基于小波变换的分形曲线维数计算方法的研究

Study on Calculation Method of Dimension of Fractal Curve Based on Wavelet Transformation

研究了基于小波变换的分形曲线维数计算方法,具有算法简单和容易实现的优点;通过构造典型分形曲线并加以应用研究,提出并总结了小波分解尺度对维数计算精度的影响规律。根据影响规律,采用小波变换计算分形曲线维数,首先应该估计曲线的采样长度,根据曲线特征选择特定的小波函数,确定最佳的小波分解尺度,这样既提高了计算精度,又缩短了计算时间;其次,当分形曲线有限长度较短时,应该采用信号周期延拓的方法可以减少计算误差。

Calculation method of fractal dimension of fractal curve was studied based on wavelet transformation, which can be realized simply and easily in algorithm. Interrelations between wavelet decomposition scale and fractal dimension precision were found and summarized by constructing the typical fractal curve. Based on these interrelations, sample dimension of fractal curve should be estimated firstly, and then ensure the best wavelet decomposition scale, which can improve the presion of calculation dimension and shorten the computational time;secondly, sample signal should be extended periodically while sample length is finite so that the computational error can be reduced.