Display Omitted We present a method to robustly track the geometry of an object that deforms over time.We fit a FEM-based model to the data leading to physically plausible results.We evaluate the performance of our method using synthetic and scanned data. We present an approach to robustly track the geometry of an object that deforms over time from a set of input point clouds captured from a single viewpoint. The deformations we consider are caused by applying forces to known locations on the object's surface. Our method combines the use of prior information on the geometry of the object modeled by a smooth template and the use of a linear finite element method to predict the deformation. This allows the accurate reconstruction of both the observed and the unobserved sides of the object. We present tracking results for noisy low-quality point clouds acquired by either a stereo camera or a depth camera, and simulations with point clouds corrupted by different error terms. We show that our method is also applicable to large non-linear deformations.
Lang and Pai @cite_41 used a surface displacement and contact force at one point along with range-flow data to estimate elastic constants of homogeneous isotropic materials using numerical optimization. Becker and Teschner @cite_17 presented an approach to estimate the elasticity parameters for isotropic materials using a linear finite element method. The approach takes as input a set of displacement and force measurements and uses them to compute the Young's modulus and Poisson's ratio (see Bro-Nielsen @cite_9 ) with the help of an efficient quadratic programming technique. @cite_1 presented a similar approach to estimate both the elasticity and viscosity parameters for viscoelastic materials using a linear finite element method. This approach reduces the problem to solving a linear system of equations and has been shown to run in real-time.
@cite_41 @cite_9 @cite_1 @cite_17
2006303959 2079263908 1982359839 852449
The linear dynamic finite element model can be formulated such that the elasticity and viscosity of the elements appear as the parameters in a linear system of equations. The resulting system of equations can be solved directly using singular value decomposition or a similar technique or through defining a quadratic functional. A priori knowledge and regularity measures can be added as equality or inequality constraints. The sensitivity of the inverse problem solution to the displacement noise and model imperfections are tested in simulations, where the parameters were successfully reconstructed with a displacement signal-to-noise ratio as low as 20 dB. Also, the viscoelastic parameters have been successfully estimated for a breast phantom with an embedded hard inclusion. The study of the computation speed demonstrates the potential of the new method for real-time implementations. This paper deals with a high-order accurate discontinuous finite element method for the numerical solution of the compressible Navier?Stokes equations. We extend a discontinuous finite element discretization originally considered for hyperbolic systems such as the Euler equations to the case of the Navier?Stokes equations by treating the viscous terms with a mixed formulation. The method combines two key ideas which are at the basis of the finite volume and of the finite element method, the physics of wave propagation being accounted for by means of Riemann problems and accuracy being obtained by means of high-order polynomial approximations within elements. As a consequence the method is ideally suited to compute high-order accurate solution of the Navier?Stokes equations on unstructured grids. The performance of the proposed method is illustrated by computing the compressible viscous flow on a flat plate and around a NACA0012 airfoil for several flow regimes using constant, linear, quadratic, and cubic elements. We propose and analyze a discontinuous Galerkin approximation for the Stokes problem. The finite element triangulation employed is not required to be conforming and we use discontinuous pressures and velocities. No additional unknown fields need to be introduced, but only suitable bilinear forms defined on the interfaces between the elements, involving the jumps of the velocity and the average of the pressure. We consider hp approximations using ℚk′–ℚk velocity-pressure pairs with k′ = k + 2, k + 1, k. Our methods show better stability properties than the corresponding conforming ones. We prove that our first two choices of velocity spaces ensure uniform divergence stability with respect to the mesh size h. Numerical results show that they are uniformly stable with respect to the local polynomial degree k, a property that has no analog in the conforming case. An explicit bound in k which is not sharp is also proven. Numerical results show that if equal order approximation is chosen for the velocity and pressure, no spurious pressure modes are present but the method is not uniformly stable either with respect to h or k. We derive a priori error estimates generalizing the abstract theory of mixed methods. Optimal error estimates in h are proven. As for discontinuous Galerkin methods for scalar diffusive problems, half of the power of k is lost for p and hp pproximations independently of the divergence stability. Realistic elasticity parameters are important for the accurate simulation of deformable objects, e. g. in medical simulations. In this paper, we present an approach for estimating elasticity parameters for isotropic elastic materials using the linear Finite Element Method. Employing the initial undeformed geometry and a measured forcedeformation relation, the method computes the elasticity parameters based on Quadratic Programming. The structure of the stiffness matrix is employed to accelerate the estimation process. Experiments suggest, that the parameter estimation approach can be used for noisy data.