentations of these cones are given by the reduced grobner bases associated witha the union of the reduced grobner bases asc varies called the universal grobner basis consists precisely of the edge directions ofst a we present geometric algorithms for computingst a the graver basis and the universal grobner basis

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

bandwidth selection for changepoint estimation in nonparametric regression nonparametric estimation of abrupt changes in a regression function involves choosing smoothing bandwidth parameters the performance of estimation procedures depends heavily on this choice so far little attention has been paid to the crucial issue of choosing appropriate bandwidth parameters in practice in this article we propose a bootstrap procedure for selecting the bandwidth parameters in a nonparametric two step estimation method this method results in a fully data driven procedure for estimating a finite but possibly unknown number of changepoints in a regression function we evaluate the performance of the data driven procedure via a simulation study which reveals that the fully automatic procedure performs quite well as an illustration we apply the procedure to some real data

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

edge detection using two dimensional local structure information abstract local intensity discontinuities commonly referred to as edges are important attributes of an image many imaging scenarios produce image regions exhibiting complex two dimensional 2d local structure such as when several edges meet to form corners and vertices traditional derivative based edge operators which typically assume that an edge can be modeled as a one dimensional 1d piecewise smooth step function give misleading results in such situations leclerc and zucker introduced the concept of local structure as an aid for locating intensity discontinuities they proposed a detailed procedure for detecting discontinuities in a 1d function they had only given a preliminary version of their scheme however for 2d images three related edge detection methods are proposed that draw upon 2d local structural information the first method greatly expands upon leclerc and zucker s 2d method the other two methods employ a mechanism similar to that used by the maximum homogeneity filter a filter used for image enhancement all three methods permit the detection of multiple edges at a point and have the flexibility to detect edges at differing spatial and angular acuity results show that the methods typically perform better than other operators

anti plane stress analysis of orthotropic rectangular planes weakened by multiple defects the solution of a volterra type screw dislocation problem in an orthotropic rectangular plane with finite length and width and various boundary conditions is obtained by means of a separation of variables technique a distributed dislocation method is employed to obtain integral equations of the plane with cracks and cavities under an anti plane traction the ensuing equations are of the cauchy singular type and have been solved numerically several examples are presented to demonstrate the applicability of the proposed solution

permutohedra and minimal matrices the notions of minimality uniqueness and additivity originated in discrete tomography they have applications to kronecker products of characters of the symmetric group and arise as the optimal solutions of quadratic transportation problems here we introduce the notion of real minimality and give geometric characterizations of all these notions for a matrix a by considering the intersection of the permutohedron determined by a with the transportation polytope in which a lies we also study the computational complexity of deciding if the properties of being additive real minimal unique and minimal hold for a given matrix and show how to efficiently construct some matrix with any of these properties

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

image analysis using multigrid relaxation methods image analysis problems posed mathematically as variational principles or as partial differential equations are amenable to numerical solution by relaxation algorithms that are local iterative and often parallel although they are well suited structurally for implementation on massively parallel locally interconnected computational architectures such distributed algorithms are seriously handi capped by an inherent inefficiency at propagating constraints between widely separated processing elements hence they converge extremely slowly when confronted by the large representations of early vision application of multigrid methods can overcome this drawback as we showed in previous work on 3 d surface reconstruction in this paper we develop multiresolution iterative algorithms for computing lightness shape from shading and optical flow and we examine the efficiency of these algorithms using synthetic image inputs the multigrid methodology that we describe is broadly applicable in early vision notably it is an appealing strategy to use in conjunction with regularization analysis for the efficient solution of a wide range of ill posed image analysis problems

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

detecting boundaries in a vector field a vector gradient approach is proposed to detect boundaries in multidimensional data with multiple attributes a vector field it is used to extend a gradient edge detector to color images the statistical effects of noise on the distribution of the amplitudes and directions of the vector gradient are characterized the noise behavior of the l sub 2 norm of the scalar gradients is also characterized for comparison when the attribute components are highly correlated as is often the case in color images use of the vector gradient shows a small gain in signal to noise ratio over that of the l sub 2 norm of the scalar gradients this small gain may or may not be significant depending on other measures an edge detector uses to deal with noise

regularization of inverse visual problems involving discontinuities inverse problems such as the reconstruction problems that arise in early vision tend to be mathematically ill posed through regularization they may be reformulated as well posed variational principles whose solutions are computable standard regularization theory employs quadratic stabilizing functionals that impose global smoothness constraints on possible solutions discontinuities present serious difficulties to standard regularization however since their reconstruction requires a precise spatial control over the smoothing properties of stabilizers this paper proposes a general class of controlled continuity stabilizers which provide the necessary control over smoothness these nonquadratic stabilizing functionals comprise multiple generalized spline kernels combined with noncontinuous continuity control functions in the context of computational vision they may be thought of as controlled continuity constraints these generic constraints are applicable to visual reconstruction problems that involve both continuous regions and discontinuities for which global smoothness constraints fail

on three dimensional surface reconstruction methods a survey is presented of some of the surface reconstruction methods that can be found in the literature the focus is on a small recent and important subset of the published reconstruction techniques the techniques are classified based on the surface representation used implicit versus explicit functions a study is made of the important aspects of the surface reconstruction techniques one aspect is the viewpoint invariance of the methods this is an important property if object recognition is the ultimate objective the robustness of the various methods is examined it is determined whether the parameter estimates are biased and the sensitivity to obscuration is addressed the latter two aspects are particularly important for fitting functions in the implicit form a detailed description is given of a parametric reconstruction method for three dimensional object surfaces that involves numeric grid generation techniques and variational principle formulations this technique is invariant to rigid motion in dimensional space

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

localized measurement of emergent image frequencies by gabor wavelets the authors derive implement and demonstrate a computational approach for the measurement of emergent image frequencies measuring emergent signal frequencies requires spectral measurements accurate in both frequency and time or space conflicting requirements that are shown to be balanced by a generalized uncertainty relationship such spectral measurements can be obtained from the responses of multiple wavelet like channel filters that sample the signal spectrum and that yield a locus of possible solutions for each locally emergent frequency it is shown analytically that this locus of solutions is maximally localized in both space and frequency if the channel filters used are gabor wavelets a constrained solution is obtained by imposing a stabilizing term that develops naturally from the assumptions on the signal the measurement of frequencies is then cast as an ill posed extremum problem regularized by the stabilizing term leading to an iterative constraint propagation algorithm the technique is demonstrated by application to a variety of 2 d textured images

the crack problem for nonhomogeneous materials under antiplane shear loading a displacement based formulation abstract this paper presents a displacement based integral equation formulation for the mode iii crack problem in a nonhomogeneous medium with a continuously differentiable shear modulus which is assumed to be an exponential function i e g x g0exp x this formulation leads naturally to a hypersingular integral equation the problem is solved for a finite crack and results are given for crack profiles and stress intensity factors the results are affected by the parameter describing the material nonhomogeneity this study is motivated by crack problems in strain gradient elasticity theories where higher order singular integral equations naturally arise even in the slope based formulation

region based strategies for active contour models the variational method has been introduced by kass et al 1987 in the field of object contour modeling as an alternative to the more traditional edge detection edge thinning edge sorting sequence since the method is based on a pre processing of the image to yield an edge map it shares the limitations of the edge detectors it uses in this paper we propose a modified variational scheme for contour modeling which uses no edge detection step but local computations instead only around contour neighborhoods as well as an anticipating strategy that enhances the modeling activity of deformable contour curves many of the concepts used were originally introduced to study the local structure of discontinuity in a theoretical and formal statement by leclerc zucker 1987 but never in a practical situation such as this one the first part of the paper introduces a region based energy criterion for active contours and gives an examination of its implications as compared to the gradient edge map energy of snakes then a simplified optimization scheme is presented accounting for internal and external energy in separate steps this leads to a complete treatment which is described in the last sections of the paper 4 and 5 the optimization technique used here is mostly heuristic and is thus presented without a formal proof but is believed to fill a gap between snakes and other useful image representations such as split and merge regions or mixed line labels image fields

invariant surface segmentation through energy minimization with discontinuities the computational problems in segmenting range data into surface patches based on the invariant surface properties i e mean curvature h and gaussian curvature k are investigated the goal is to obtain reliable hk surface maps two commonly encountered problems are firstly the noise effect in computing derivative estimates and secondly the smoothing across discontinuities here the segmentation is formulated as finding minimization solutions of energy functionals involving discontinuities a two stage approach to the goal is presented stage 1 from a range image to curvature images and stage 2 from the curvature images to the hk maps in both stages solutions are found through minimizing energy functionals that measure the degree of bias of a solution from two constraints the closeness of the solution to the data and the smoothness of the solution controlled by predetermined discontinuities propagation across discontinuities is prevented during minimization which preserves the original surface shapes experimental results are given for a variety of test images

symmetric shape from shading using self ratio image in this paper we present a symmetric shape from shading sfs approach to recover both shape and albedo for symmetric objects lambertian surfaces with unknown varying albedo and orthographic projections are assumed in our formulation of symmetric sfs we have two image irradiance equations one is the standard equation used in sfs and the other is a self ratio image irradiance equation this new image irradiance equation relates the self ratio image which is defined as the ratio of two halves of the input image to light source and surface shape the introduction of the self ratio image facilitates the direct use of symmetry cue based on the self ratio image a new model based symmetric source from shading algorithm is also presented we then propose symmetric sfs algorithms to recover both shape and albedo from a single image and present experimental results the new symmetric sfs scheme has one important property the existence of a unique global solution which consists of unique local solutions at each point simultaneously obtained using the intensity information at that point and the surrounding local region and the assumption of a cal c 2 surface proofs for the existence of a unique solution in the cases of unknown constant and non constant albedos are provided

computation of surface orientation and structure of objects using grid coding in this correspondence algorithms are introduced to infer surface orientation and structure of visible object surfaces using grid coding we adopt the active lighting technique to spatially encode the scene for analysis the observed objects which can have surfaces of arbitrary shape are assumed to rest on a plane base plane in a scene which is encoded with light cast through a grid plane two orthogonal grid patterns are used where each pattern is obtained with a set of equally spaced stripes marked on a glass pane the scene is observed through a camera and the object surface orientation is determined using the projected patterns on the object surface if the surfaces under consideration obey certain smoothness constraints a dense orientation map can be obtained through proper interpolation the surface structure can then be recovered given this dense orientation map both planar and curved surfaces can be handled in a uniform manner the algorithms we propose yield reasonably accurate results and are relatively tolerant to noise especially when compared to shape from shading techniques in contrast to other grid coding techniques reported which match the grid junctions for depth reconstruction under the stereopsis principle our techniques use the direction of the projected stripes to infer local surface orientation and do not require any correspondence relationship between either the grid lines or the grid junctions to be specified the algorithm has the ability to register images and can therefore be embedded in a system which integrates knowledge from multiple views

minimal nonnegative integral matrices and uniquely determined 0 1 matrices abstract in this note we give an elementary proof of a theorem that characterizes those three dimensional 0 1 matrices that are determined by their plane sum vectors

on the computational complexity of reconstructing three dimensional lattice sets from their two dimensional x rays abstract a generalization of a classical discrete tomography problem is considered reconstruct three dimensional lattice sets from their two dimensional x rays parallel to three coordinate planes first we prove that this reconstruction problem is np hard then we propose some greedy algorithms that provide approximate solutions of the problem

a geometric buchberger algorithm for integer programming let ip a c denote the family of integer programs of the form min cx ax b x nn obtained by varying the right hand side vector b but keeping a and c fixed a test set for ipa c is a set of vectors in zn such that for each nonoptimal solution to a program in this family there is at least one element g in this set such that g has an improved cost value as compared to we describe a unique minimal test set for this family called the reduced grobner basis of ip a c an algorithm for its construction is presented which we call a geometric buchberger algorithm for integer programming and we show how an integer program may be solved using this test set the reduced grobner basis is then compared with some other known test sets from the literature we also indicate an easy procedure to construct test sets with respect to all cost functions for a matrix a zn 2 n of full row rank

psychophysical and computational studies towards a theory of human stereopsis psychophysical studies are described which pose a strong challenge to models of human stereopsis based on the processing of disparity information within independent spatial frequency tuned binocular channels these studies support instead the proposal that the processes of human binocular combination integrally relate the extraction of disparity information with the construction of raw primal sketch assertions this proposal implies global binocular combination rules using principles of figural continuity and cross channel correspondence to disambiguate local matches found independently within spatial frequency channels exploratory small scale computational experiments with stereo algorithms based on these rules are described and found to be successful in dealing with a variety of stereo inputs the constraints presented by objects which are exploited by these algorithms are discussed

surfaces from stereo integrating feature matching disparity estimation and contour detection an approach is described that integrates the processes of feature matching contour detection and surface interpolation to determine the three dimensional distance or depth of objects from a stereo pair of images integration is necessary to ensure that the detected surfaces are smooth surface interpolation takes into account detected occluding and ridge contours in the scene interpolation is performed within regions enclosed by these contours planar and quadratic patches are used as local models of the surface occluded regions in the image are identified and are not used for matching and interpolation a coarse to fine algorithm is presented that generates a multiresolution hierarchy of surface maps one at each level of resolution experimental results are given for a variety of stereo images

logical linear operators for image curves we propose a language for designing image measurement operators suitable for early vision we refer to them as logical linear l l operators since they unify aspects of linear operator theory and boolean logic a family of these operators appropriate for measuring the low order differential structure of image curves is developed these l l operators are derived by decomposing a linear model into logical components to ensure that certain structural preconditions for the existence of an image curve are upheld tangential conditions guarantee continuity while normal conditions select and categorize contrast profiles the resulting operators allow for coarse measurement of curvilinear differential structure orientation and curvature while successfully segregating edge and line like features by thus reducing the incidence of false positive responses these operators are a substantial improvement over thresholded linear operators which attempt to resolve the same class of features

the complexity of three way statistical tables multiway tables with specified marginals arise in a variety of applications in statistics and operations research we provide a comprehensive complexity classification of three fundamental computational problems on tables existence counting and entry security one outcome of our work is that each of the following problems is intractable already for slim 3 tables with constant number 3 of rows 1 deciding existence of 3 tables with specified 2 marginals 2 counting all 3 tables with specified 2 marginals 3 deciding whether a specified value is attained in a specified entry by at least one of the 3 tables having the same 2 marginals as a given table this implies that a characterization of feasible marginals for such slim tables sought by much recent research is unlikely to exist another consequence of our study is a systematic efficient way of embedding the set of 3 tables satisfying any given 1 marginals and entry upper bounds in a set of slim 3 tables satisfying suitable 2 marginals with no entry bounds this provides a valuable tool for studying multi index transportation problems and multi index transportation polytopes remarkably it enables us to automatically recover a famous example due to vlach of a real feasible integer infeasible collection of 2 marginals for 3 tables of smallest possible size 3 4 6

the local structure of image discontinuities in one dimension the detailed structure of intensities in the local neighborhood of an edge can often indicate the nature of the physical event givinig rise to that edge we argue that the limit as we approach arbitrarily close to either side of an edge of such image parameters as type of texture texture gradient color appropriate directional derivatives of intensity etc is a key aspect of this structure however the general problem of capturing this local structure is surprisingly complex thus we restrict ourselves in this paper to a relatively simple domain one dimensional cuts through idealized images modeled by piecewise smooth c1 functions corrupted by gaussian noise within this domain we define local structure to be the limit of the uncorrupted intensity and of its derivatives as we approach arbitrarily close to either side of a discontinuity we develop a technique that captures this local structure while simultaneously locating the discontinuities and demonstrate that these tasks are in fact inseparable the technique is an extension using estimation theory of the classical definition of discontinuity it handles in a consistent fashion both jump discontinuities in the function and jump discontinuities in its first derivative so called step edges are a special case of the former and roof edges of the latter it also integrates again in a consistent fashion information derived from a number of different neighborhood sizes

two perfectly bonded dissimilar orthotropic strips with an interfacial crack normal to the boundaries the problem of an interface crack between two bonded dissimilar semi infinitely long orthotropic strips of finite width is analyzed under arbitrary anti plane shear loading by using the finite fourier transform technique the mixed boundary value problem is reduced to triple series equations which are then transformed to a singular integral equation for the case of either stress free or clamped boundaries the solutions to the problem are obtained in closed form respectively in particular explicit expressions for stress field and further stress intensity factors at each crack tip are determined for uniform anti plane shear loading some the well known results can be taken as the special cases of the present results

surface parametrization and curvature measurement of arbitrary 3 d objects five practical methods curvature sampling of arbitrary fully described 3 d objects e g tomographic medical images is difficult because of surface patch parameterization problems five practical solutions are presented and characterized the sander zucker approach two novel methods based on direct surface mapping a piecewise linear manifold technique and a turtle geometry method one of the new methods called the cross patch cp method is shown to be very fast robust in the presence of noise and is always based on a proper surface parameterization provided the perturbations of the surface over the patch neighborhood are isotropically distributed

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

sets of uniqueness and minimal matrices abstract in this note we give an algebraic characterization of sets of uniqueness in terms of matrices with non negative integer coefficients and prescribed row and column sums and of the dominance order of partitions or majorization our proof uses some identities involving characters of the symmetric group as an application we describe all sets of uniqueness contained in the box b 2 2 r for all r

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

constructing simple stable descriptions for image partitioning a new formulation of the image partitioning problem is presented construct a complete and stable description of an image in terms of a specified descriptive language that is simplest in the sense of being shortest we show that a descriptive language limited to a low order polynomial description of the intensity variation within each region and a chain code like description of the region boundaries yields intuitively satisfying partitions for a wide class of images the advantage of this formulation is that it can be extended to deal with subsequent steps of the image understanding problem or to deal with other attributes such as texture in a natural way by augmenting the descriptive language experiments performed on a variety of both real and synthetic images demonstrate the superior performance of this approach over partitioning techniques based on clustering vectors of local image attributes and standard edge detection techniques

correspondence problem in image sequence analysis abstract an algorithm to address the correspondence problem in image sequence analysis is proposed the underlying philosophy of this algorithm is reductionist and is based on the assertion that measurements pertaining to motion that are obtained from the whole image sequence must be very similar to the measurements that are obtained from corresponding portions of the image sequence the algorithm has been extensively tested on synthesized data as well as on real image sequences it appears that the assumption underlying the proposed algorithm is quite useful and applicable to a large class of images the proposed algorithm has a high degree of inherent parallelism and is thus suited for implementation on parallel machines

analysis of perfectly bonded wedges and bonded wedges with an interfacial crack under antiplane shear loading antiplane shear deformation of perfectly bonded wedges as well as bonded wedges with an interface crack are studied in this paper the solution of governing differential equations is accomplished by means of the mellin transform for two edge bonded isotropic wedges with perfect bonding along the common edge closed form solutions are obtained for stress fields and analytical relations are given for the strength of singularity at the apex however for bonded wedges with an interfacial crack first it is necessary to express the traction free condition of the crack faces in the form of a singular integral equation which is done in this paper by describing an exact analytical method the resultant singular integral equations are then solved analytically and the obtained results including the stress intensity factors at the crack tips are plotted a comparison of the results in the special cases shows a complete agreement with those cited in the literature however when the crack tip coincides with the wedge apex a strength of singularity of unity has been observed

the classification of minimal matrices of size 2 q abstract minimal matrices were introduced to give an algebraic characterization of sets of uniqueness a notion of interest in discrete tomography they have also been used to produce minimal summands in kronecker products of complex irreducible characters of the symmetric group in this paper motivated by these two applications we classify all minimal matrices of size 2 q

on the algorithmic inversion of the discrete radon transform the present paper deals with the computational complexity of the discrete inverse problem of reconstructing finite point sets and more general functionals with finite support that are accessible only through some of the values of their discrete radon transform it turns out that this task behaves quite differently from its well studied companion problem involving 1 dimensional x rays concentrating on the case of coordinate hyperplanes in rd and on functionals zd d with d 0 1 r n0 for some arbitrary but fixed r we show in particular that the problem can be solved in polynomial time if information is available for m such hyperplanes when m d 1 but is np hard for m d and d 0 1 r however for d n0 a case that is relevant in the context of contingency tables the problem is still in p similar results are given for the task of determining the uniqueness of a given solution and for a related counting problem

darboux frames snakes and super quadrics geometry from the bottom up a representational and a computational model for deriving 3 d articulated volumetric descriptions of objects from laser rangefinder data is described this method is purely bottom up it relies on general assumptions cast in terms of differential geometry darboux frames snakes and superquadrics form the basis of this representation and curvature consistency provides the computational framework the organization is hierarchical darboux frames are used to describe the local surface whereas snakes are used to interpolate between features particularly those that serve to partition a surface into its constituent parts superquadrics are used to characterize the 3 d shape of each surface partition the result is a set of connected volumetric primitives that serve to describe the overall shape of an object examples that show how the approach performs on data acquired with a laser rangefinder are included

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

shape from patterns regularization we present a theory for the recovery of the shape of a surface covered with small elements texels the theory is based on the apparent surface pattern distortion in the image and fits the regularization paradigm recently introduced in computer vision by poggio et al 1985 a mapping is defined on the basis of measurement of the local distortions of a repeated unknown texture pattern due to the image projection from this a constraint on the gradient orientation is determined from the apparent area of a texture element the analysis is done under an approximation of the perspective projection called paraperspective the resulting algorithm is applied to several synthetic and real images to demonstrate its performance

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

intravital leukocyte detection using the gradient inverse coefficient of variation the problem of identifying and counting rolling leukocytes within intravital microscopy is of both theoretical and practical interest currently methods exist for tracking rolling leukocytes in vivo but these methods rely on manual detection of the cells in this paper we propose a technique for accurately detecting rolling leukocytes based on bayesian classification the classification depends on a feature score the gradient inverse coefficient of variation gicov which serves to discriminate rolling leukocytes from a cluttered environment the leukocyte detection process consists of three sequential steps the first step utilizes an ellipse matching algorithm to coarsely identify the leukocytes by finding the ellipses with a locally maximal gicov in the second step starting from each of the ellipses found in the first step a b spline snake is evolved to refine the leukocytes boundaries by maximizing the associated gicov score the third and final step retains only the extracted contours that have a gicov score above the analytically determined threshold experimental results using 327 rolling leukocytes were compared to those of human experts and currently used methods the proposed gicov method achieves 78 6 leukocyte detection accuracy with 13 1 false alarm rate

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

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

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

interpreting line drawings as three dimensional surfaces understanding how line drawings convey tri dimensionality is of fundamental importance in explaining surface perception when photometry is either uninformative or too complex to model analytically we put forward here a computational model for interpreting line drawings as three dimensional surfaces based on constraints on local surface orientation along extremal and discontinuity boundaries specific techniques are described for two key processes recovering the three dimensional conformation of a space curve e g a surface boundary from its two dimensional projection in an image and interpolating smooth surfaces from orientation constraints along extremal boundaries the relevance of the model to a general theory of low level vision is discussed

majorization permutahedra and 0 1 matrices a majorization permutahedron m v is a polytope associated with a majorization x v in rn defined by m v x rn x v several properties of these polytopes are investigated and a connection to discrete convexity is established these results are used to obtain a generalization of the gale ryser theorem for 0 1 matrices with given line sums

directional quasi convexity asymmetric schur convexity and optimality of consecutive partitions the current paper has the following distinct goals 1 to generalize standard quasi convexity to obtain a weaker property of functions that suffices for optimality of extreme points specifically it is required that intersections of the level sets of the function with line segments having direction in a prescribed set are convex 2 to characterize schur convexity for symmetric functions through the above generalization of quasi convexity thereby obtaining a previously unknown relationship of schur convexity and standard convexity the new characterization is used to extend the definition of schur convexity to functions which are not symmetric 3 to obtain new sufficient conditions for the optimality of consecutive partitions by using the new definition of schur convexity for functions that are not necessarily symmetric the conclusion that schur convexity is an instance of a convexity property that implies the optimality of extreme points unifies two approaches that were used in the literature to prove optimality of subsets of the domain of real valued functions the two tools quasi convexity and schur convexity were previously considered as distinct techniques

the topology of boundaries abstract high level representations used in reasoning distinguish a special set of boundary locations at which function values can change abruptly and across which adjacent regions may not be connected standard models of space and time based on segmenting r n do not allow these possibilities because they have the wrong topological structure at boundaries this mismatch has made it difficult to develop formal mathematical models for high level reasoning algorithms this paper shows how to modify an r n model so as to have an appropriate topological structure it then illustrates how the new models support standard reasoning algorithms provide simple models for previously difficult situations and suggest interesting new analyses based on change or non change in scene topology

edge junction and corner detection using color distributions for over 30 years 1970 2000 researchers in computer vision have been proposing new methods for performing low level vision tasks such as detecting edges and corners one key element shared by most methods is that they represent local image neighborhoods as constant in color or intensity with deviations modeled as noise due to computational considerations that encourage the use of small neighborhoods where this assumption holds these methods remain popular the research presented models a neighborhood as a distribution of colors the goal is to show that the increase in accuracy of this representation translates into higher quality results for low level vision tasks on difficult natural images especially as neighborhood size increases we emphasize large neighborhoods because small ones often do not contain enough information we emphasize color because it subsumes gray scale as an image range and because it is the dominant form of human perception we discuss distributions in the context of detecting edges corners and junctions and we show results for each

on the problem of correspondence in range data and some inelastic uses for elastic nets in this work the authors propose a novel method to obtain correspondence between range data across image frames using neural like mechanisms the method is computationally efficient and tolerant of noise and missing points elastic nets which evolved out of research into mechanisms to establish ordered neural projections between structures of similar geometry are used to cast correspondence as an optimization problem this formulation is then used to obtain approximations to the motion parameters under the assumption of rigidity inelasticity these parameter scan be used to recover correspondence experimental results are presented to establish the veracity of the scheme and the method is compared to earlier attempts in this direction

an algebraic approach to shape from image problems abstract this paper presents a new method for recovering three dimensional shapes of polyhedral objects from their single view images the problem of recovery is formulated in a constrained optimization problem in which the constraints reflect the assumption that the scene is composed of polyhedral objects and the objective function to be minimized is a weighted sum of quadric errors of surface information such as shading and texture for practical purpose it is decomposed into the two more tractable problems a linear programming problem and an unconstrained optimization problem in the present method the global constraints placed by the polyhedron assumption are represented in terms of linear algebra whereas similar constraints have usually been represented in terms of a gradient space moreover superstrictness of the constraints can be circumvented by a new concept position free incidence structure for this reason the present method has several advantages it can recover the polyhedral shape even if image data are incorrect due to vertex position errors it can deal with perspective projection as well as orthographic projection the number of variables in the optimization problem is very small three or a little greater than three and any kinds of surface information can be incorporated in a unifying manner

significant edges in the case of non stationary gaussian noise in this paper we propose an edge detection technique based on some local smoothing of the image followed by a statistical hypothesis testing on the gradient an edge point being defined as a zero crossing of the laplacian it is said to be a significant edge point if the gradient at this point is larger than a threshold s e defined by if the image i is pure noise then the probability of email protected i x s e conditionally on di x 0 is less than e in other words a significant edge is an edge which has a very low probability to be there because of noise we will show that the threshold s e can be explicitly computed in the case of a stationary gaussian noise in the images we are interested in which are obtained by tomographic reconstruction from a radiograph this method fails since the gaussian noise is not stationary anymore nevertheless we are still able to give the law of the gradient conditionally on the zero crossing of the laplacian and thus compute the threshold s e we will end this paper with some experiments and compare the results with those obtained with other edge detection methods