摘要： 提出了一种快速计算Zernike矩的改进q-递归算法，该方法通过同时降低核函数中Zernike多项式和Fourier函数的计算复杂度以提高Zernike矩的计算效率。采用 q-递归法快速计算Zernike多项式以避免复杂的阶乘运算，再利用x轴、y轴、x=y和x=-y 4条直线将图像域分成8等分。计算Zernike矩时，仅计算其中1个区域的核函数的值，其他区域的值可以通过核函数关于4条直线的对称性得到。该方法不仅减少了核函数的存储空间，而且大大降低了Zernike矩的计算时间。试验结果表明，与现有方法相比，改进q-递归算法具有更好的性能。

关键词: 改进q-递归算法, q-递归公式, 对称性, Zernike矩

Abstract: The paper proposes a modified q-recursive algorithm of fast computing Zernike moments. The method improves the efficiency of calculating Zernike moments by reducing the computational complexities of the Zernike polynomials and the Fourier functions of the kernel functions. In the first step, the q-recursive method, which avoids the factorial operations and the power series of radius involved in radial polynomials, is employed to compute the Zernike polynomials. In the second step, the image domain is divided into eight equal parts by four lines, which are x=0, y=0, x=y and x=-y. On computing Zernike moments, the kernel functions are merely calculated in one part. The function values of the other parts can be obtained by the symmetry property about the four lines of the kernel functions. It not only saves the storages for the kernel polynomials but also reduces the computation time. The performance of the algorithm is experimentally examined using a binary image, and it shows that the computational speed of Zernike moments has been substantially improved over the present methods.

Key words: modified q-recursive algorithm, q-recurrence relation, symmetry, Zernike moments

中图分类号: 

• TP391