Computation and Visualization of Local Deformation for Multiphase Metallic Materials by Infimal Convolution of TV-Type Functionals

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

doi:10.1007/978-3-319-18461-6_31

Cited by 5 publications

(3 citation statements)

References 19 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In the previous paper [3], we assumed that u = v + w can be decomposed additively into a (componentwise) non-smooth part v ∈ BV(Ω, R 2 ) and a smooth part w ∈ BH(Ω, R 2 ) and suggested under the above smoothness assumptions the prior…”

Section: Modelmentioning

confidence: 99%

“…of the strain. In the conference paper [3], we built up on the assumption that the displacement field u is additively composed of a nonsmooth part v and a smooth part w. Then, we penalized the Jacobian of v and the second order derivative of w by an infimal convolution prior. The infimal convolution (IC) of first and second order derivatives was introduced in imaging by Chambolle and Lions [12].…”

Section: Introductionmentioning

confidence: 99%

“…We mention that there is a software package corresponding to [33] available since 2015. Our first code in [3] was written before any public software package with TGV or infimal convolution prior was available. Our applications show the potential of the method in an impressive way.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Strain analysis by a total generalized variation regularized optical flow model

Balle

Beck

Eifler

et al. 2018

Inverse Problems in Science and Engineering

Self Cite

View full text Add to dashboard Cite

In this paper we deal with the important 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 field. 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 prior splits the Jacobian of the displacement field 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. Our algorithm 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 for strain analysis our method can resolve local phenomena much better.Remark 7. The soft shrinkage (14) is obtained in the special case λ 1 = λ 2 andx 1 =x 2 .

show abstract

Section: Modelmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%