Fast computation of geometric moments using a symmetric kernel

This paper presents a novel set of geometric moments with symmetric kernel (SGM) obtained using an appropriate transformation of image coordinates. By using this image transformation, the computational complexity of geometric moments (GM) is reduced significantly through the embedded symmetry and separability properties. In addition, it minimizes the numerical instability problem that occurs in high order GM computation. The novelty of the method proposed in this paper lies in the transformation of GM kernel from interval [0, ∞] to interval [- 1, 1]. The transformed GM monomials are symmetry at the origin of principal Cartesian coordinate axes and hence possess symmetrical property. The computational complexity of SGM is reduced significantly from order O (N⁴) using the original form of computation to order O (N³) for the proposed symmetry-separable approach. Experimental results show that the percentage of reduction in computation time of the proposed SGM over the original GM is very significant at about 75.0% and 50.0% for square and non-square images, respectively. Furthermore, the invariant properties of translation, scaling and rotation in Hu's moment invariants are maintained. The advantages of applying SGM over GM in Zernike moments computation in terms of efficient representation and computation have been shown through experimental results.