基于小波变换和分形维数的表面微观形貌分析

Analysis of Micro Surface Topography Based on Wavelet Transform and Fractal Dimension

针对传统三维参数和单一分形维数在表面微观形貌分析中的不足,提出了一种基于小波变换和分形维数的表面微观形貌分析方法。该方法通过小波变换对表面形貌的灰度图像进行分解和单支重构,利用改进的差分盒维法计算原图像和重构子图像的分形维数,依据原图像和重构子图像的分形维数构成的数组对表面微观形貌进行分析。最后,利用本文提出的方法对一组零件的表面微观形貌进行了分析,结果表明原图像和重构子图像的分形维数不仅能够反映表面微观形貌的整体特征还能反映表面不同分辨率下的细节特征。

Aiming at the deficiency of 3-D parameters and single fractal dimension in analyzing micro surface topography,a new method was advanced based on the wavelet transform and fractal dimension.The gray images of surface topography were decomposed and reconstructed solely by wavelet method,fractal dimensions of the images and their reconstructed sub-images were counted by the improved differential box-counting method,and the micro surface topographies were analyzed based on the fractal dimensions.At last,a group of micro surface topographies were analyzed by the method advanced in it,and its result showed that fractal dimensions of the images and their reconstructed sub-images can not only reflected the whole surface topography,but also reflected the detail characteristic of surfaces in different scales.