Nowadays image acquisition in materials science allows the resolution of grains at atomic scale. Grains are material regions with different lattice orientation which are frequently in addition elastically stressed. At the same time, new microscopic simulation tools allow to study the dynamics of such grain structures. Single atoms are resolved experimentally as well as in simulation results on the data microscale, whereas lattice orientation and elastic deformation describe corresponding physical structures mesoscopically. 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 the microscopic image data. Based on a Mumford