二维窗口傅里叶变换轮廓术和二维S变换轮廓术比较  

Comparing 2D S-transform profilometry with 2D windowed Fourier transform profilometry

作　　者：谌秋菊[1] 陈文静[1] 钟敏[1] 苏显渝[1] 

机构地区：[1]四川大学电子信息学院光电系,成都610064

出　　处：《四川大学学报（自然科学版）》2013年第5期1011-1019,共9页Journal of Sichuan University(Natural Science Edition)

基　　金：国家自然科学基金(61177010);"973"课题(2011CB301804)

摘　　要：窗口傅里叶变换和S变换都是常用的时频分析技术.窗口傅里叶变换采用大小固定的时频分析窗口对信号在时域和频域进行处理.S变换采用受到信号瞬时频率控制的可变窗口对信号进行分析,它集合了窗口傅里叶变换和小波变换的优点.论文对比分析了基于"脊"处理思想的二维(2-D)窗口傅里叶和2-D S变换在基于结构光投影的光学三维面形测量中的应用.推导了他们用于条纹图相位场计算的表达式,并对比了他们的三维重建效果.模拟和实验都表明:基于"脊"处理的二维S变换方法比二维窗口傅里叶变换方法有更高的相位提取精度,即使分析严重噪声污染的条纹,采用二维S变换也能得到满意的三维重建效果.The windowed Fourier transform and S transform are common time-frequency analysis tech- nologies. The windowed Fourier transform adopts a fixed size time-frequency analysis window to process a signal in both time and frequency domain, while S transform analyses a signal with variable size win dows controlled by the instantaneous frequency of the tested signal. Therefore, S transform combines the advantages of both the windowed Fourier Transform and the multi-scale strategy of the Wavelet transform. This paper focuses on studying the applications of two-dimensional（2D） windowed Fourier transform ＇ridge^method and the two-dimensional（2D） S transform ＇ridge^method in the optical three dimensional （3D） surface measurement based on the structured-light illumination. The theoretical ex- pressions of the phase maps modulated into the deformed fringe patterns are detailedly derived by emplo ying the definition of the 2D windowed Fourier transform and 2D S transform, respectively. In addition, the comparison of the reconstructed results of the two methods has been carried out. The simulations and experiments show that the 2D S transform method based on the idea of the ＂ridge＂ has higher phase extraction accuracy than 2D windowed Fourier Transform. Even if the captured fringe patterns are seri- ously polluted by noises, a satisfactory result of 3D reconstruction can be obtained by 2D S Transform.

关 键 词：光学三维测量 条纹相位解调 二维窗口傅里叶变换 二维S变换 

分 类 号：O438[机械工程—光学工程]