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
2129494071 2006303959 852449
Modeling the deformation of human organs for surgery simulation systems has turned out to be quite a challenge. Not only is very little known about the physical properties of general human tissue but in addition, most conventional modeling techniques are not applicable because of the timing requirements of simulation systems. To produce a video-like visualization of a deforming organ, the deformation must be determined at rates of 10-20 times s. In the fields of elasticity and related modeling paradigms, the main interest has been the development of accurate mathematical models. The speed of these models has been a secondary interest. But for surgery simulation systems, the priorities are reversed. The main interest is the speed and robustness of the models, and accuracy is of less concern. Recent years have seen the development of different practical modeling techniques that take into account the reversed priorities and can be used in practice for real-time modeling of deformable organs. The paper discusses some of these new techniques in the reference frame of finite element models. In particular, it builds on the recent work by the author on fast finite element models and discusses the advantages and disadvantages of these models in comparison to previous models. 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. 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.