Fast invariant recognition of color 3D images based on triplet-quaternion-valued moments and invariants

In this work we proposed an elegant theory of invariants of color 3D images. Our theory is based on the theory of triplet numbers and quaternions. We propose triplet-quaternion-valued invariants, which are related to the descriptions of objects as the zero sets of implicit polynomials. These are global invariants which show great promise for recognition of complicated objects. Triplet-quaternion-valued invariants have good discriminating power for computer recognition of 3D colour objects using statistical pattern recognition methods. For fast computation of triplet--quaternion--valued invariants we use modular arithmetic of Galois fields and rings, which maps calculation of invariants to fast number theoretical Fourier--Galois--Hamilton--transform.