分数阶的Zernike矩

Fractional Order Zernike Moment

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.

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 transformed to replace the integer order polynomial of the traditional Zernike moment by the fractional orderpolynomial, which makes the traditional Zernike only a special case of the construction. Then, the orthogonality and rotation invariance of the proposed fractional order Zernike moment are proved. At last, experimental results show that fractional order Zernike moments with better performance for noise and reconstruction can be constructed by the proposed method.