利用小波变换实现基于结构光投影的S变换轮廓术

Using Wavelet Transform to Actualize S Transform Profilometry Based on Structured Light Projection

S变换是一种集合了窗口傅里叶变换和小波变换优点的时-频分析技术,将一维的信号映射到二维的时-频空间,具有良好的时频分辨能力。由于S变换谱和傅里叶变换频谱之间存在直接联系,且具有类似于小波变换的多分辨率能力,S变换可以通过快速傅里叶变换算法实现,也可以通过小波变换算法实现。研究了基于小波变换算法的S变换在基于结构光投影的三维光学测量中的应用,给出了理论分析,特别讨论了S变换中频率因子的选择,并同基于快速傅里叶变换算法的S变换轮廓术结果进行了比较。完成了计算机模拟和实验研究。

S transform is a time-frequency analysis Fourier transform and wavelet transform. It maps technique which combines the advantages of both short-time a one-dimensional spatial signal into two-dimensional timefrequency domain and has a perfect time-frequency resolution. S transform has direct relation with Fourier transform and wavelet transform, and has the similar multiresolution ability of wavelet transform. It can be derived from Fourier transform coefficient and wavelet transform coefficient of a signal respectively, but the key technology that the implementation of S transform by wavelet analysis algorithm applied in three-dimensional optical measurements is rarely related at present. Focusing on the implementation of S transform by wavelet analysis algorithm, the application of S transform in three-dimensional optical measurement based on structured light projection is disussed, especially the selection of the frequency factor in S transform for obtaining good reconstruction. The reconstructed results of S transform profilometry based on fast Fourier transform and that based on wavelet transform are compared. The computer simulations and experiments verify our analysis.