The Independence of the Affine Moment Invariants
Tomáš Suk, Jan Flusser · AIP conference proceedings · 2006
The affine moment invariants are important tool for recognition of geometrically deformed images for many years. Nevertheless, the proof of independence of a chosen set of them is still problem. This contribution presents a new approach to these proofs, the affine moment invariants are compared with the corresponding set of the normalized moments. The normalized moments are complete and independent and if the values of the normalized moments can be computed unambiguously from the values of the affine moment invariants and vice versa, then the set of the affine moment invariants is complete and independent, too. The proof for invariants up to the fourth order is presented directly. The proof for higher orders can be more complicated, but it can be simplified, if we compute the solution not in the whole space of the feature values, but in some suitably chosen specific values.