3d structure recovery and unwarping of surfaces applicable to planes the deformation of applicable surfaces such as sheets of paper satisfies the differential geometric constraints of isometry lengths and areas are conserved and vanishing gaussian curvature we show that these constraints lead to a closed set of equations that allow recovery of the full geometric structure from a single image of the surface and knowledge of its undeformed shape we show that these partial differential equations can be reduced to the hopf equation that arises in non linear wave propagation and deformations of the paper can be interpreted in terms of the characteristics of this equation a new exact integration of these equations is developed that relates the 3 d structure of the applicable surface to an image the solution is tested by comparison with particular exact solutions we present results for both the forward and the inverse 3d structure recovery problem

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

surface reconstruction using deformable models with interior and boundary constraints the authors introduce a technique for 3d surface reconstruction using elastic deformable models the model used is an imaginary elastic grid which is made of membranous thin plate type material the elastic grid can bent twisted compressed and stretched into any desired 3d shape which is specified by the shape constraints derived automatically from images of a real 3d object shape reconstruction is guided by a set of imaginary springs that enforce the consistency in the position orientation and or curvature measurements of the elastic grid and the desired shape the dynamics of a surface reconstruction process is regulated by hamilton s principle or the principle of the least action furthermore a 1d deformable template that borders the elastic grid may be used this companion boundary template is attracted repelled by image forces to conform with the silhouette of the imaged object implementation results using simple analytic shapes and images of real objects are presented

convergence of two point pade approximants to series of stieltjes abstract in this paper we study the convergence of two point pade approximants to stieltjes series a carleman type condition given by gragg 1980 in the context of convergence theory for continued fractions is here established in the framework of orthogonal laurent polynomials jones njastad and thron 1984 jones and thron 1981 njastad and thron 1983 1986 a bound for the error is also given

two point pade approximants for the expansions of stieltjes functions in real domain the fundamental inequalities for the sequences of subdiagonal and diagonal one point pade approximants to stieltjes function has been extended to the case of certain two point pade approximants the results can be applied to the theory of inhomogeneous media for calculating the bounds for the effective transport coefficients of two components heterogeneous materials

the numerical viscosity of entropy stable schemes for systems of conservation laws i discrete approximations to hyperbolic systems of conservation laws are studied the amount of numerical viscosity present in such schemes is quantified and related to their entropy stability by means of comparison to this end conservative schemes which are also entropy conservative are constructed these entropy conservative schemes enjoy second order accuracy moreover they can be interpreted as piecewise linear finite element methods and hence can be formulated on various mesh configurations it is then shown that conservative schemes are entropy stable if and for three point schemes only they contain more viscosity than that present in the above mentioned entropy conservative ones

incremental model building of polyhedral objects using structured light abstract a vision method using active sensing to construct the complete geometric model of a polyhedral object is presented the model is constructed incrementally from multiple views each view produces a partial object model three different methods are described for integrating all the partial models into a final complete model theorems regarding the sufficient number of views required and how these views can be set up during the reconstruction process are also given from theoretical analysis and experimental results our method is shown to produce an accurate object geometric model not just an approximate model furthermore it does not rely on a precise object to image space transformation moreover the method is fast and robust since the basic geometric entity it derives is a face instead of a point

representation and shape matching of 3 d objects a three dimensional scene analysis system for the shape matching of real world 3 d objects is presented various issues related to representation and modeling of 3 d objects are addressed a new method for the approximation of 3 d objects by a set of planar faces is discussed the major advantage of this method is that it is applicable to a complete object and not restricted to single range view which was the limitation of the previous work in 3 d scene analysis the method is a sequential region growing algorithm it is not applied to range images but rather to a set of 3 d points the 3 d model of an object is obtained by combining the object points from a sequence of range data images corresponding to various views of the object applying the necessary transformations and then approximating the surface by polygons a stochastic labeling technique is used to do the shape matching of 3 d objects the technique matches the faces of an unknown view against the faces of the model it explicitly maximizes a criterion function based on the ambiguity and inconsistency of classification it is hierarchical and uses results obtained at low levels to speed up and improve the accuracy of results at higher levels the objective here is to match the individual views of the object taken from any vantage point details of the algorithm are presented and the results are shown on several unknown views of a complicated automobile casting

characterizing three dimensional surface structures from visual images a new technique for computing intrinsic surface properties is presented intrinsic surface properties are those properties of a surface that are not affected by the choice of the coordinate system the position of the viewer relative to the surface and the particular parametric representation used to describe the imaged surface since intrinsic properties are characteristics of a surface they are ideal for the purposes of representation and recognition the intrinsic properties of interest are the principal curvatures the gaussian curvatures and the lines of curvature it is proposed that a structured light sensing configuration where a grid pattern is projected to encode the imaged surfaces for analysis be adopted at each stripe junction the curvatures of the projected stripes on the imaged surface are computed and related to those of the normal sections that share the same tangential directional as the projected curves the principal curvatures and their directions at the stripe junction under consideration are then recovered using euler s theorem results obtained using both synthetic and real images are presented

determining surface orientation by projecting a stripe pattern a method is presented for determining the surface orientations of an object by projecting a stripe pattern on to it assuming orthographical projection as a camera model and parallel light projection of the stripe pattern the method obtains a 2 1 2 d representation of objects by estimating surface normals from the slopes and intervals of the stripes in the image the 2 1 2 d image is further divided into planar or singly curved surfaces by examining the distribution of the surface normals in gradient space a simple application to finding a planar surface and determining its orientation and shape is shown the error in surface orientation is discussed

error analysis of 3d shape construction from structured lighting abstract in this paper we present a detailed model and analysis of several error sources and thier effects on measuring three dimensional 3d surface properties using the structured lighting technique the analysis is based on a general system configuration and identifies three types of error surces system modeling error image processing error and experimental error absolute and relative error bounds in obtaining 3d surface orientation and curvature measurements using structured lighting are derived in terms of the system parameters and likely error sources in addition to the quantization error other likely error sources in system modeling and experimental setup are also considered even though our analysis is on structured lighting the results are readily applicable to other triangulation based techniques such as stereopsis finally our analysis focuses on error in inferring surface orientation and principal surface curvature such analyses to our knowledge have never been attempted before

two point pade expansions for a family of analytic functions abstract each member g z of a family of analytic functions defined by stieltjes transforms is shown to be represented by a positive t fraction the approximants of which form the main diagonal in the two point pade table of g z the positive t fraction is shown to converge to g z throughout a domain d a b z z b a uniformly on compact subsets in addition truncation error bounds are given for the approximants of the continued function these bounds supplement previously known bounds and apply in part of the domain of g z not covered by other bounds the proofs of our results employ properties of orthogonal l polynomials laurent polynomials and l gaussian quadrature which are of some interest in themselves a number of examples are considered

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

surface orientation from a projected grid two simple methods are given for obtaining the surface shape using a projected grid after the camera is calibrated to the 3 d workspace the only input date needed for the computation of surface normals are grid intersect points in a single 2 d image the first method performs nonlinear computations based on the distortion of the lengths of the grid edges and does not require a full calibration matrix the second method requires that a full parallel projection model of the imaging is available which enables it to compute 3 d normals using simple linear computations the linear method performed better overall in the experiments but both methods produced normals within 4 8 degrees of known 3 d directions these methods appear to be superior to methods based on shape from shading because the results are comparable yet the equipment setup is simpler and the processing is not very sensitive to object reflectance

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

a modified fractional step method for the accurate approximation of detonation waves the numerical approximation of combustion processes may lead to numerical difficulties which are caused by different time scales of the transport part and the reactive part of the model equations here we consider a modified fractional step method that overcomes this difficulty on standard test problems and allows the use of a mesh width and time step determined by the nonreactive part without precisely resolving the very small reaction zone high resolution godunov methods are employed and the structure of the riemann solution is used to determine where burning should occur in each time step the modification is implemented in the software package clawpack numerical results for 1d and 2d detonation waves are shown including a detonation wave diffracting around a corner

structured light using pseudorandom codes we solve the correspondence problem in active stereo vision using a novel pseudorandom coded structured light sl this coding scheme performs well in the presence of occlusion in settings where color coding is feasible 3d information can be obtained using a single image

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

implicit explicit schemes for flow equations with stiff source terms in this paper we design stable and accurate numerical schemes for conservation laws with stiff source terms a prime example and the main motivation for our study is the reactive euler equations of gas dynamics furthermore we consider widely studied scalar model equations we device one step imex implicit explicit schemes for these equations that treats the convection terms explicitly and the source terms implicitly for the non linear scalar equation we use a novel choice of initial data for the resulting newton solver and obtain correct propagation speeds even in the difficult case of rarefaction initial data for the reactive euler equations we choose the numerical diffusion suitably in order to obtain correct wave speeds on under resolved meshes we prove that our implicit explicit scheme converges in the scalar case and present a large number of numerical experiments to validate our scheme in both the scalar case as well as the case of reactive euler equations furthermore we discuss fundamental differences between the reactive euler equations and the scalar model equation that must be accounted for when designing a scheme

the visual interpretation of surface contours this article examines the computational problems underlying the 3 d interpretation of surface contours a surface contour is the image of a curve across a physical surface such as the edge of a shadow cast across a surface a gloss contour wrinkle seam or pigmentation marking surface contours by and large are not as restricted as occluding contours and therefore pose a more difficult interpretation problem nonetheless we are adept at perceiving a definite 3 d surface from even simple line drawings e g graphical depictions of continuous functions of two variables the solution of a specific surface shape comes by assuming that the physical curves are particularly restricted in their geometric relationship to the underlying surface these geometric restrictions are examined

asymptotic studies of closely spaced highly conducting cylinders we consider the solution of the scalar transport problem for a pair of nearly touching cylinders of high conductivity we obtain an expression for the set of multipole moments of the potential distribution for this problem in terms of the hypergeometric function we apply this expression in the estimation of truncation errors occurring in the matrix solution of the corresponding transport problem for the square array of cylinders consequently we are able to calculate the array transport coefficient for arbitrarily high cylinder conductivities and arbitrarily small cylinder separations we derive and verify an expression for this coefficient which is uniformly valid throughout the whole asymptotic region when highly conducting cylinders approach touching

continued fractions two point pade approximants and errors in the stieltjes case a stieltjes function is expanded in mixed t and s continued fraction the relations between approximants of this continued fraction and two point pade approximants are established the method used by gilewicz and magnus j comput appl math 49 1993 79 integral transforms special functions 1 1993 9 has been adapted to obtain the exact relations between the errors of the contiguous two point pade approximants in the whole cut complex plane

n point pade approximants to real valued stieltjes series with nonzero radii of convergence abstract by employing special continued fractions to two stieltjes series with nonzero radii of convergence we extend the inequalities for one point pade approximants reported by baker 1975 corollory 17 1 to the case of two point pade approximants we prove that some convergents of the continued fractions form a monotone sequences of upper and lower bounds converging uniformly to stieltjes function x1 x on compact subsets of r where r is a radius of convergence of an expansion of x f1 x at x 0 for an illustration of theoretical results we provide nontrivial numerical examples as an application to real physical problems second order pade approximants bounds on the effective conductivity of a square array of cylinders are evaluated

detection of rotationally symmetric shape orientations by fold invariant shape specific points abstract two new types of shape specific points called fold invariant centroid fic and fold invariant radius weighted mean firwm are introduced for detecting the orientations of rotationally symmetric shapes a given rotationally symmetric shape is first transformed into a new fold invariant shape the centroid and the radius weighted mean of the new shape are then transformed back to obtain the proposed fic and firwm respectively fic and firwm points are proved to be invariant to translation rotation and scaling and so can be used for matching rotationally symmetric shapes using the proposed fold invariant shape specific points to detect the orientations of rotationally symmetric shapes is easier to implement than that of using the fold principal axes some illustrative examples and a method to avoid the case where the proposed fold invariant shape specific points are too close to the centroid are also given

a posteriori error analysis of imex multi step time integration methods for advection diffusion reaction equations abstract implicit explicit imex schemes are an important and widely used class of time integration methods for both parabolic and hyperbolic partial differential equations we develop accurate a posteriori error estimates for a user defined quantity of interest for two classes of multi step imex schemes for advection diffusion reaction problems the analysis proceeds by recasting the imex schemes into a variational form suitable for a posteriori error analysis employing adjoint problems and computable residuals the a posteriori estimates quantify distinct contributions from various aspects of the spatial and temporal discretizations and can be used to evaluate discretization choices numerical results are presented that demonstrate the accuracy of the estimates for a representative set of problems

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

zero reaction limit for hyperbolic conservation laws with source terms abstract in this paper we study the zero reaction limit of the hyperbolic conservation law with stiff source term t u x f u 1 e u 1 u 2 for the cauchy problem to the above equation we prove that as e 0 its solution converges to piecewise constant 1 solution where the two constants are the two stable local equilibria the constants are separated by either shocks that travel with speed 1 2 f 1 f 1 as determined by the rankine hugoniot jump condition or a non shock discontinuity that moves with speed f 0 where 0 is the unstable equilibrium our analytic tool is the method of generalized characteristics similar results for more general source term 1 e g u having finitely many simple zeros and satisfying ug u

bounds for effective parameters of heterogeneous media by analytic continuation we give a mathematical formulation of a method for obtaining bounds on effective parameters developed by d bergman and g w milton this method in contrast to others used before does not rely on a variational principle but exploits the properties of the effective parameter as an analytic function of the component parameters the method is at present restricted to two component media