Fast computation of moment invariants

摘要

The subject of moment invariants has found wide application in pattern recognition since it was proposed. In the present paper, we propose a fast algorithm for the calculation of moment invariants. Firstly, we propose using Green's theorem for double integral to transform moment calculation to a simple integration along the boundary, which reduces the complexity from O(N2) to O(N). Secondly, the relation between the monomials for successive pixels along a curve is analysed and the Pascal triangle matrix transform is proposed to calculate the monomials for a pixel from those for the preceding one. An iterative algorithm is thus proposed for moment calculation which needs no multiplications, and the number of additions needed is reduced to O(N). Moreover, a very simple systolic structure is proposed to implement the Pascal triangle transformation, and the proposed algorithm can thus be realized by simple hardware to further accelerate the calculation. Comparison of the computational complexity with some known methods is also given, which shows that our algorithm significantly reduces the complexity.