B. Berkels, A. Rätz, M. Rumpf, and A. Voigt.
Identification of grain boundary contours at atomic scale.
In First International Conference on Scale Space Methods and
Variational Methods in Computer Vision, volume 4485 of Lecture Notes in
Computer Science, pages 765-776. Springer, 2007.
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Nowadays image acquisition in materials science allows the resolution of grains at atomic scale. Grains are material regions with different lattice orientation which are typically not in equilibrium. At the same time, new microscopic simulation tools allow to study the dynamics of such grain structures. Single atoms are resolved in the experimental and in the simulation results. A qualitative study of experimental images and simulation results and the comparison of simulation and experiment requires the robust and reliable extraction of mesoscopic properties from these microscopic data sets. Based on a Mumford-Shah type functional, grain boundaries are described as free discontinuity sets at which the orientation parameter for the lattice jumps. The lattice structure itself is encoded in a suitable integrand depending on the local lattice orientation. In addition the approach incorporates solid-liquid interfaces. The resulting Mumford-Shah functional is approximated with a level set active contour model following the approach by Chan and Vese. The implementation is based on a finite element discretization in space and a step size controlled gradient descent algorithm.