accurate and scalable surface representation and reconstruction from images we introduce a new surface representation method called patchwork to extend three dimensional surface reconstruction capabilities from multiple images a patchwork is the combination of several patches that are built one by one this design potentially allows for the reconstruction of an object with arbitrarily large dimensions while preserving a fine level of detail we formally demonstrate that this strategy leads to a spatial complexity independent of the dimensions of the reconstructed object and to a time complexity that is linear with respect to the object area the former property ensures that we never run out of storage and the latter means that reconstructing an object can be done in a reasonable amount of time in addition we show that the patchwork representation handles equivalently open and closed surfaces whereas most of the existing approaches are limited to a specific scenario an open or closed surface but not both the patchwork concept is orthogonal to the method chosen for surface optimization most of the existing optimization techniques can be cast into this framework to illustrate the possibilities offered by this approach we propose two applications that demonstrate how our method dramatically extends a recent accurate graph technique based on minimal cuts we first revisit the popular carving techniques this results in a well posed reconstruction problem that still enjoys the tractability of voxel space we also show how we can advantageously combine several image driven criteria to achieve a finely detailed geometry by surface propagation these two examples demonstrate the versatility and flexibility of patchwork reconstruction they underscore other properties inherited from patchwork representation although some min cut methods have difficulty in handling complex shapes e g with complex topologies they can naturally manipulate any geometry through the patchwork representation while preserving their intrinsic qualities the above properties of patchwork representation and reconstruction are demonstrated with real image sequences

a chain code for representing 3d curves abstract a chain code for representing three dimensional 3d curves is defined any 3d continuous curve can be digitalized and represented as a 3d discrete curve this 3d discrete curve is composed of constant straight line segments thus the chain elements represent the orthogonal direction changes of the constant straight line segments of the discrete curve the proposed chain code only considers relative direction changes which allows us to have a curve descriptor invariant under translation and rotation also this curve descriptor may be starting point normalized for open and closed curves and invariant under mirroring transformation in the content of this work the main characteristics of this chain code are presented this chain code is inspired by the work of guzman mcc technical report number aca 254 87 july 13 1987 for representing 3d stick bodies finally we present some results of this chain code to represent and process 3d discrete curves as linear features over the terrain by means of digital elevation model dem data also we use this chain code for representing solids composed of voxels thus each solid represents a dem which is described by only one chain

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

on the number of limit cycles near a homoclinic loop with a nilpotent singular point abstract in this article we study the expansion of the first melnikov function appearing by perturbing an integrable and reversible system with a homoclinic loop passing through a nilpotent singular point and obtain formulas for computing the first coefficients of the expansion based on these coefficients we obtain a lower bound for the maximal number of limit cycles near the homoclinic loop moreover as an application of our main results we consider a type of integrable and reversible polynomial systems obtaining at least 3 4 or 5 limit cycles respectively

motion estimation in image sequences using the deformation of apparent contours the problem of determining the camera motion from apparent contours or silhouettes of a priori unknown curved 3d surfaces is considered in a sequence of images it is shown how to use the generalized epipolar constraint on apparent contours one such constraint is obtained for each epipolar tangency point in each image pair an accurate algorithm for computing the motion is presented based on a maximum likelihood estimate it is shown how to generate initial estimates on the camera motion using only the tracked contours it is also shown that in theory the motion can be calculated from the deformation of a single contour the algorithm has been tested on several real image sequences for both euclidean and projective reconstruction the resulting motion estimate is compared to motion estimates calculated independently using standard feature based methods the motion estimate is also used to classify the silhouettes as curves or apparent contours the statistical evaluation shows that the technique gives accurate and stable results

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

introducing a new problem shape from silhouette when the relative positions of the viewpoints is unknown 3d shapes can be reconstructed from 2d silhouettes by back projecting them from the corresponding viewpoints and intersecting the resulting solid cones however in many practical cases as observing an aircraft or an asteroid the positions of the viewpoints with respect to the object are not known in these cases the relative position of the solid cones is not known and the intersection cannot be performed the purpose of this paper is introducing and stating in a theoretical framework the problem of understanding 3d shapes from silhouettes when the relative positions of the viewpoints are unknown the results presented provide a first insight into the problem in particular the case of orthographic viewing directions parallel to the same plane is thoroughly discussed and sets of inequalities are presented which allow determining objects compatible with the silhouettes

optimum approximation for residual stiffness in linear system identification a new method of system identification uti 1 i zes projector m atrix theory and the moorepenrose generalized inverse to derive an analytical stiffness matrix which when combined with the analytical mass matrix will more closely p redict modal test results weighting matrices a re used to enforce connectivity and make weighted corrections to the original analytical stiffness matrix a simple and straightforward mathematical formulation is obtained the method is compared and contrasted with other methods found in the literature and a simple numerical example is presented

free form object reconstruction from silhouettes occluding edges and texture edges a unified and robust operator based on duality in this paper the duality in differential form is developed between a 3d primal surface and its dual manifold formed by the surface s tangent planes that is each tangent plane of the primal surface is represented as a four dimensional vector that constitutes a point on the dual manifold the iterated dual theorem shows that each tangent plane of the dual manifold corresponds to a point on the original 3d surface that is the dual of the dual goes back to the primal this theorem can be directly used to reconstruct 3d surface from image edges by estimating the dual manifold from these edges in this paper we further develop the work in our original conference papers resulting in the robust differential dual operator we argue that the operator makes good use of the information available in the image data by using both points of intensity discontinuity and their edge directions we provide a simple physical interpretation of what the abstract algorithm is actually estimating and why it makes sense in terms of estimation accuracy our algorithm operates on all edges in the images including silhouette edges self occlusion edges and texture edges without distinguishing their types thus resulting in improved accuracy and handling locally concave surface estimation if texture edges are present the algorithm automatically handles various degeneracies and the algorithm incorporates new methodologies for implementing the required operations such as appropriately relating edges in pairs of images evaluating and using the algorithm s sensitivity to noise to determine the accuracy of an estimated 3d point experiments with both synthetic and real images demonstrate that the operator is accurate robust to degeneracies and noise and general for reconstructing free form objects from occluding edges and texture edges detected in calibrated images or video sequences

epipolar parameterization for reconstructing 3d rigid curve abstract this paper describes a new method for reconstructing a 3d rigid curve from a sequence of uncalibrated images using 31 epipolar parameterization the approach can be divided into the following two steps first a nonlinear discrete method is presented for point by point reconstruction of the curve instead of whole curve reconstruction projective and euclidean geometric tools are used second the parametric representation of the curve is defined by 31 b spline curves a linear method is proposed to interpolate the reconstructed points to obtain a complete curve thus it is proved that the 31 curve interpolation is equivalent to determining a set of control points of 3d regularized b spline curves it is shown that the 3d epipolar parameterization is an efficient method for reconstructing a 31 curve from image sequences experimental results are presented for real data

the cyclicity of the elliptic segment loops of the reversible quadratic hamiltonian systems under quadratic perturbations abstract denote by q h and q r the hamiltonian class and reversible class of quadratic integrable systems there are several topological types for systems belong to q h q r one of them is the case that the corresponding system has two heteroclinic loops sharing one saddle connection which is a line segment and the other part of the loops is an ellipse in this paper we prove that the maximal number of limit cycles which bifurcate from the loops with respect to quadratic perturbations in a conic neighborhood of the direction transversal to reversible systems called in reversible direction is two we also give the corresponding bifurcation diagram

robust structure and motion from outlines of smooth curved surfaces this paper addresses the problem of estimating the motion of a camera as it observes the outline or apparent contour of a solid bounded by a smooth surface in successive image frames in this context the surface points that project onto the outline of an object depend on the viewpoint and the only true correspondences between two outlines of the same object are the projections of frontier points where the viewing rays intersect in the tangent plane of the surface in turn the epipolar geometry is easily estimated once these correspondences have been identified given the apparent contours detected in an image sequence a robust procedure based on ransac and a voting strategy is proposed to simultaneously estimate the camera configurations and a consistent set of frontier point projections by enforcing the redundancy of multiview epipolar geometry the proposed approach is in principle applicable to orthographic weak perspective and affine projection models experiments with nine real image sequences are presented for the orthographic projection case including a quantitative comparison with the ground truth data for the six data sets for which the latter information is available sample visual hulls have been computed from all image sequences for qualitative evaluation

on orbit damage assessment for large space structures the need for monitoring the dynamic characteristics of large structural systems for the purpose of assessing the potential degradation of structural properties has been established this paper develops a theory for assessing the occurrence location and extent of potential damage utilizing on orbit response measurements the feasibility of the method is demonstrated using a simple structural system as an example

shape sensing of 3d frame structures using an inverse finite element method abstract a robust and efficient computational method for reconstructing the elastodynamic structural response of truss beam and frame structures using measured surface strain data is presented known as shape sensing this inverse problem has important implications for real time actuation and control of smart structures and for monitoring of structural integrity the present formulation based on the inverse finite element method ifem uses a least squares variational principle involving section strains also known as strain measures of timoshenko theory for stretching torsion bending and transverse shear the present ifem methodology is based on strain displacement relations only without invoking force equilibrium consequently both static and time varying displacement fields can be reconstructed without the knowledge of material properties applied loading or damping characteristics two finite elements capable of modeling frame structures are derived using interdependent interpolations in which interior degrees of freedom are condensed out at the element level in addition relationships between the order of kinematic element interpolations and the number of required strain gauges are established several example problems involving cantilevered beams and three dimensional frame structures undergoing static and dynamic response are discussed to simulate experimentally measured strains and to establish reference displacements high fidelity msc nastran finite element analyses are performed furthermore numerically simulated measurement errors based on gaussian distribution are also considered in order to verify the stability and robustness of the methodology the ifem solution accuracy is examined with respect to various levels of discretization and the number of strain gauges

limit cycle bifurcations by perturbing a quadratic integrable system with a triangle abstract finding cyclicity of homoclinic or heteroclinic loops in quadratic systems is an open problem which is related to the second part of hilbert s 16th problem this paper mainly considers the problem of limit cycle bifurcation for quadratic polynomial systems near a triangle it is proved that the cyclicity of the triangle in quadratic systems is at least three

random exploration of the procedural space for single view 3d modeling of buildings in this paper we tackle the problem of 3d modeling for urban environment using a modular flexible and powerful approach driven from procedural generation to this end typologies of architectures are modeled through shape grammars that consist of a set of derivation rules and a set of shape dictionary elements appearance from statistical point of view with respect to the individual pixel s properties of the dictionary elements is then learned using a set of training images image classifiers are trained towards recovering image support with respect to the semantics then given a new image and the corresponding footprint the modeling problem is formulated as a search of the space of shapes that can be generated on the fly by deriving the grammar on the input axiom defining an image based score function for the produced instances using the trained classifiers the best rules are selected making sure that we keep exploring the space by allowing some rules to be randomly selected new rules are then generated by resampling around the selected rules at the finest level these rules define the 3d model of the building promising results on complex and varying architectural styles demonstrate the potential of the presented method

using canny s criteria to derive a recursively implemented optimal edge detector a highly efficient recursive algorithm for edge detection is presented using canny s design 1 we show that a solution to his precise formulation of detection and localization for an infinite extent filter leads to an optimal operator in one dimension which can be efficiently implemented by two recursive filters moving in opposite directions in addition to the noise truncature immunity which results the recursive nature of the filtering operations leads with sequential machines to a substantial saving in computational effort five multiplications and five additions for one pixel independent of the size of the neighborhood the extension to the two dimensional case is considered and the resulting filtering structures are implemented as two dimensional recursive filters hence the filter size can be varied by simply changing the value of one parameter without affecting the time execution of the algorithm performance measures of this new edge detector are given and compared to canny s filters various experimental results are shown

structural damage detection based on static and modal analysis the present paper describes an approach for structural damage assessment that has its basis in methods of system identification response of a damaged structure differs from predictions obtained from an analytical model of the original structure where the analytical model is typically a finite element representation the out put error approach of system identification is employed to determine changes in the analytical model necessary to minimize differences between the measured and predicted response structural damage is represented by changes in element stiffness matrices resulting from variations in geometry or material properties of the structure during damage measurements of static deflections and vibration modes are used in the identification procedure the identification methodology is implemented for representative structural systems principal shortcomings in the proposed approach and methods to circumvent these problems are also discussed of obtaining poor results these difficulties are clearly evi denced by the results obtained smith and hendricks8 follow a similar approach using two different identification methods to identify the stiffness matrix based on the minimum deviation approach and using eigenmodes as experimental data similar difficulties are re ported in their work the entries of the stiffness matrix corre sponding to the damaged members do show considerable vari ations however entries corresponding to undamaged members are also affected thereby making the damage detec tion process more uncertain the analysis of changes in the stiffness matrix is typically cumbersome may not always yield correct answers and does not permit the determination of the extent of damage this paper presents an approach that is designed to circum vent the problems just discussed the output error method or structural identification9 is used wherein the analytical model is refined to minimize the difference between the predicted and measured response of the structure iterative nonlinear pro gramming methods are employed to determine a solution to the unconstrained optimization problem damage is repre sented by reduction in the elastic extensional and shear moduli of the element and those are designated as the design varia bles of the problem the use of static structural displacements as the measured response is a departure from the standard practice of using eigenmodes alone for the identification pro blem numerical evidence clearly indicates that when eigen modes alone are used for identification the location and ex tent of damage predicted by the optimization approach is dependent on the number of modes used to match the measured and the predicted response higher modes are diffi cult to determine and measure and the use of static displace ments obtained by a loading that simulates higher modes is proposed as a solution to this problem the paper also presents an implementation of the proposed damage assessment strategies with special focus on problems of practical significance in this context the use of incomplete modal or static displacement information in the identification problem is discussed further the approach of treating the modulus of each structural element as an independent design variable results in a large dimensionality problem this results in significant computational costs when using a gradient based nonlinear programming algorithm for function minimization the use of a reduced set of dominant design variables and the construction of equivalent reduced order models for damage assessment are explored with some success

stiffness matrix adjustment using mode data a procedure is introduced that uses in addition to mode data structural connectivity information to optimally adjust deficient stiffness matrices the adjustments performed are such that the percentage change to each stiffness coefficient is minimized the physical configuration of the analytical model is preserved and the adjusted model will exactly reproduce the modes used in the identification the theoretical development is presented and the procedure is demonstrated by numerical simulation of a test problem

affine reconstruction of curved surfaces from uncalibrated views of apparent contours in this paper we consider uncalibrated reconstruction of curved surfaces from apparent contours since apparent contours are not fixed features viewpoint independent we cannot directly apply the recent results of the uncalibrated reconstruction from fixed features we show that nonetheless curved surfaces can be reconstructed up to an affine ambiguity from their apparent contours viewed from uncalibrated cameras with unknown linear translations furthermore we show that even if the reconstruction is nonmetric non euclidean we can still extract useful information for many computer vision applications just from the apparent contours we first show that if the camera motion is linear translation but arbitrary direction and magnitude the epipolar geometry can be recovered from the apparent contours without using any optimization process the extracted epipolar geometry is next used for reconstructing curved surfaces from the deformations of the apparent contours viewed from uncalibrated cameras the result is applied to distinguishing curved surfaces from fixed features in images it is also shown that the time to contact to the curved surfaces can be computed from simple measurements of the apparent contours

efficient polyhedral modeling from silhouettes modeling from silhouettes is a popular and useful topic in computer vision many methods exist to compute the surface of the visual hull from silhouettes but few address the problem of ensuring good topological properties of the surface such as manifoldness this article provides an efficient algorithm to compute such a surface in the form of a polyhedral mesh it relies on a small number of geometric operations to compute a visual hull polyhedron in a single pass such simplicity enables the algorithm to combine the advantages of being fast producing pixel exact surfaces and repeatably yield manifold and watertight polyhedra in general experimental conditions with real data as verified with all datasets tested the algorithm is fully described its complexity analyzed and modeling results given

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

the local projective shape of smooth surfaces and their outlines this article examines projectively invariant local geometric properties of smooth curves and surfaces oriented projective differential geometry is proposed as a general framework for establishing such invariants and characterizing the local projective shape of surfaces and their outlines it is applied to two problems 1 the projective generalization of koenderink s famous characterization of convexities concavities and inflections of the apparent contours of solids bounded by smooth surfaces and 2 the image based construction of rim meshes which provide a combinatorial description of the arrangement induced on the surface of an object by the contour generators associated with multiple cameras observing it

inhomogeneous fuchs equations and the limit cycles in a class of near integrable quadratic systems we study the bifurcation of limit cycles in general quadratic perturbations of the particular quadratic system which represents one of two codimension five components in the intersection of two strata in the centre manifold and q 4 the study of limit cycles for this degenerate case requires us to investigate not the first but the second variation m 2 of the displacement function we prove that up to three limit cycles can emerge from the period annulus surrounding the centre this implies that the cyclicity of period annuli of nearby systems in and q 4 is at most three as well our approach relies upon the possibility of deriving appropriate picard fuchs equations satisfied by the four independent integrals included in m 2

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

local bifurcations and a survey of bounded quadratic systems abstract this paper presents a survey of the known results for bounded quadratic systems as well as a study of the local bifurcations that occur at critical points of such systems it is shown that the only finite codimension bifurcations that occur at a critical point of a bounded quadratic system are the saddle node and the hopf takens bifurcations of codimensions 1 and 2 and the bogdanov takens bifurcations of codimensions 2 and 3 furthermore it is shown that whenever a bounded quadratic system has one of these critical points then a full generic unfolding of the critical point exists in the class of bounded quadratic systems finally we give a complete list of those limit periodic sets whose finite cyclicity still needs to be established in order to obtain the existence of a finite upper bound for the number of limit cycles that can occur in a bounded quadratic system

representing stereo data with the delaunay triangulation abstract this article proposes a coherent way of interpolating three dimensional data obtained by stereo for example with a simplicial polyhedral surface the proposed method is based on the use of the constrained delaunay triangulation the polyhedral surface is obtained by using a simple visibility property to mark tetrahedra likely to be empty the method is intrinsically discontinuity preserving works for multiple viewpoints and yields both a surface representation of objects and a volume representation of free space which may be useful in robotics algorithms to implement the method are described and their complexity analyzed in the worst case and average case situations where tools of probabilistic geometry are used

hole crack identification by static strains from multiple loading modes a method using static strains measured from multiple loading modes for the identification of holes and cracks in linear anisotropic elastic materials is introduced because of the localized effects of holes cracks their existence may not be clearly reflected by a single set of remotely measured boundary strains by the combining of the concept of multiple loading modes with the technique of nonlinear optimization several examples of hole crack identification have been done during the iteration procedure the values of the static strains corresponding to the assumed hole crack geometry and location are obtained by using a recently developed boundary element which is for linear anisotropic elastic materials and has also been extended to piezoelectric materials the identified results show that our method for hole crack identification is stable and accurate for the model problem considered and shows that the method has promise for more complex problems in addition the generality of hole profile the tolerance of measurement error the spacing and arrangement of sensors and the flexibility of multiple loading modes are all discussed in detail

secant method adjustment for structural models on orbit testing will be required for final tuning and validation of any mathematical model of large space structures identification methods using limited response data to produce optimally adjusted property matrices seem ideal for this purpose but difficulties exist in the application of previously published methods to large space truss structures this article presents new stiffness matrix adjustment methods that generalize optimal update secant methods found in quasi newton approaches for nonlinear optimization many aspects of previously published methods of stiffness matrix adjustment may be better understood within this new framework of secant methods one of the new methods preserves realistic structural connectivity with minimal storage requirements and computational effort a method for systematic compensation for errors in measured data is introduced that also preserves structural connectivity two demonstrations are presented to compare the new methods results to those of previously published techniques

a least squares variational method for full field reconstruction of elastic deformations in shear deformable plates and shells abstract a variational principle is formulated for the inverse problem of full field reconstruction of three dimensional plate shell deformations from experimentally measured surface strains the formulation is based upon the minimization of a least squares functional that uses the complete set of strain measures consistent with linear first order shear deformation theory the formulation which accommodates for transverse shear deformation is applicable for the analysis of thin and moderately thick plate and shell structures the main benefit of the variational principle is that it is well suited for c 0 continuous displacement finite element discretizations thus enabling the development of robust algorithms for application to complex civil and aeronautical structures the methodology is especially aimed at the next generation of aerospace vehicles for use in real time structural health monitoring systems

numerical size estimates of inclusions in kirchhoff love elastic plates abstract the size estimates approach for kirchhoff love elastic plates allows to determine upper and lower bounds of the area of an unknown elastic inclusion by measuring the work developed by applying a couple field on the boundary of the plate although the analytical process by which such bounds are determined is of constructive type it leads to rather pessimistic evaluations in this paper we show by numerical simulations how to obtain such bounds for practical applications of the method the computations are developed for a square plate under various boundary loads and for inclusions of different position shape and stiffness the sensitivity of the results with respect to the relevant parameters is also analyzed

projective visual hulls this article presents a novel method for computing the visual hull of a solid bounded by a smooth surface and observed by a finite set of cameras the visual hull is the intersection of the visual cones formed by back projecting the silhouettes found in the corresponding images we characterize its surface as a generalized polyhedron whose faces are visual cone patches edges are intersection curves between two viewing cones and vertices are frontier points where the intersection of two cones is singular or intersection points where triples of cones meet we use the mathematical framework of oriented projective differential geometry to develop an image based algorithm for computing the visual hull this algorithm works in a weakly calibrated setting that is it only requires projective camera matrices or equivalently fundamental matrices for each pair of cameras the promise of the proposed algorithm is demonstrated with experiments on several challenging data sets and a comparison to another state of the art method

unfolding of a quadratic integrable system with two centers and two unbounded heteroclinic loops abstract in this paper we present a complete study of quadratic 3 parameter unfoldings of some integrable system belonging to the classqr3 and having two centers and two unbounded heteroclinic loops we restrict to unfoldings that are transverse toqr3 obtain a versal bifurcation diagram and all global phase portraits including the precise number and configuration of the limit cycles it is proved that 3 is the maximal number of limit cycles surrounding a single focus and only the 1 1 configuration can occur in case of simultaneous nests of limit cycles essentially the proof relies on a careful analysis of a related non conservative abelian integral

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

robust shape recovery from occluding contours using a linear smoother recovering the shape of an object from two views fails at occluding contours of smooth objects because the extremal contours are view dependent for three or more views shape recovery is possible and several algorithms have recently been developed for this purpose we present a new approach to the multiframe stereo problem that does not depend on differential measurements in the image which may be noise sensitive instead we use a linear smoother to optimally combine all of the measurements available at the contours and other edges in all of the images this allows us to extract a robust and reasonably dense estimate of surface shape and to integrate shape information from both surface markings and occluding contours results are presented which empirically show that in the presence of noise smoothing over more than three views reduces the error even when the epipolar curve is nonplanar

the cyclicity of the period annulus of the quadratic hamiltonian systems with non morsean point abstract in this paper we investigate the quadratic hamiltonian systems with non morsean point it is proved that in this situation the cyclicity of the period annulus under quadratic perturbations is equal to two

improvement of a large analytical model using test data a method has been developed which uses measured normal modes and natural frequencies to improve an analytical mass and stiffness matrix model of a structure the method directly identifies without iteration a set of minimum changes in the analytical matrices which force the eigensolutions to agree with the test measurements an application is presented in which the analytical model had 508 degrees of freedom and 19 modes were measured at 101 locations on the structure the resulting changes in the model are judged to be small compared to expectations of error in the analysis thus the improved model is accepted as a reasonable model of the structure with improved dynamic response characteristics in addition it is shown that the procedure may be a useful tool in identifying apparent measured modes which are not true normal modes of the structure nomenclature analytical matrix matrix of changes identity matrix full improved stiffness and mass matrices n x n full analytical k m matrices n x n partitions of ka ma corresponding to test coordinates partitions of ka ma corresponding to coupling elements partitions of ka ma corresponding to unmea sured coordinates number of measured modes number of degrees of freedom in the model measures of changes eqs 15 17 matrix norm sum of the squares of all the elements rectangular modal matrix normalized n x m th mode th column of measured and unmeasured partitions of diagonal matrix of measured natural frequencies m xm natural frequency of th mode 12 17 sum of the squares of all elements of matrix

the cyclicity of triangles and segments in quadratic systems abstract the paper deals with quadratic systems having separatrix contour in the form of a triangle or a conic segment the limit cycles appearing near this configuration after quadratic perturbation is studied the maximal number of limit cycles is 3 for the bounded triangle and 2 for the unbounded triangle and for the bounded segment

direct identification of non uniform beams using static strains abstract a method for identifying the flexural rigidities of a non uniform beam is developed in this paper the finite element method is used to derive the equilibrium equation of the beam the identification problem is then formulated as an optimization program in which the error norm of the equilibrium equation is minimized the proposed method has the following features 1 it uses longitudinal strains as the primary test data 2 the solution is unique and global minimal 3 the method can be applied to a whole beam as well as a part of a beam 4 the method is very stable the identifiability of the inverse problem is studied in depth two numerical examples are presented to demonstrate the proposed method finally a model test is performed to examine the effectiveness of the method in real applications

the cyclicity of the period annulus of the quadratic hamiltonian triangle abstract the paper studies quadratic hamiltonian centers surrounded by a separatrix contour having a form of a triangle it is proved that in this situation the cyclicity of the period annulus under quadratic perturbations is equal to three