Efficient computation of radial moment functions using symmetrical property

The applications of radial moment functions such as orthogonal Zernike and pseudo-Zernike moments in real-world have been limited by the computational complexity of their radial polynomials. The common approaches used in reducing the computational complexity include the application of recurrence relations between successive radial polynomials and coefficients. In this paper, a novel approach is proposed to further reduce the computation complexity of Zernike and pseudo-Zernike polynomials based on the symmetrical property of radial polynomials. By using this symmetrical property, the real-valued radial polynomials computation is reduced to about one-eighth of the full set polynomials while the computation of the exponential angle values is reduced by half. This technique can be integrated with existing fast computation methods to further improve the computation speed. Besides significant reduction in computation complexity, it also provides vast reduction in memory storage.