Fast spectral algorithms of invariants calculation

The recognition of objects independent of their position, size and orientation is an important problem in pattern recognition. In this paper we propose a new fast algorithm of moment invariant computation, which needs almost no multiplications. We use modular arithmetic of the finite Galois field GF(Q) to map the geometrical moments calculation to a fast Fourier-Mellin-Galois transform, which reduces the computational complexity of moments from O(N⁴) to O(N²log₂ N). We introduce orthogonal Fourier-Mellin-Galois moments based on a complete set of orthogonal characters of the multiplicative group of the GF(Q). These moments are modular remainders modulo Q of the classical geometrical moments