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.
Several authors suggested learning the parameters of linear finite element models from a set of observations. We use such a method in combination with a tracking method to find an accurate tracking result of the observed and the unobserved side of the model. For a summary of linear finite element methods for elastic deformations, refer to Bro-Nielsen @cite_9 .
@cite_9
2006303959 852449 2135085348 2161084987
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. This paper presents an algorithm for learning the time-varying shape of a non-rigid 3D object from uncalibrated 2D tracking data. We model shape motion as a rigid component (rotation and translation) combined with a non-rigid deformation. Reconstruction is ill-posed if arbitrary deformations are allowed. We constrain the problem by assuming that the object shape at each time instant is drawn from a Gaussian distribution. Based on this assumption, the algorithm simultaneously estimates 3D shape and motion for each time frame, learns the parameters of the Gaussian, and robustly fills-in missing data points. We then extend the algorithm to model temporal smoothness in object shape, thus allowing it to handle severe cases of missing data. We review an algorithm for the finite element simulation of elastoplastic solids which is capable of robustly and efficiently handling arbitrarily large deformation. In fact, the model remains valid even when large parts of the mesh are inverted. The algorithm is straightforward to implement and can be used with any material constitutive model, and for both volumetric solids and thin shells such as cloth. We also discuss a mechanism for controlling plastic deformation, which allows a deformable object to be guided towards a desired final shape without sacrificing realistic behavior, and an improved method for rigid body collision handling in the context of mixed explicit implicit time-stepping. Finally, we present a novel extension of our method to arbitrary element types including specific details for hexahedral elements.