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Strain analysis by a total generalized variation regularized optical flow model

: Balle, Frank; Beck, Tilmann; Eifler, Dietmar; Fitschen, Jan Henrik; Schuff, Sebastian; Steidl, Gabriele


Inverse problems in science and engineering 27 (2019), Nr.4, S.540-564
ISSN: 1741-5977
ISSN: 1741-5985
Deutsche Forschungsgemeinschaft DFG

Stochastic Models for Innovations in the Engineering Sciences
Fraunhofer EMI ()
strain analysis; optical flow; total generalized variation; image processing; variational method; materials science; tensile tests; convex optimization

In this paper, we deal with the problem of estimating the local strain tensor from a sequence of micro-structural images realized during deformation tests of engineering materials. Since the strain tensor is defined via the Jacobian of the displacement field, we propose to compute the displacement field by a variational model which takes care of properties of the Jacobian of the displacement. In particular, we are interested in areas of high strain. The data term of our variational model relies on the brightness invariance property of the image sequence. As prior we choose the second order total generalized variation of the displacement field. This splits the Jacobian into a smooth and a non-smooth part. The latter reflects the material cracks. An additional constraint is incorporated to handle physical properties of the non-smooth part for tensile tests. We prove that the resulting convex model has a minimizer and show how a primal-dual method can be applied to find a minimizer. The corresponding algorithm has the advantage that the strain tensor is directly computed within the iteration process. It is further equipped with a coarse-to-fine strategy to cope with larger displacements. Numerical examples with simulated and experimental data demonstrate the very good performance of our algorithm. In comparison to state-of-the-art engineering software, our method can resolve local phenomena much better.