Description of shape characteristics through Fourier and wavelet analysis

In this paper, Fourier and Wavelet transformation were adopted to analyze shape char- acteristics, with twelve simple shapes and two types of second phases from real microstructure mor- phology. According to the results of Fast Fourier transformation （FFT）, the Fourier descriptors can be used to characterize the shape from the aspects of the first eight Normalization amplitudes, the number of the largest amplitudes to inverse reconstruction, similarity of shapes and profile roughness. And the Diepenbroek Roughness was rewritten by Normalization amplitudes of FFT results. Moreover, Sum Square of Relative Errors （SSRE） of Wavelet transformation （WT） signal sequence, including approximation signals and detail signals, was introduced to evaluate the simi- larity and relative orientation among shapes. As a complement to FFT results, the WT results can retain more detailed information of shapes including their orientations. Besides, the geometric sig- natures of the second phases were extracted by image processing and then were analyzed by means of FFT and WT.