On the use of 2-D moment invariants for the automated classification of particle shapes

A mathematical method is introduced to describe quantitatively the shape and shape evolution of precipitates in a two-phase microstructure. The method relies on the concept of moment invariants, i.e. combinations of second-order moments that are invariant with respect to affine and/or similarity transformations. Examples are given for special two-dimensional (2-D) shapes, including rectangles, ellipses and regular polygons, and the concept of the moment invariant density map is introduced. Three applications to 2-D phase field simulations of γ–γ′ superalloy microstructures are discussed: average particle shape, shape evolution and particle consolidation.