3D rotation invariants by complex moments

•The 3D rotation complex moment invariants are presented.•They are derived by the group representation theory.•The algorithm for automatic generation of the invariants is proposed.•The linearly dependent (reducible) invariants are eliminated.•The invariants are experimentally tested on both triangulated and volumetric data.

A generalization of the complex moments from 2D to 3D is described. Group representation theory is used to construct 3D rotation invariants from them. The algorithm for automatic generating of the invariants of higher orders is proposed. An algorithm for automatic generation of higher order invariants is proposed. The linearly dependent invariants are eliminated. The invariants are experimentally tested on 3D graphical models and also on real volumetric data.