real time visual tracking of complex structures presents a framework for three dimensional model based tracking graphical rendering technology is combined with constrained active contour tracking to create a robust wire frame tracking system it operates in real time at video frame rate 25 hz on standard hardware it is based on an internal cad model of the object to be tracked which is rendered using a binary space partition tree to perform hidden line removal a lie group formalism is used to cast the motion computation problem into simple geometric terms so that tracking becomes a simple optimization problem solved by means of iterative reweighted least squares a visual servoing system constructed using this framework is presented together with results showing the accuracy of the tracker the paper then describes how this tracking system has been extended to provide a general framework for tracking in complex configurations the adjoint representation of the group is used to transform measurements into common coordinate frames the constraints are then imposed by means of lagrange multipliers results from a number of experiments performed using this framework are presented and discussed

analysis of a finite element method for maxwell s equations the use of finite elements to discretize the time dependent maxwell equations on a bounded domain in three dimensional space is analyzed energy norm error estimates are provided when general finite element methods are used to discretize the equations in space in addition it is shown that if some curl conforming elements due to nedelec are used error estimates may also be proved in the l 2 norm

lyapunov coefficients for an invisible fold fold singularity in planar piecewise hamiltonian systems abstract we study the stability of an invisible fold fold singularity of planar piecewise smooth hamiltonian vector fields by computing some kind of lyapunov coefficients we obtain the general expressions for the first five lyapunov coefficients as a consequence the bifurcation diagrams illustrating the number types and positions of the bifurcating small amplitude crossing limit cycles for these vector fields are determined

regularization and singular perturbation techniques for non smooth systems abstract this paper is concerned with some aspects of the qualitative geometric theory of non smooth systems we present a survey of the state of the art on the connection between the regularization process of non smooth vector fields and the singular perturbation problems as a matter of fact the main results in our setting fill a gap between these areas exploiting such results applications to constrained differential equations are discussed

h based a φ approaches of approximating eddy current problem by way of solving different systems inside and outside the conductor in this paper we suggest some new algorithms to realize approximating magnetic field equations derived from the basic eddy current model in the bounded domain these algorithms are based on solving two different equation systems inside and outside the conductor in which eddy current is formed in addition we extend relative results to the corresponding unbounded domain problem by the coupling of finite elements and natural boundary elements and the domain decomposition method based on the natural boundary reduction respectively meanwhile some error estimates are given

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

regularization around a generic codimension one fold fold singularity abstract this paper is devoted to study the generic fold fold singularity of filippov systems on the plane its unfoldings and its sotomayor teixeira regularization we work with general filippov systems and provide the bifurcation diagrams of the fold fold singularity and their unfoldings proving that under some generic conditions is a codimension one embedded submanifold of the set of all filippov systems the regularization of this singularity is studied and its bifurcation diagram is shown in the visible invisible case the use of geometric singular perturbation theory has been useful to give the complete diagram of the unfolding specially the appearance and disappearance of periodic orbits that are not present in the filippov vector field in the case of a linear regularization we prove that the regularized system is equivalent to a general slow fast system studied by krupa and szmolyan 10

preconditioning of the second kind boundary integral equations for 3d eddy current problems starting from the time harmonic maxwell equations at low frequency eddy current approximation the h formulation is presented an equivalent system of boundary integral equations of the second kind on the conductor surface resp the conductor dielectric is derived discretizing these equations with a boundary element method bem yields a block linear equation system left begin array cc a 1 b 1 tfrac mu mu 0 tilde b 2 a 2 end array right left begin array c j sigma end array right left begin array c b 1 b 2 end array right with a fully populated stiffness matrix this system is non symmetric and for large 0 of interest in practice ill conditioned iterative solvers like gmres converge very slowly in general we propose a new preconditioner which depends on we present numerical results with a serial and parallel version of this preconditioner also on large industrial eddy current problems with compex geometry the performance of preconditioned gmres is found to be practically independent of 0 copyright 2001 john wiley sons ltd

on a finite element method for solving the three dimensional maxwell equations abstract the aim of this paper is to present a method for solving the time domain three dimensional maxwell equations which can be coupled with a particle solver for this purpose maxwell s equations are reformulated as a constrained wave equation system with lagrange multipliers associated to the conditions 0 and e e 0 we approximate both the fields and the lagrange multipliers with a finite element method using a taylor hood element

direct discretization of planar div curl problems a control volume method is proposed for planar div curl systems the method is independent of potential and least squares formulations and works directly with the div curl system the novelty of the technique lies in its use of a single local vector field component and two control volumes rather than the other way round a discrete vector field theory comes quite naturally from this idea and is developed in the paper error estimates are proved for the method and other ramifications investigated

a hybrid finite element method for stokes flow part ii stability and convergence studies abstract in part i we have presented a hybrid finite element method based on an assumed stress field which has the features i the unknowns in the final system of finite element equations are a the nodal velocities and b the constant term in the arbitrary pressure field over each element ii exact integrations were performed for each element in the following we present studies of stability and convergence of the above hybrid finite element method

application of lie algebras to visual servoing a novel approach to visual servoing is presented which takes advantage of the structure of the lie algebra of affine transformations the aim of this project is to use feedback from a visual sensor to guide a robot arm to a target position the target position is learned using the principle of teaching by showing in which the supervisor places the robot in the correct target position and the system captures the necessary information to be able to return to that position the sensor is placed in the end effector of the robot the camera in hand approach and thus provides direct feedback of the robot motion relative to the target scene via observed transformations of the scene these scene transformations are obtained by measuring the affine deformations of a target planar contour under the weak perspective assumption captured by use of an active contour or snake deformations of the snake are constrained using the lie groups of affine and projective transformations properties of the lie algebra of affine transformations are exploited to provide a novel method for integrating observed deformations of the target contour these can be compensated with appropriate robot motion using a non linear control structure the local differential representation of contour deformations is extended to allow accurate integration of an extended series of small perturbations this differs from existing approaches by virtue of the properties of the lie algebra representation which implicitly embeds knowledge of the three dimensional world within a two dimensional image based system these techniques have been implemented using a video camera to control a 5 dof robot arm experiments with this implementation are presented together with a discussion of the results

degenerate grazing sliding bifurcations in planar filippov systems abstract in this paper we contribute to a class of degenerate grazing sliding bifurcations in planar filippov systems assuming that the unperturbed system has a generalized homoclinic loop to a fold fold point depending on the type of this fold fold point we exhibit some codimension 2 bifurcation diagrams as well as the asymptotics of all bifurcation curves our work not only reports several complete unfoldings in the investigation of degenerate grazing sliding bifurcations but also answers the open problem about the maximum number of limit cycles bifurcating from the generalized homoclinic loop for the case of fold fold presented in liang et al 2013 30

relaxation oscillation and canard explosion abstract we give a geometric analysis of relaxation oscillations and canard cycles in singularly perturbed planar vector fields the transition from small hopf type cycles to large relaxation cycles which occurs in an exponentially thin parameter interval is described as a perturbation of a family of singular cycles the results are obtained by means of two blow up transformations combined with standard tools of dynamical systems theory the efficient use of various charts is emphasized the results are applied to the van der pol equation

some new error estimates for ritz galerkin methods with minimal regularity assumptions new uniform error estimates are established for finite element approximations u h of solutions u of second order elliptic equations lu f using only the regularity assumption u 1 c f 1 using an aubin nitsche type duality argument we show for example that for arbitrary fixed e sufficiently small there exists an h 0 such that for 0 h h 0 u u h 0 e u u h 1 here s denotes the norm on the sobolev space h s other related results are established

least squares finite element approximations to solutions of interface problems a least squares finite element method for second order elliptic boundary value problems having interfaces due to discontinuous media properties is proposed and analyzed both dirichlet and neumann boundary data are treated the boundary value problems are recast into a first order formulation to which a suitable least squares principle is applied among the advantages of the method are that nonconforming with respect to the interface approximating subspaces may be used moreover the grids used on each side of an interface need not coincide along the interface error estimates are derived that improve on other treatments of interface problems and a numerical example is provided to illustrate the method and the analyses

a new family of mixed finite elements in ir 3 we introduce two families of mixed finite element on conforming inh div and one conforming inh curl these finite elements can be used to approximate the stokes system

convergence analysis of a covolume scheme for maxwell s equations in three dimensions this paper contains error estimates for covolume discretizations of maxwell s equations in three space dimensions several estimates are proved first an estimate for a semi discrete scheme is given second the estimate is extended to cover the classical interlaced time marching technique third some of our unstructured mesh results are specialized to rectangular meshes both uniform and nonuniform by means of some additional analysis it is shown that the spatial convergence rate is one order higher than for the unstructured case

generic bifurcations of low codimension of planar filippov systems abstract in this article some qualitative and geometric aspects of non smooth dynamical systems theory are discussed the main aim of this article is to develop a systematic method for studying local and global bifurcations in non smooth dynamical systems our results deal with the classification and characterization of generic codimension 2 singularities of planar filippov systems as well as the presentation of the bifurcation diagrams and some dynamical consequences

finite element methods and their convergence for elliptic and parabolic interface problems in this paper we consider the finite element methods for solving second order elliptic and parabolic interface problems in two dimensional convex polygonal domains nearly the same optimal l 2 norm and energy norm error estimates as for regular problems are obtained when the interfaces are of arbitrary shape but are smooth though the regularities of the solutions are low on the whole domain the assumptions on the finite element triangulation are reasonable and practical

finite element methods with matching and nonmatching meshes for maxwell equations with discontinuous coefficients we investigate the finite element methods for solving time dependent maxwell equations with discontinuous coefficients in general three dimensional lipschitz polyhedral domains both matching and nonmatching finite element meshes on the interfaces are considered and optimal error estimates for both cases are obtained the analysis of the latter case is based on an abstract framework for nested saddle point problems along with a characterization of the trace space for h curl d a new extension theorem for h curl d functions in any lipschitz domain d and a novel compactness argument for deriving discrete inf sup conditions

a singular approach to discontinuous vector fields on the plane in this paper we deal with discontinuous vector fields on r 2 and we prove that the analysis of their local behavior around a typical singularity can be treated via singular perturbation the regularization process developed by sotomayor and teixeira is crucial for the development of this work

incremental model based estimation using geometric constraints we present a model based framework for incremental adaptive object shape estimation and tracking in monocular image sequences parametric structure and motion estimation methods usually assume a fixed class of shape representation splines deformable superquadrics etc that is initialized prior to tracking since the model shape coverage is fixed a priori the incremental recovery of structure is decoupled from tracking thereby limiting both processes in their scope and robustness in this work we describe a model based framework that supports the automatic detection and integration of low level geometric primitives lines incrementally such primitives are not explicitly captured in the initial model but are moving consistently with its image motion the consistency tests used to identify new structure are based on trinocular constraints between geometric primitives the method allows not only an increase in the model scope but also improves tracking accuracy by including the newly recovered features in its state estimation the formulation is a step toward automatic model building since it allows both weaker assumptions on the availability of a prior shape representation and on the number of features that would otherwise be necessary for entirely bottom up reconstruction we demonstrate the proposed approach on two separate image based tracking domains each involving complex 3d object structure and motion

a φ approaches of an eddy current problem based on solving certain potentials in this paper we propose novel finite element a approaches to realize the approximation of a three dimensional eddy current problem in a bounded domain containing a simply connected conductor region where the eddy current is formed these algorithms are based on solving a vector potential in the whole domain by using the edge finite element method and a local scalar potential only in the conductor region by using the nodal finite element method further error estimates for coupled and decoupled a schemes are given