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中文摘要：
针对3D Zernike矩计算复杂度过高的问题,研究了3D Zernike径向多项式的性质和快速算法.发现了3D和2D Zernike径向多项式之间的关系,并利用该关系将2D Zernike径向多项式的重要性质及其包含的4种快速算法推广到3D情形.从计算3D Zernike径向多项式全集的角度,对推广得到的4种3D快速算法做进一步优化融合,设计了一种比单独使用任何一种算法都更加快速的3D混合算法.对这5种算法进行了复杂度分析,并针对不同的最高阶,对5种算法求3D Zernike径向多项式全集所用的CPU时间进行比较.结果表明,3D混合算法显著降低了复杂度,明显提高了运算速度,并且阶数越高优化的效果越明显.
英文摘要：
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.
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