3D optical flow for large CT data of materials microstructures

Abstract

We compute three‐dimensional displacement vector fields to estimate the deformation of microstructural data sets in mechanical tests. For this, we extend the well‐known optical flow by Brox et al. to three dimensions, with special focus on the discretization of nonlinear terms. We evaluate our method first by synthetically deforming foams and comparing against this ground truth and second with data sets of samples that underwent real mechanical tests. Our results are compared to those from state‐of‐the‐art algorithms in materials science and medical image registration. By a thorough evaluation, we show that our proposed method is able to resolve the displacement best among all chosen comparison methods.

Ex- and in-situ tests of materials: From design to materials parameters via motion estimation

“…In [12], we showed the superior performance of this approach compared to state-of-the-art methods. The averaging nature (also visually observable in [12]) of DVC based methods inhibits representation of small scale behavior in the computed displacement fields. Subvolume based methods will almost always overlook delicate behavior like breaking struts or crack initiation.…”

“…The use of total variation for motion estimation is very well established in 2D applications and small displacements since the seminal work of Brox et al [4] from 2004. We recently extended this work to 3D and applied it in materials science [12]. The idea is to use a differentiable approximation to the L 1 norm as distance function, i.e.…”

“…The benefit of such an additional term is demonstrated in [12]. Eventually, the displacement u = (u, v, w), is found by minimizing…”

Mathematical morphology on directional data

“…The foam is expected to fail very suddenly due to its thin struts. Nogatz et al [40] computed the displacement field for the transition from strain level 1% to 3.8% which is shown in Figure 9a. During compression, a fault zone forms which is now postprocessed by directional morphology.…”

Mathematical morphology on directional data

“…The foam is expected to fail very suddenly due to its thin struts. Nogatz et al [40] computed the displacement field for the transition from strain level 1% to 3.8% which is shown in Figure 9a. During compression, a fault zone forms which is now post-processed by directional morphology.…”