interpreting perspective images a fundamental problem in computer vision is how to determine the 3 d spatial orientation of curves and surfaces appearing in an image the problem is generally underconstrained and is complicated by the fact that metric properties such as orientation and length are not invariant under projection under perspective projection the correct model for most real images the transform is nonlinear and therefore hard to invert two constructive methods are presented the first finds the orientation of parallel lines and planes by locating vanishing points and vanishing lines the second determines the orientation of planes by backprojection of two intrinsic properties of contours angle magnitude and curvature

using points at infinity for parameter decoupling in camera calibration the majority of camera calibration methods including the gold standard algorithm use point based information and simultaneously estimate all calibration parameters in contrast we propose a novel calibration method that exploits line orientation information and decouples the problem into two simpler stages we formulate the problem as minimization of the lateral displacement between single projected image lines and their vanishing points unlike previous vanishing point methods parallel line pairs are not required additionally the invariance properties of vanishing points mean that multiple images related by pure translation can be used to increase the calibration data set size without increasing the number of estimated parameters we compare this method with vanishing point methods and the gold standard algorithm and demonstrate that it has comparable performance

dynamic formulation for geometrically exact sandwich shells abstract extending our recent works on geometrically exact sandwich beams and one dimensional plates see e g vu quoc and ebcio lu 1995 vu quoc and deng 1995c vu quoc and deng 1995a we present here a geometrically exact sandwich shell theory entirely in terms of stress resultants which accommodates finite deformations in membrane bending and transverse shear the motion of the shell are referred directly to the inertial frame the transverse fiber of the sandwich shell has a motion identical to that of a chain of three rigid links connected by revolute joints an important approximated theory is developed from the general nonlinear equations the classical linear theory is recovered by the consistent linearization

inverse formulation for geometrically exact stress resultant shells the inverse elastostatics method tackles a class of problems in which the deformed geometry and the applied load are known while the initial geometry and the stress in the deformed state are to be determined the method is imperative for many biomechanics applications particularly for image based stress analysis of living organs as the geometry captured by imaging often correspond to a pre deformed configuration 3 4 the computational aspects of inverse elastostatics i e the inverse formulations have been established for general elastic solids 1 2 3 in this work the inverse formulation of thin walled structures modeled as geometrically exact stress resultant shell 5 is presented the inverse formulation builds on a fundamental assumption of the elastic media that the stress depends on local relative motion of the body if either the reference or the deformed configuration is given the other can be found from the elastostatic equilibrium the shell formulation follows the same logic albeit involving shell kinematics and kinetics regardless of the additional assumptions introduced in the shell theory the fundamental premise underlying inverse analysis remains the same in the proposed formulation the inverse problem is solved by using the standard week form of shell balance equations which are yet parameterized and linearized in terms of the inverse motion to facilitate an effective numerical computation an invariant approached is used to formulate the constitutive equations a consistent reduction from 3d energy function is also introduced numerical examples involving both isotopic and anisotropic materials are provided for validating the formulation applications to several biological thin walled structures demonstrate the practical utility of the method

on the well balanced numerical discretization of shallow water equations on unstructured meshes we consider in this work a finite volume numerical approximation of weak solutions of the shallow water equations with varying topography on unstructured meshes relying on an alternative formulation of the shallow water equations that involves the free surface as a conservative variable instead of the water height we introduce a simple discretization of the bed slope source term together with some suitable conservative variables reconstructions the resulting scheme is automatically consistent and well balanced for any given consistent numerical flux for the homogeneous system we obtain a very simple formulation which do not need to be modified when second order accuracy muscl reconstructions are adopted additionally the positivity of the water height is preserved under a relevant stability condition as soon as the numerical flux for the associated homogeneous system does numerical assessments involving dry areas and complex geometry are performed

contribution to the determination of vanishing points using hough transform we propose a method to locate three vanishing points on an image corresponding to three orthogonal directions of the scene this method is based on two cascaded hough transforms we show that even in the case of synthetic images of high quality a naive approach may fail essentially because of the errors due to the limitation of the image size we take into account these errors as well as errors due to detection inaccuracy of the image segments and provide a method efficient even in the case of real complex scenes

a ground truth based vanishing point detection algorithm a bayesian probability based vanishing point detection algorithm is presented which introduces the use of multiple features and training with ground truth data to determine vanishing point locations the vanishing points of 352 images were manually identified to create ground truth data each intersection is assigned a probability of being coincident with a ground truth vanishing point based upon conditional probabilities of a number of features the results of this algorithm are demonstrated to be superior to the results of a similar algorithm where each intersection is considered to be of equal importance the advantage of this algorithm is that multiple features derived from ground truth training are used to determine vanishing point location

geometrically exact sandwich shells the static case the present formulation offers a general method for analyzing the static response of geometrically exact sandwich shells undergoing large deformation the layer directors at a point in the reference surface are connected to each other by universal joints and form a chain of rigid links finite rotations of the directors in every layer are allowed with shear deformation independently accounted for in each layer the thickness and the length of each layer can be arbitrary thus allowing the modeling of an important class of multilayer structures having ply drop offs the present formulation is thus suitable to model shell structures with patches of constrained viscoelastic materials or of piezoelectric materials the nonlinear weak form of the governing equations of equilibrium is constructed here and then the linearization of the weak form and the associated inextensible directors update are derived leading to a symmetric tangent stiffness matrix a galerkin finite element projection of the linearized equilibrium equations results in a system of nonlinear algebraic equations in which the interpolation accounts for the finite rotations of the directors we present extensive numerical examples including sandwich shells with three identical layers and ply drop offs to illustrate the applicability and versatility of the proposed formulation

finite volume schemes with equilibrium type discretization of source terms for scalar conservation laws we develop here a new class of finite volume schemes on unstructured meshes for scalar conservation laws with stiff source terms the schemes are of equilibrium type hence with uniform bounds on approximate solutions valid in cell entropy inequalities and exact for some equilibrium states convergence is investigated in the framework of kinetic schemes numerical tests show high computational efficiency and a significant advantage over standard cell centered discretization of source terms equilibrium type schemes produce accurate results even on test problems for which the standard approach fails for some numerical tests they exhibit exponential type convergence rate in two of our numerical tests an equilibrium type scheme with 441 nodes on a triangular mesh is more accurate than a standard scheme with 50002 grid points

on the physical meaning of the dynamical equations governing geometrically exact multilayer shells in this paper the physical meaning of the equations governing geometrically exact multilayer shells is provided through a totally new derivation by means of dynamic equilibrium consideration starting from a 3 d continuum setting in curvilinear coordinates the theory is valid for large deformation and large overall motion as characteristic of geometrically exact formulations the dynamic equilibrium derivation offers a clear physical insight into the meaning of the terms in the equations of motion such insight was not afforded by previous derivations based on the principle of virtual power in particular we obtain directly the balance of angular momentum in true resultant couples without the need to use the constitutive restriction as in our previous papers moreover we also obtain here new expressions for the inertia operators that will greatly simplify the computational formulation when compared to our previous work in addition an analytical justification of the inertial operators is also provided the present formulation is independent of any kinematic assumption along the shell director and is in particular valid for the case of shells with variable length director e g for modeling through the thickness deformation and higher order kinematic assumptions

the riemann problem for the shallow water equations with discontinuous topography the wet dry case abstract in this paper we consider riemann problems for the shallow water equations with discontinuous topography whose initial conditions correspond to a wet dry front at time t 0 there is vacuum on the right or on the left of the step besides the theoretical interest of this analysis the results may be useful to design numerical methods and or to produce reference solutions to compare different schemes we show that depending on the state at the wet side 0 1 or 2 self similar solutions can be constructed by composing simple waves in problems with 0 solutions the step acts as an obstacle for the fluid and physically meaningful solutions can be constructed by interpreting the problem as a partial riemann problems for the homogeneous shallow water system some numerical results are shown where different numerical methods are compared in particular it is shown that in the non uniqueness cases the numerical solutions can converge to one or to the other solution what is the reason that explains the huge differences observed when different numerical methods are applied to the shallow water system with abrupt changes in the bottom moreover problems with zero solutions will be reinterpreted as partial riemann problems for the homogeneous system what will allow us to build a physically solution when one side of the step is wet and the other one is dry we will specify the regions where we can find zero one or two solutions giving the form of the solution when it is possible and giving an alternative when it is not possible

scalable extrinsic calibration of omni directional image networks we describe a linear time algorithm that recovers absolute camera orientations and positions along with uncertainty estimates for networks of terrestrial image nodes spanning hundreds of meters in outdoor urban scenes the algorithm produces pose estimates globally consistent to roughly 0 1 2 milliradians and 5 centimeters on average or about four pixels of epipolar alignment we assume that adjacent nodes observe overlapping portions of the scene and that at least two distinct vanishing points are observed by each node the algorithm decouples registration into pure rotation and translation stages the rotation stage aligns nodes to commonly observed scene line directionss the translation stage assigns node positions consistent with locally estimated motion directions then registers the resulting network to absolute earth coordinates the paper s principal contributions include extension of classic registration methods to large scale and dimensional extents a consistent probabilistic framework for modeling projective uncertaintys and a new hybrid of hough transform and expectation maximization algorithms we assess the algorithm s performance on synthetic and real data and draw several conclusions first by fusing thousands of observations the algorithm achieves accurate registration even in the face of significant lighting variations low level feature noise and error in initial pose estimates second the algorithm s robustness and accuracy increase with image field of view third the algorithm surmounts the usual tradeoff between speed and accuracys it is both faster and more accurate than manual bundle adjustment

reliability of first order numerical schemes for solving shallow water system over abrupt topography we compare some first order well balanced numerical schemes for shallow water system with special interest in applications where there are abrupt variations of the topography we show that the space step required to obtain a prescribed error depends on the method moreover the solutions given by the numerical scheme can be significantly different if not enough space resolution is used we shall pay special attention to the well known hydrostatic reconstruction technique where it is shown that the effect of large bottom discontinuities might be missed and a modification is proposed to avoid this problem

single view metrology we describe how 3d affine measurements may be computed from a single perspective view of a scene given only minimal geometric information determined from the image this minimal information is typically the vanishing line of a reference plane and a vanishing point for a direction not parallel to the plane it is shown that affine scene structure may then be determined from the image without knowledge of the camera s internal calibration e g focal length nor of the explicit relation between camera and world pose in particular we show how to i compute the distance between planes parallel to the reference plane up to a common scale factor s ii compute area and length ratios on any plane parallel to the reference planes iii determine the camera s location simple geometric derivations are given for these results we also develop an algebraic representation which unifies the three types of measurement and amongst other advantages permits a first order error propagation analysis to be performed associating an uncertainty with each measurement we demonstrate the technique for a variety of applications including height measurements in forensic images and 3d graphical modelling from single images

why many theories of shock waves are necessary convergence error in formally path consistent schemes we are interested in nonlinear hyperbolic systems in nonconservative form arising in fluid dynamics and for solutions containing shock waves we investigate the convergence of finite difference schemes applied to such systems according to dal maso lefloch and murat s theory a shock wave theory for a given nonconservative system requires prescribing a priori a family of paths in the phase space in the present paper we consider schemes that are formally consistent with a given family of paths and we investigate their limiting behavior as the mesh is refined we first generalize to systems a property established earlier by hou and lefloch for scalar conservation laws and we prove that nonconservative schemes generate at the level of the limiting hyperbolic system an convergence error source term which provided the total variation of the approximations remains uniformly bounded is a locally bounded measure this convergence error measure is supported on the shock trajectories and as we demonstrate here is usually small in the special case that the scheme converges in the sense of graphs a rather strong convergence property often violated in practice then this measure source term vanishes we also discuss the role of the equivalent equation associated with a difference scheme here the distinction between scalar equations and systems appears most clearly since for systems the equivalent equation of a scheme that is formally path consistent depends upon the prescribed family of paths the core of this paper is devoted to investigate numerically the approximation of several simplified or full hyperbolic models arising in fluid dynamics this leads us to the conclusion that for systems having nonconservative products associated with linearly degenerate characteristic fields the convergence error vanishes for more general models this measure is evaluated very accurately especially by plotting the shock curves associated with each scheme under consideration as we demonstrate plotting the shock curves provide a convenient approach for evaluating the range of validity of a given scheme

enhancement of the labswe for shallow water flows in the lattice boltzmann method for the shallow water equations labswe the force term involves the first order derivative related to a bed slope which has to be determined using the centred scheme for an accurate solution however such calculation contradicts the spirit of only simple arithmetic calculations required in the lattice boltzmann method this paper shows how to remove this drawback from the labswe by incorporating the bed level into the lattice boltzmann equation in a consistent manner with the lattice boltzmann approach three numerical tests have been presented to verify the proposed method

vanishing point detection without any a priori information even though vanishing points in digital images result from parallel lines in the 3d scene most of the proposed detection algorithms are forced to rely heavily either on additional properties like orthogonality or coplanarity and equal distance of the underlying 3d lines or on knowledge of the camera calibration parameters in order to avoid spurious responses in this work we develop a new detection algorithm that relies on the helmoltz principle recently proposed for computer vision by desolneux et al 2001 2003 both at the line detection and line grouping stages this leads to a vanishing point detector with a low false alarms rate and a high precision level which does not rely on any a priori information on the image or calibration parameters and does not require any parameter tuning

a scaled thickness conditioning for solid and solid shell discretizations of thin walled structures the numerical discretization of thin shell structures yields ill conditioned stiffness matrices due to an inherent large eigenvalue spectrum finite element parametrization that depends on shell thickness like relative displacement shells solid shells and other solid finite elements even add to the ill conditioning by introducing high eigenmodes to overcome this numerical issue we present a scaled thickness conditioning stc approach a mechanically motivated preconditioner for thin walled structures discretized with continuum based element formulations the proposed approach is motivated by the scaled director conditioning sdc method for relative displacement shell elements in contrast to sdc the novel stc approach yields a preconditioner for the effective linear system it is applicable independently of element technology employed coupling to other physical fields boundary conditions applied and additional algebraic constraints and can be easily extended to multilayer shell formulations the effect of the proposed preconditioner on the conditioning of the effective stiffness matrix and its eigenvalue spectrum is studied it is shown that the condition number of the modified system becomes almost independent from the aspect ratio of the employed elements the improved conditioning has a positive influence on the convergence behavior of iterative linear solvers in particular in combination with algebraic multigrid preconditioners the number of iterations could be decreased by more than 85 for some examples and the computation time could be reduced by about 60

energy stable staggered schemes for the shallow water equations abstract we focus on the development and analysis of staggered schemes for the two dimensional non linear shallow water equations with varying bathymetry semi implicit and fully explicit time discretizations are proposed particular attention is paid on non linear stability results principally considered here through discrete energy dissipation arguments to address such an issue specific convective fluxes are employed implying diffusive terms relying on the pressure gradient in addition of providing an explicit control of the discrete energy budget the method is shown to preserve motionless steady states as well as the positivity of the water height these properties are still satisfied in a fully explicit context provided an appropriate discretization of the pressure gradient these stability results make the approach particularly robust and efficient for both coastal flows and low froude number regimes as a result in addition of a great ease of implementation the presented schemes meet the operational requirements attached to the simulation of large and small scale oceanic flows

dynamics of geometrically exact sandwich beams 1 d plates computational aspects a galerkin projection of the complete equations of motion of geometrically exact sandwich beams applicable to 1 d plates is presented here the beam can take any arbitrary initial position in the 2 d space each layer of the beam can have different material constants with no restriction on the mass distribution and layer thickness further each layer can take on different length thus allowing the modeling of multilayer structures with ply drop offs finite rotation and shear deformation are accommodated for in each layer the deformed cross section of the beam is continuous piecewise linear the continuity of displacement across the interlayer boundaries is exactly enforced extensive numerical examples including sandwich beams with three identical layers sandwich structures with ply drop off free flying and spin up maneuver of sandwich beams are presented to illustrate the applicability and versatility of the proposed formulation

weak solutions for partial differential equations with source terms application to the shallow water equations weak solutions of problems with m equations with source terms are proposed using an augmented riemann solver defined by m 1 states instead of increasing the number of involved equations these weak solutions use propagating jump discontinuities connecting the m 1 states to approximate the riemann solution the average of the propagated waves in the computational cell leads to a reinterpretation of the roe s approach and in the upwind treatment of the source term of vazquez cendon it is derived that the numerical scheme can not be formulated evaluating the physical flux function at the position of the initial discontinuities as usually done in the homogeneous case positivity requirements over the values of the intermediate states are the only way to control the global stability of the method also it is shown that the definition of well balanced equilibrium in trivial cases is not sufficient to provide correct results it is necessary to provide discrete evaluations of the source term that ensure energy dissipating solutions when demanded the one and two dimensional shallow water equations with source terms due to the bottom topography and friction are presented as case study the stability region is shown to differ from the one defined for the case without source terms and it can be derived that the appearance of negative values of the thickness of the water layer in the proximity of the wet dry front is a particular case of the wet wet fronts the consequence is a severe reduction in the magnitude of the allowable time step size if compared with the one obtained for the homogeneous case starting from this result 1d and 2d numerical schemes are developed for both quadrilateral and triangular grids enforcing conservation and positivity over the solution allowing computationally efficient simulations by means of a reconstruction technique for the inner states of the weak solution that allows a recovery of the time step size

estimating the perspective pose of texture planes using spectral analysis on the unit sphere multiple vanishing point detection provides the key to recovering the perspective pose of textured planes if vanishing points are to be detected from spectral information then there are two computational problems that need to be solved firstly the search of the extended image plane is unbounded and hence the location of vanishing points at or near infinity is difficult secondly correspondences between local spectra need to be established so that vanishing points can be triangulated in this paper we offer a way of overcoming these two difficulties we overcome the problem of unbounded search by mapping the information provided by local spectral moments onto the unit sphere according to our representation the position and direction of each local spectrum maps onto a great circle on the unit sphere the need for correspondences is overcome by accumulating the great circle intercepts vanishing points occur at local accumulator maxima on the unit sphere to improve the accuracy of the recovered perspective pose parameters for highly slanted planes we use an adaptive spectral window this selects the window so as to reduce spectral defocusing by minimising the determinant of the spectral covariance matrix we experiment with the new shape from texture technique on both synthetic and real world data here it proves to be an accurate and robust means of estimating perspective pose

short note a comment on the computation of non conservative products we are interested in the solution of non conservative hyperbolic systems and consider in particular the so called path conservative schemes see e g 2 3 which rely on the theoretical work in 1 the example of the standard euler equations for a perfect gas is used to illuminate some computational issues and shortcomings of this approach

a new hydrostatic reconstruction scheme based on subcell reconstructions a key difficulty in the analysis and numerical approximation of the shallow water equations is the nonconservative product of measures due to the gravitational force acting on a sloped bottom solu

the surface gradient method for the treatment of source terms in the shallow water equations a novel scheme has been developed for data reconstruction within a godunov type method for solving the shallow water equations with source terms in contrast to conventional data reconstruction methods based on conservative variables the water surface level is chosen as the basis for data reconstruction this provides accurate values of the conservative variables at cell interfaces so that the fluxes can be accurately calculated with a riemann solver the main advantages are 1 a simple centered discretization is used for the source terms 2 the scheme is no more complicated than the conventional method for the homogeneous terms 3 small perturbations in the water surface elevation can be accurately predicted and 4 the method is generally suitable for both steady and unsteady shallow water problems the accuracy of the scheme has been verified by recourse to both steady and unsteady flow problems excellent agreement has been obtained between the numerical predictions and analytical solutions the results indicate that the new scheme is accurate simple efficient and robust

performance evaluation and analysis of vanishing point detection techniques vanishing point detection algorithms based on a gaussian sphere representation have been employed in a variety of computer vision systems for extracting 3d line orientations as a first step towards object detection typically these algorithms have been applied to imagery with strong perspective effects and with little noise or texture resulting in good solutions for line orientations however these algorithms can fail if perspective effects are weak or if texture edges are predominant they also fail to take advantage of knowledge about the objects to be detected in this paper two new techniques for robust vanishing point detection on the gaussian sphere are presented primitive based vanishing point analysis and interpretation plane error modeling the performance of these methods along with two other existing methods from the literature are quantitatively evaluated and compared for the task of building detection in complex aerial imagery

optimal solid shells for non linear analyses of multilayer composites ii dynamics abstract we are presenting a simple low order solid shell element formulation having only displacement degrees of freedom dofs i e without rotational dofs that has an optimal number of parameters to pass the patch tests and thus allows for efficient and accurate analyses of large deformable multilayer shell structures using elements at extremely high aspect ratio with the dynamics referred to a fixed inertial frame the elements can be used to analyze multilayer shell structures undergoing large overall motion the formulation of this element is based on the mixed hu washizu variational principle leading to a novel enhancing strain tensor enhanced assumed strain eas method that renders the computation particularly efficient with improved in plane and out of plane bending behavior poisson thickness locking especially in refined analyses of composite structures involving a large number of high aspect ratio layers the energy momentum conserving algorithm in the context of current solid shell element is presented we discuss the eas formulation based on the displacement gradient and its complexity compared to formulation on the green lagrange strain shear locking and curvature thickness locking are treated using the assumed natural strain ans method the element has an optimal combination of the ans method and the minimal number of eas parameters required to pass the plate bending patch test numerical examples involving dynamic analyses with conservation of energy and momentum of multilayer shell structures having a large range of element aspect ratios are presented several implicit direct integration methods with without numerical dissipation are used and compared in terms of the accuracy stability and cost in multilayer shell structure finally we note that the topic in this paper is a fitting dedication to professor ekkehard ramm who has made important pioneering contributions in this research direction

on shear correction factors in the non linear theory of elastic shells abstract theoretical values of two correction factors s 5 6 and t 7 10 are established for the respective transverse shear stress resultants and stress couples within the general dynamically and kinematically exact six field theory of elastic shells these values do not depend on the shell material symmetry geometry of the base surface the shell thickness or any kind of kinematic and or dynamic constraints the analysis is based on the complementary energy density following from the transverse shear stresses acting only on the shell cross section the appropriate quadratic and cubic distributions of the stresses across the thickness allow one to derive the consistent constitutive equations for the transverse shear stress resultants and stress couples with s and t as the respective correction factors four numerical examples of highly non linear shell structures illustrate the influence of different values of s and t on the results in particular some influence of t is noticed on the placement of bifurcation points in dynamic problem of flight of three intersecting plates analysed with newmark type temporal algorithm the value of t influences the moment at which the relative error of total energy of the system begins to grow indefinitely leading to the solution failure

a conservative high order discontinuous galerkin method for the shallow water equations with arbitrary topography a conservative high order godunov type scheme is presented for solving the balance laws of the 1d shallow water equations swe the scheme adopts a finite element runge kutta rk discontinuous galerkin dg framework based on an overall third order accurate formulation the model is referred to as rkdg3 treatment of topographic source term is built in the dg approximation simplified formulae for initializing bed data at a discrete level are derived by assuming a local linear bed function to ease practical flow simulations owing to the adverse effects caused by using an uncontrolled global limiting process in an rkdg3 scheme rkdg3 gl a new conservative rkdg3 scheme with user parameter free local limiting method rkdg3 ll is designed to gain better accuracy and conservativeness the advantages of the new rkdg3 ll model are demonstrated by applying to several steady and transient benchmark flow tests with irregular either differentiable or non differentiable topography copyright 2010 john wiley sons ltd

multilayer shells geometrically exact formulation of equations of motion we present here a formulation for geometrically exact multilayer shells where the number of layers is completely arbitrary and not necessarily restricted to three as in the case of sandwich shells based entirely in terms of stress resultants the formulation accommodates finite deformation in membrane bending and shear deformation typical of geometrically exact formulation the kinematics of the shell is referred directly to an inertial frame and not by means of a floating frame the motion of a transverse fiber of an n layer shell is exactly that of a chain of n rigid links connected by universal joints in three dimensional space the kinematics of deformation in each layer is expressed in terms of the deformation of an arbitrary layer chosen as a reference layer the thickness and side dimensions of each layer are also arbitrary these features allow a convenient modeling of multilayer shells with ply drop offs we also show that the present formulation reduces exactly to the case of multilayer beams