Abstract：To solve the too high computational complexity of 3D Zernike moments, the properties and fast algorithms of 3D Zernike radial polynomials were investigated. The relationship between 3D and 2D Zernike radial polynomials was discovered to generalize some important properties of 2D Zernike radial polynomials and four fast algorithms to 3D case. The obtained four 3D fast algorithms were optimized and fused to design one faster hybrid algorithm for computing full set of 3D Zernike radial polynomials. The complexity of the five algorithms was analyzed. For different maximum orders, the full sets of 3D Zernike radial polynomials were computed with the five algorithms, and the elapsed CPU times were compared. The results show that the proposed hybrid algorithm can significantly reduce the complexity and improve the operation speed. The optimization effect becomes more obviously as the order increases.
郭芸, 刘纯平, 龚声蓉. 3D Zernike径向多项式的性质和快速算法[J]. 江苏大学学报（自然科学版）, 2016, 37(2): 188-193.
GUO Yun, LIU Chun-Ping, GONG Sheng-Rong. Properties and fast algorithms of 3D Zernike radial polynomials[J]. Journal of Jiangsu University(Natural Science Eidtion)
, 2016, 37(2): 188-193.
2016, Vol. 37 
