  Characterizing the grain structure of polycrystalline material is an
important task in material science. The present paper introduces the concept of
generalized balanced power diagrams as a concise alternative to voxelated
mappings. Here, each grain is represented by (measured approximations of) its
center-of-mass position, its volume and, if available, by its second-order
moments (in the non-equiaxed case). Such parameters may be obtained from 3D
x-ray diffraction. As the exact global optimum of our model results from the
solution of a suitable linear program it can be computed quite efficiently.
Based on verified real-world measurements we show that from the few parameters
per grain (3, respectively 6 in 2D and 4, respectively 10 in 3D) we obtain
excellent representations of both equiaxed and non-equiaxed structures. Hence
our approach seems to capture the physical principles governing the forming of
such polycrystals in the underlying process quite well.

Materials Science;Optimization and Control