invariant properties of straight homogeneous generalized cylinders and their contours a fundamental group in computer vision is the recovery of three dimensional shape from image data while this problem is in general underconstrained the authors show that it can be simplified in the case where the objects being viewed are generalized cylinders they consider the class of straight homogeneous generalized cylinders shgcs without any further assumption on the viewing direction or the precise shape of these objects they present a rigorous mathematical study of the geometry of shgcs and characterize their gaussian curvature and occluding contours and use these results to prove several new invariant properties of the contours of shgcs these properties are in turn used in two implemented algorithms for recovering shgc descriptions from image contours several examples of segmentation of real images are given other applications are also discussed

surface shape from the deformation of apparent contours the spatiotemporal analysis of deforming silhouettes apparent contours is here extended using the mathematics of perspective projections and tools from differential geometry analysis of the image motion of a silhouette or apparent contour enables computation of local surface curvature along the corresponding contour generator on the surface assuming viewer motion is known to perform the analysis a spatiotemporal parameterization of image curve motion is needed but is underconstrained a manifestation of the well known aperture problem it is shown that an epipolar parameterization is most naturally matched to the recovery of surface curvature

automatic model construction and pose estimation from photographs using triangular splines this paper addresses the automatic construction of complex spline object models from a few photographs our approach combines silhouettes from registered images to construct a g sup 1 continuous triangular spline approximation of an object with unknown topology we apply a similar optimization procedure to estimate the pose of a modeled object from a single image experimental examples of model construction and pose estimation are presented for several complex objects

majorizations of hadamard products of matrix powers abstract this paper presents a number of intervening terms for the weak majorization i k n i a b i k n i ab for k 1 2 n where a b 0 more specifically it proves for r 0 1 that i k n i a b i k n i 1 r a r b r i k n e i l log a log b i k n e i log a log b i k n i 1 r a r b r i k n i ab for k 1 n it also shows that behind many of these inequalities are stronger ones

perceptual grouping for generic recognition we address the problem of recognition of generic objects from a single intensity image this precludes the use of purely geometric methods which assume that models are geometrically and precisely designed instead we propose to use descriptions in terms of features and their qualitative geometric relationships to succeed it is clear that these features need to be high level rather than points or lines we propose to detect groups using perceptual organization criteria such as proximity symmetry parallelism and closure the detection of these features is performed in an efficient way using proximity indexing since many groups are created we also perform selection of relevant groups by organizing them into sets of similar perceptual content finally we present an implementation of a recognition system using these sets as primitives it is an efficient colored graph matching algorithm using the adjacency matrix representation of a graph using indexing we retrieve matching hypotheses which are verified against each other with respect to topological constraints groups of consistent hypotheses represent detected model instances in a scene the complete system is illustrated on real images we also discuss further extensions

a weak majorization involving the matrices a b and ab abstract let a and b be n n positive definite matrices and let the eigenvalues of a b and ab be arranged in decreasing order then for all r 0 i k n i r ab i k n i r a b for k 1 n furthermore it is shown that i k n i r a b i k n i r ab for k 1 n is a limiting case of the weak majorization above which settles a conjecture of bapat and johnson

a comparison of acceleration procedures for the two dimensional periodic green s function alternate acceleration procedures are evaluated for the two dimensional free space periodic green s function two of these techniques yield exponential convergence rates and are preferable if high accuracies are required numerical aspects of these procedures are described

efficient computation of the 2 d green s function for 1 d periodic structures using the ewald method the ewald method is applied to accelerate the evaluation of the green s function of an infinite periodic phased array of line sources the ewald representation for a cylindrical wave is obtained from the known representation for the spherical wave and a systematic general procedure is applied to extend previous results only a few terms are needed to evaluate ewald sums which are cast in terms of error functions and exponential integrals to high accuracy singularities and convergence rates are analyzed and a recipe for selecting the ewald splitting parameter spl epsiv is given to handle both low and high frequency ranges indeed it is shown analytically that the choice of the standard optimal splitting parameter spl epsiv sub 0 will cause overflow errors at high frequencies numerical examples illustrate the results and the sensitivity of the ewald representation to the splitting parameter spl epsiv

an efficient approach for the computation of 2 d green s functions with 1 d and 2 d periodicities in homogeneous media this paper presents an algorithm for the acceleration of the series involved in the computation of 2 d homogeneous green s functions with 1 d and 2 d periodicities the algorithm is based on an original implementation of the spectral kummer poisson s method and it can be applied to the efficient computation of a wide class of infinite series in the algorithm the number of asymptotic terms retained in kummer s transformation is externally controlled so that any of the series that has to be accelerated is split into one series with exponential convergence and another series with algebraic convergence of arbitrarily large order numerical simulations have shown that there is an ldquooptimumrdquo number of asymptotic terms retained in kummer s transformation for which the cpu time needed in the summation of the series is minimized the cpu times required by ewald s method for the evaluation of 2 d green s functions with 1 d and 2 d periodicities have been compared with those required by the present algorithm and the algorithm has been found to be between 1 2 and 3 times faster than ewald s method when working in ldquooptimumrdquo operation conditions

majorization relations for hadamard products abstract we settle affirmatively the conjecture of johnson and bapat on the hadamard product a b of positive definite matrices a b i k n i a b ab k 1 2 n

full volumetric descriptions from three intensity images we address the problem of recovering high level volumetric and segmented or part based descriptions of objects from intensity images as input we use three closely spaced images of an object and recover descriptions based on generalized cylinders gcs we start by extracting a hierarchy of groups from contour images in the three views grouping is based on proximity parallelism and symmetry the groups in the three views are matched and their contours are labeled as true edges we then infer the gc axis its cross section and the scaling function the cross section is recovered if seen in the images else it is inferred using the visible surfaces and gc properties we consider groups with true edges limb edges or a combination of both the coarse volumetric descriptions obtained are refined to include surface details as seen in the intensity images we demonstrate results on real images of moderately complex objects with texture and shadows

epipolar plane image analysis an approach to determining structure from motion we present a technique for building a three dimensional description of a static scene from a dense sequence of images these images are taken in such rapid succession that they form a solid block of data in which the temporal continuity from image to image is approximately equal to the spatial continuity in an individual image the technique utilizes knowledge of the camera motion to form and analyze slices of this solid these slices directly encode not only the three dimensional positions of objects but also such spatiotemporal events as the occlusion of one object by another for straight line camera motions these slices have a simple linear structure that makes them easier to analyze the analysis computes the three dimensional positions of object features marks occlusion boundaries on the objects and builds a three dimensional map of free space in our article we first describe the application of this technique to a simple camera motion and then show how projective duality is used to extend the analysis to a wider class of camera motions and object types that include curved and moving objects

an efficient numerical evaluation of the green s function for the helmholtz operator on periodic structures abstract numerical methods which are based on boundary integral formulations require the numerical evaluation of the green s function associated with the problem in the case of periodic structures the green s function is often an infinite series this infinite series may converge slowly making numerical evaluation expensive here we present a practical computer implementation of a technique which dramatically speeds up the convergence of the infinite series green s function associated with the helmholtz operator to show the consequences of using this technique we include some numerical examples

efficient computation of the 3d green s function for the helmholtz operator for a linear array of point sources using the ewald method the ewald method is applied to accelerate the evaluation of the green s function gf of an infinite equispaced linear array of point sources with linear phasing only a few terms are needed to evaluate ewald sums which are cast in terms of error functions and exponential integrals to high accuracy it is shown analytically that the choice of the standard optimal ewald splitting parameter e0 causes overflow errors at high frequencies period large compared to the wavelength and convergence rates are analyzed a recipe for selecting the ewald splitting parameter is provided

rapidly convergent representations for 2d and 3d green s functions for a linear periodic array of dipole sources hybrid spectral spatial representations are introduced to rapidly calculate periodic scalar and dyadic green s functions of the helmholtz equation for 2d and 3d configurations with a 1d linear periodicity the presented schemes work seamlessly for any observation location near the array and for any practical array periodicities including electrically small and large periodicities the representations are based on the expansion of the periodic green s functions in terms of the continuous spectral integrals over the transverse to the array spectral parameters to achieve high convergence and numerical efficiency the introduced integral representations are cast in a hybrid form in terms of i a small number of contributions due to sources located around the unit cell of interest ii a small number of symmetric combinations of the floquet modes and iii an integral evaluated along the steepest descent path sdp the sdp integral is regularized by extracting the singular behavior near the saddle point of the integrand and integrating the extracted components in closed form efficient quadrature rules are established to evaluate this integral using a small number of quadrature nodes with arbitrary small error for a wide range of structure parameters strengths of the introduced approach are demonstrated via extensive numerical examples

shape from contour straight homogeneous generalized cylinders and constant cross section generalized cylinders we analyze the properties of straight homogeneous generalized cylinders shgcs and constant cross section generalized cylinders cgcs and derive the types of symmetries that the limb boundaries and cross sections of these objects produce on the image plane the constraints on the 3d shape of the objects are formulated based on the symmetries and from the geometry of the projection models finally the methods that recover the 3d shape from the image of their contours are discussed and recovered surfaces are shown for sample objects

1 d periodic green s function for leaky and complex waves using the ewald method the ewald method for evaluating the free space 1 d periodic green s function is extended to leaky waves by allowing for complex wavenumbers it is shown that care must be taken when choosing the path of integration in the complex plane in the derivation of the ewald method in order to obtain solutions that correspond to physical leaky wave solutions the use of different paths results in an evaluation of the ewald method using an analytical continuation of the exponential integral function previously used when the wavenumber is real the extension of the ewald method to complex wavenumbers allows for the treatment of practical periodic leaky wave antennas and periodic guiding structures with losses as well as metamaterials including 1 d chains of plasmonic nanoparticles

uniqueness and estimation of three dimensional motion parameters of rigid objects with curved surfaces two main results are established in this paper first we show that seven point correspondences are sufficient to uniquely determine from two perspective views the three dimensional motion parameters within a scale factor for the translations of a rigid object with curved surfaces the seven points should not be traversed by two planes with one plane containing the origin nor by a cone containing the origin second a set of essential parameters are introduced which uniquely determine the motion parameters up to a scale factor for the translations and can be estimated by solving a set of linear equations which are derived from the correspondences of eight image points the actual motion parameters can subsequently be determined by computing the singular value decomposition svd of a 3 3 matrix containing the essential parameters

snakes active contour models a snake is an energy minimizing spline guided by external constraint forces and influenced by image forces that pull it toward features such as lines and edges snakes are active contour models they lock onto nearby edges localizing them accurately scale space continuation can be used to enlarge the capture region surrounding a feature snakes provide a unified account of a number of visual problems including detection of edges lines and subjective contours motion tracking and stereo matching we have used snakes successfully for interactive interpretation in which user imposed constraint forces guide the snake near features of interest

accelerating the convergence of series representing the free space periodic green s function a method for improving the convergence of the series representing the doubly periodic free space green s function is presented the method consists of successively applying three different transformations to the green s function spectral representation kummer s transformation is first applied to convert the slowly converging spectral representation into the sum of a rapidly converging series and a slowly converging series the latter series is recognized as the spectral representation of the original periodic source distribution radiating in a medium with an imaginary wavenumber application of the poisson transformation to this series renders it exponentially convergent since it effectively represents propagation of point source contributions through a medium with imaginary wavenumber finally shanks transform is plotted versus the number of terms taken in the series numerical results confirm that an improvement in the convergence rate of the series is achieved for a particular convergence criterion

lattice sums for the helmholtz equation a survey of different representations for lattice sums for the helmholtz equation is made these sums arise naturally when dealing with wave scattering by periodic structures one of the main objectives is to show how the various forms depend on the dimension d of the underlying space and the lattice dimension d lambda lattice sums are related to and can be calculated from the quasi periodic green s function and this object serves as the starting point of the analysis

rapidly convergent representations for periodic green s functions of a linear array in layered media green s function representations are presented to rapidly compute the fields resulting from a linear 1d periodic array of dipole current sources on or near a planarly layered medium in 2d and 3d space the representation is formulated as spectral integral which accounts for the reflected continuous spectrum of fields and a series that accounts for the discrete spectrum of guided modes it is exponentially convergent for observation points on and near the array axis and surface and for complex phase shifts between periodic unit cells it can be defined on alternate riemann sheets with respect to any of the diffraction modes characterizing the array a complete dyadic green s function is derived to fully account for the reflected fields for all source current orientations this green s function representation can greatly accelerate the simulation of printed 1d periodic structures in optics and microwave engineering

rapidly convergent two dimensional quasi periodic green function throughout the spectrum including wood anomalies we introduce a new methodology based on new quasi periodic green functions which converge rapidly even at and around wood anomaly configurations for the numerical solution of problems of scattering by periodic rough surfaces in two dimensional space as is well known the classical quasi periodic green function ceases to exist at wood anomalies the approach introduced in this text produces fast green function convergence throughout the spectrum on the basis of a certain finite differencing approach and smooth windowing of the classical green function lattice sum the resulting green function convergence is super algebraically fast away from wood anomalies and it reduces to an arbitrarily high user prescribed algebraic order of convergence at wood anomalies

an integral representation of the green function for a linear array of acoustic point sources we present a new algorithm for the evaluation of the quasi periodic green function for a linear array of acoustic point sources such as those arising in the analysis of line array loudspeakers a variety of classical algorithms based on spatial and spectral representations ewald transformation etc have been implemented in the past to evaluate these acoustic fields however as we show these methods become unstable and or impractically expensive as the frequency of use of the sources increases here we introduce a new numerical scheme that overcomes some of these limitations allowing for simulations at unprecedentedly large frequencies the method is based on a new integral representation derived from the classic spatial form and on suitable further manipulations of the relevant integrands to render the integrals amenable to efficient and accurate approximations through standard quadrature formulas we include a variety of numerical results that demonstrate that our algorithm compares favorably with several classical methods both for points close to the line where the poles are located and at high frequencies while remaining competitive with them in every other instance

efficient calculation of the free space periodic green s function electromagnetic scattering from periodic structures can be formulated in terms of an integral equation that has as its kernel a periodic green s function the periodic green s function can be derived as a response to an array of line point sources spatial domain or as a response to series of current sheets spectral domain these responses are a fourier transform pair and are slowly convergent summations the convergence problems in each domain arise from unavoidable singularities in the reciprocal domain a method is discussed to overcome the slow convergence by using the poisson summation formula and summing in a combination of spectral and spatial domains a parameter study is performed to determine an optimum way to weigh the combination of domains simple examples of scattering from a one dimensional array of strips and two dimensional array of plates are used to illustrate the concepts

a robust technique for matching two uncalibrated images through the recovery of the unknown epipolar geometry abstract this paper proposes a robust approach to image matching by exploiting the only available geometric constraint namely the epipolar constraint the images are uncalibrated namely the motion between them and the camera parameters are not known thus the images can be taken by different cameras or a single camera at different time instants if we make an exhaustive search for the epipolar geometry the complexity is prohibitively high the idea underlying our approach is to use classical techniques correlation and relaxation methods in our particular implementation to find an initial set of matches and then use a robust technique the least median of squares lmeds to discard false matches in this set the epipolar geometry can then be accurately estimated using a meaningful image criterion more matches are eventually found as in stereo matching by using the recovered epipolar geometry a large number of experiments have been carried out and very good results have been obtained regarding the relaxation technique we define a new measure of matching support which allows a higher tolerance to deformation with respect to rigid transformations in the image plane and a smaller contribution for distant matches than for nearby ones a new strategy for updating matches is developed which only selects those matches having both high matching support and low matching ambiguity the update strategy is different from the classical winner take all which is easily stuck at a local minimum and also from loser take nothing which is usually very slow the proposed algorithm has been widely tested and works remarkably well in a scene with many repetitive patterns

integral equation based analysis of scattering from 3 d inhomogeneous anisotropic bodies this paper presents an integral equation based scheme to analyze scattering from inhomogeneous bodies with anisotropic electromagnetic properties both the permittivity and permeability are assumed to be generalized tensors requisite integral equations are derived using volume equivalence theorem with the electric and magnetic flux densities being the unknown quantities matrix equations are derived by discretizing these unknowns using three dimensional rao wilton glisson basis functions reduction of the integral equation to a corresponding matrix equation is considerably more involved due to the presence of anisotropy and the use of vector basis function methods for evaluation of the integrals involved in the construction of this matrix is elucidated in detail the method of moments technique is augmented with the fast multipole method and a compression scheme the latter two enable large scale analysis finally several numerical results are presented and compared against analytical solutions to validate the proposed scheme an appendix provides analytical derivations for the formulae that are used to validate numerical method and the necessary formulae that extends the approach presented herein to the analysis of scattering bianisotropic bodies

self calibration of turntable sequences from silhouettes this paper addresses the problem of recovering both the intrinsic and extrinsic parameters of a camera from the silhouettes of an object in a turntable sequence previous silhouette based approaches have exploited correspondences induced by epipolar tangents to estimate the image invariants under turntable motion and achieved a weak calibration of the cameras it is known that the fundamental matrix relating any two views in a turntable sequence can be expressed explicitly in terms of the image invariants the rotation angle and a fixed scalar it will be shown that the imaged circular points for the turntable plane can also be formulated in terms of the same image invariants and fixed scalar this allows the imaged circular points to be recovered directly from the estimated image invariants and provide constraints for the estimation of the imaged absolute conic the camera calibration matrix can thus be recovered a robust method for estimating the fixed scalar from image triplets is introduced and a method for recovering the rotation angles using the estimated imaged circular points and epipoles is presented using the estimated camera intrinsics and extrinsics a euclidean reconstruction can be obtained experimental results on real data sequences are presented which demonstrate the high precision achieved by the proposed method

using extremal boundaries for 3 d object modeling the extremal boundaries of 3 d curved objects are the images of special curves drawn on the object and are called rims they are viewpoint dependent and characterized by the fact that the optical rays of their points are tangential to the surface of the object the mathematics of the relationship between the extremal boundaries and the surface of the object is studied this study makes it possible to design an algorithm for detecting those boundaries in the images that are likely to be extremal once this has been done one can reconstruct the rims and compute the differential properties of the surface of the object along them up to the second order if a qualitative description is sufficient the sign of the gaussian curvature of the surface along the rim can be computed in a much simpler way experimental results are presented on synthetic and real images the work provides a better understanding of the relationship between the apparent and real shape of a 3 d object as well as algorithms for reconstructing the local shape of such an object along the rims

scattering and radiation from by 1 d periodic metallizations residing in layered media an efficient technique is proposed to compute the scattering or radiation from by 1 d periodic structures residing in a layered background medium the technique is based on a mixed potential integral equation mpie combined with the method of moments mom solving for the unknown current density flowing within a unit cell of the periodic structure the formalism requires the knowledge of the pertinent layered medium green s functions with 1 d periodicity here these green s functions are derived in closed form by invoking the perfectly matched layer pml paradigm the stationary phase method is applied to determine the far field of the infinite periodic structure leading to a series of floquet modes in addition approximating this series leads to an efficient technique to estimate the scattering or radiation from by large but finite periodic structures with a 1 d periodic character the theory is illustrated and validated by means of various examples stemming from scattering and radiation applications from by antenna arrays residing on microstrip substrates the efficiency of the method is also demonstrated

on recognizing and positioning curved 3 d objects from image contours an approach for explicitly relating the shape of image contours to models of curved three dimensional objects is presented this relationship is used for object recognition and positioning object models consist of collections of parametric surface patches and their intersection curves this includes nearly all representations used in computer aided geometric design and computer vision the image contours considered are the projections of surface discontinuities and occluding contours elimination theory provides a method for constructing the implicit equation of these contours for an object observed under orthographic or perspective projection this equation is parameterized by the object s position and orientation with respect to the observer determining these parameters is reduced to a fitting problem between the theoretical contour and the observed data points the proposed approach readily extends to parameterized models it has been implemented for a simple world composed of various surfaces of revolution and tested on several real images

a modification of the kummer s method for efficient computation of the 2 d and 3 d green s functions for 1 d periodic structures an auxiliary function in the form of standing spherical waves with attenuation is proposed in the kummer s method for accelerating the convergence of the spectral series representing the green s function of doubly periodic structures in free space expressions for the amplitude and phase constants of the auxiliary waves versus their attenuation constant are derived at which the spectral difference series formed as a result of the kummer s transformation converges in the worst case as the floquet mode propagation constant in the power of minus 5 9 and 13 for the cases of using one two and three auxiliary waves respectively while the spatial series formed by the auxiliary waves converges exponentially some examples allowing determination of optimum values for the attenuation constant are considered and some comparative results characterizing the effectiveness of the technique proposed are presented and discussed

some eigenvalue inequalities for positive semidefinite matrix power products abstract we study the eigenvalues of positive semidefinite matrix power products and obtain some inequalities most of which are in terms of majorization in particular for a b 0 0 we prove log 1 a b log 1 a b the result is a generalization of some work of marcus lieb thirring le couteur bushell and trustrum

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

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

comparative analysis of acceleration techniques for 2 d and 3 d green s functions in periodic structures along one and two directions the problem of accelerating the calculation of the periodic green s function is addressed here for both 3 d and 2 d free space configurations in the 3 d case periodicity is considered both along one axis and along two generally skew axes a comprehensive review of the existing methods is first presented and some extensions are developed the possibility of treating the case of complex phase shifts between unit cells necessary for the study of complex modes in periodic structures is also investigated comparisons among the various acceleration methods are performed thus providing fundamental information on their actual efficiency in typical problems

parametric reconstruction of generalized cylinders from limb edges the three dimensional 3 d reconstruction of generalized cylinders gcs is an important research field in computer vision one of the main difficulties is that some contour features in images cannot be reconstructed by traditional stereovision because they do not correspond to reflectance discontinuities of surface in space in this paper we present a novel parametric approach for the 3 d reconstruction of circular generalized cylinders cgcs only from the limb edges of cgcs in two images instead of exploiting the invariant and quasiinvariant properties of some specific subclasses of gcs in projections our reconstruction is achieved by some general assumptions on gcs and can therefore be applied to a broader subclass of gcs in order to improve robustness we perform the extraction and labeling of the limb edge interactively and estimate the epipolar geometry between two images by an optimal algorithm then for different types of gcs three kinds of symmetries parallel symmetry skew symmetry and local smooth symmetry are employed to compute the symmetry of limb edges the surface points corresponding to limb edges in images are reconstructed by integrating the recovered epipolar geometry and the properties induced from the assumptions that we make on the gcs finally a homography based method is exploited to further refine the 3 d description of the gc with a coplanar curved axis

stable and efficient evaluation of periodized green s functions for the helmholtz equation at high frequencies a difficulty that arises in the context of infinite d periodic rough surface scattering relates to the effective numerical evaluation of the corresponding quasi periodic green function g q p due to its relevance in a variety of applications this problem has generated significant interest over the last 40 years and a variety of numerical methods have been devised for this purpose none of these methods to evaluate g q p however were designed for high frequency calculations as a result in this regime these methods become prohibitively expensive and or unstable here we present a novel scheme that can be shown to outperform every alternative numerical evaluation procedure and is especially effective for high frequency calculations our new algorithm is based on the use of some exact integrals that arise on judicious manipulation of the integral representation of g q p and which reduce the overall problem to that of evaluation of a sequence of simpler integrals that can be effectively handled by standard quadrature formulas we include a variety of numerical results that confirm that indeed our algorithm compares favorably with alternative methods

matrices with some extremal properties abstract for a complex matrix a there are many inequalities related to its eigenvalues diagonal elements and three types of singular values we investigate the conditions on the matrices for which those inequalities become equalities it is shown that in many cases the conditions are both necessary and sufficient for the matrices to be unitarily similar to matrices of lower orders moreover we get alternative proofs of various characterization theorems of different classes of matrices

lattice sums and the two dimensional periodic green s function for the helmholtz equation many algorithms that are currently used for the solution of the helmholtz equation in periodic domains require the evaluation of the green s function g x x0 the fact that the natural representat

eigenvalue equalities for ordinary and hadamard products of powers of positive semidefinite matrices abstract let a and b be n n positive semidefinite matrices and 0 let a b denote the hadamard product of a and b and a l denote the leading l l principal submatrix of a let 1 x n x denote the eigenvalues of an n n matrix x ordered when they are all real in this paper those matrices that satisfy any of the following equalities are determined i 1 a b i 1 a b i 1 n i 1 a l i 1 a l i 1 l i 1 a b i 1 a b i 1 n the results are extended to equalities involving more than one eigenvalue as an application for any 1 k n those a and b that satisfy i 1 k n i 1 a b i 1 k n i 1 a b where b b or b t the transpose of b are also determined

a computational approach to edge detection this paper describes a computational approach to edge detection the success of the approach depends on the definition of a comprehensive set of goals for the computation of edge points these goals must be precise enough to delimit the desired behavior of the detector while making minimal assumptions about the form of the solution we define detection and localization criteria for a class of edges and present mathematical forms for these criteria as functionals on the operator impulse response a third criterion is then added to ensure that the detector has only one response to a single edge we use the criteria in numerical optimization to derive detectors for several common image features including step edges on specializing the analysis to step edges we find that there is a natural uncertainty principle between detection and localization performance which are the two main goals with this principle we derive a single operator shape which is optimal at any scale the optimal detector has a simple approximate implementation in which edges are marked at maxima in gradient magnitude of a gaussian smoothed image we extend this simple detector using operators of several widths to cope with different signal to noise ratios in the image we present a general method called feature synthesis for the fine to coarse integration of information from operators at different scales finally we show that step edge detector performance improves considerably as the operator point spread function is extended along the edge

global surface reconstruction by purposive control of observer motion abstract what viewpoint control strategies are important for performing global visual exploration tasks such as searching for specific surface markings building a global model of an arbitrary object or recognizing an object in this paper we consider the task of purposefully controlling the motion of an active monocular observer in order to recover a global description of a smooth arbitrarily shaped object we formulate global surface reconstruction as the task of controlling the motion of the observer so that the visible rim slides over the maximal connected reconstructible surface regions intersecting the visible rim at the initial viewpoint we show that these regions are bounded by a subset of the visual event curves defined on the surface by studying the epipolar parameterization we develop two basic strategies that allow reconstruction of a surface region around any point in a reconstructible surface region these strategies control viewpoint to achieve and maintain a well defined geometric relationship with the object s surface rely only on information extracted directly from images e g tangents to the occluding contour and are simple enough to be performed in real time we then show how global surface reconstruction can be provably achieved by 1 appropriately integrating these strategies to iteratively grow the reconstructed regions and 2 obeying four simple rules

calculation of the free space periodic green s function using equivalent finite array we present a novel method for the calculation of the 2d and 3d free space periodic green s function pgf especially efficient when observation points are in the vicinity of the array plane a case for which both spatial and spectral domain forms of pgf are known to be slowly convergent the pgf is approximated by a truncation of the original array and the assignment of new fictitious amplitudes to maintained sources both 2d and 3d numerical tests show that a highly accurate approximation of the pgf can be obtained with such an equivalent finite array composed of a few sources making the method especially relevant for fast electromagnetic computation of periodic structures with the method of moments mom for example

interpreting line drawings of curved objects in this thesis we study the problem of interpreting line drawings of scenes composed or opaque regular solid objects bounded by piecewise smooth surfaces with no markings or texture on them it is assumed that the line drawing has been formed by orthographic projection of such a scene under general viewpoint that the line drawing is error free and that there are no lines due to shadows or specularities our definition implicitly excludes laminae wires and the apices of cones a major component of the interpretation of line drawings is line labelling by line labelling we mean a classification of each image curve as corresponding to either a depth or orientation discontinuity in the scene and b further subclassification of each kind of discontinuity for a depth discontinuity we determine whether it is a limb a locus of points on the surface where the line of sight is tangent to the surface or an occluding edge a tangent plane discontinuity of the surface for an orientation discontinuity we determine whether it corresponds to a convex or concave edge this thesis presents the first mathematically rigorous scheme for labelling line drawings of the class of scenes described by analysing the projection of the neighborhoods of different kinds of points on a piecewise smooth surface we are able to catalog all local labelling possibilities for the different types of junctions in a line drawing an algorithm is developed which utilizes this catalog to determine all legal labellings of the line drawing a local minimum complexity rule at each vertex select those labellings which correspond to the minimum number of faces meeting at the vertex is used in order to prune highly counter intuitive interpretations the labelling scheme was implemented and tested on a number of line drawings the labellings obtained are few and by and large in accordance with human interpretations

two dimensional method of moments modelling of lossless overmoded transverse magnetic cavities we present a method of moment mom analysis technique allowing to model overmoded transverse magnetic tm cavities in two dimensions this technique uses the single series form of the green s function of the empty cavity the convergence behaviour of this series is analysed in detail

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

perception of 3 d surfaces from 2 d contours inference of 3 d shape from 2 d contours in a single image is an important problem in machine vision the authors survey classes of techniques proposed in the past and provide a critical analysis they show that two kinds of symmetries in figures which are known as parallel and skew symmetries give significant information about surface shape for a variety of objects they derive the constraints imposed by these symmetries and show how to use them to infer 3 d shape they also discuss the zero gaussian curvature zgc surfaces in depth and show results on the recovery of surface orientation for various zgc surfaces

detection and segmentation of generic shapes based on affine modeling of energy in eigenspace this paper presents a novel approach for detection and segmentation of man made generic shapes in cluttered images the set of shapes to be detected are members of affine transformed versions of basic geometric shapes such as rectangles circles etc the shape set is represented by its vectorial edge map transformed over a wide range of affine parameters we use vectorial boundary instead of regular boundary to improve the robustness to noise background clutter and partial occlusion our approach consists of a detection stage and a verification stage in the detection stage we first derive the energy from the principal eigenvectors of the set next an a posteriori probability map of energy distribution is computed from the projection of the edge map representation in a vectorial eigen space local peaks of the posterior probability map are located and indicate candidate detections we use energy probability based detection since we find that the underlying distribution is not gaussian and resembles a hypertoroid in the verification stage each candidate is verified using a fast search algorithm based on a novel representation in angle space and the corresponding pose information of the detected shape is obtained the angular representation used in the verification stage yields better results than a euclidean distance representation experiments are performed in various interfering distortions and robust detection and segmentation are achieved

recovery of the three dimensional shape of an object from a single view given a single picture which is a projection of a three dimensional scene onto the two dimensional picture plane we usually have definite ideas about the 3 d shapes of objects to do this we need to use assumptions about the world and the image formation process since there exist a large number of shapes which can produce the same picture the purpose of this paper is to identify some of these assumptions mostly geometrical ones by demonstrating how the theory and techniques which exploit such assumptions can provide a systematic shape recovery method the method consists of two parts the first is the application of the origami theory which models the world as a collection of plane surfaces and recovers the possible shapes qualitatively the second is the technique of mapping image regularities into shape constraints for recovering the probable shapes quantitatively actual shape recovery from a single view is demonstrated for the scenes of an object such as a box and a chair given a single image the method recovers the 3 d shapes of an object in it and generates images of the same object as we would see it from other directions