Finite element based tracking of deforming surfaces

Abstract

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.

Constraining dense hand surface tracking with elasticity

“…This work does not handle self-collisions and recent work [Smith et al 2018] has shown that ARAP and its co-rotational extension produce unacceptable artifacts when used to model human flesh, making this technique less than ideal for modeling a hand. A similar method instead performs an initial pass of surface tracking with a data term and surface regularizer followed by a solve with a volumetric tetrahedral mesh and a linear elastic model to improve tracking quality in unobserved regions [Wuhrer et al 2015]. Linear elasticity is not suited for modeling large deformations [Müller et al 2002], however, and this work is thus forced to reinitialize the mesh's rest state at each frame, leading to artificial plasticity and limiting the method to small deformations.…”

A hybrid approach to 3d tongue modeling from vocal tract MRI using unsupervised image segmentation and mesh deformation

“…Finally, we use the method of Wuhrer et al [12] to deform a template mesh M := (V, F) to match the point cloud data P. Here, V := {⃗ v i } denotes the vertex set of the mesh with ⃗ v i ∈ R 3 and F its face set. To obtain a deformation, the approach computes a set A := {A i } where A i : R 3 → R 3 is a rigid body motion for the vertex ⃗ v i by minimizing the following energy:…”

“…In order to find a minimizer A, we use a similar strategy like [12]: As a preprocessing step, we perform an automatic rigid alignment to find a good position for the template that is near the point cloud. Afterwards, we minimize a series of energies E t Def (A t ) where t ∈ [1,t max ].…”

“…As arg min ⃗ p j ∈P (•) then does not depend on A t , the energy becomes differentiable and we can use a quasi-Newton technique [13] to compute the minimizer. In contrast to [12], we fix the weight β for all E t Def because the weights used in the experiments are not high enough to apply their relaxation technique. Eventually, we obtain A as A t max .…”

“…Furthermore, the optimization process is embedded in a coarse-to-fine strategy to account for large deformations [12].…”