To improve the performance of Zernike moment, this paper focuses on the fractional order Zernike moment, which is a generalization of the traditional integer order one. An algorithm is proposed to construct these fractional order Zernike moments. Firstly, the radial part of traditional Zernike polynomial is trans-formed to replace the integer order polynomial of the traditional Zernike moment by the fractional order polynomial, which makes the traditional Zernike only a special case of the construction. Then, the orthogo-nality and rotation invariance of the proposed fractional order Zernike moment are proved. At last, experi-mental results show that fractional order Zernike moments with better performance for noise and reconstruc-tion can be constructed by the proposed method.%为改善Zernike矩的抗噪、重构等性能,将仅能取整数阶的传统Zernike矩推广为分数阶Zernike矩,提出一种分数阶Zernike矩构造算法.首先改造传统Zernike多项式的径向部分,以分数阶多项式替代传统Zernike矩中的整数阶多项式,使传统的Zernike矩仅是这种构造的特例;其次证明了所提分数阶Zernike矩的正交性和旋转不变性.实验结果表明,该算法可构造出比传统Zernike矩重构性能好、抗噪性能强的分数阶Zernike矩.
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