Convex relaxation for grain segmentation at atomic scale

Grains are material regions with different lattice orientation at atomic scale. They can be resolved on material surfaces with recent image acquisition technology. Simultaneously, new microscopic simulation tools allow to study mechanical models of grain structures. The robust and reliable identification and visualization of grain boundaries - in images both from simulation and from experiments - is of central importance in the field of material surface analysis. In this work, we compare a variety of variational approaches for grain boundary estimation from microscopy and simulation images. In particular, we show that grain boundary estimation can be solved by means of recently introduced convex relaxation techniques. These techniques allow to compute global solutions or solutions within a known bound of the optimum. Moreover, experimental results both on simulated and on transmission electron microscopy images confirm that the convex relaxation techniques provide significant improvements of the estimated grain boundaries over previously employed multiphase level set formulations.