几种傅里叶子的深入比较研究

Comparative study of Fourier descriptors

用于模式识别的傅里叶子主要有基于极半径函数、转角函数和曲率函数等三种方法 ,通过比较研究 ,找出一种运算简便且精度高的傅里叶子。对不同的图形用三种方法分别计算出原函数和傅里叶频谱 ,然后从大到小依次选取k个 (k =1,2 ,… ,N)傅里叶系数进行反变换 ,计算出反变换函数与原函数之间存在的误差 ,根据误差随k变化的曲线判断三种方法的优劣。实验结果表明 ,基于极半径函数的傅里叶子最为理想。将它用于孢子的识别和计数 ,正确识别率达 99%。

Three algorithms of Fourier descriptors(FDs) based on polar radius function, rotation angle function and contour curvature function, respectively, are chiefly used in pattern recognition. An accurate algorithm was found out through comparative study of FDs. The original function values and their Fourier frequency spectrums of different shapes were calculated using three algorithms, respectively. Then inverse Fourier transformations were made by employed k (k=1,2,...,N) Fourier coefficients sequenced from large to small, and the errors between the restored and the original functions were computed. These three algorithms were evaluated according to the curve of error with respect to k . Based on the experimental results, it was proved that the algorithm of FDs based on polar radius function is the best one among them, and the recognition ratio arrives at 99% when it is conducted in the identification of spores.