实Gauss小波在三维面形测量中的应用

在基于连续小波变换(CWT)的三维面形测量过程中,小波函数的选择起到关键作用。已有文献对实墨西哥帽小波的表现展开了讨论。考虑到墨西哥帽小波、莫莱小波、DOG犬小波和盖博小波均由Gauss窗函数生成,墨西哥帽小波是Gauss函数的二阶导数,本文对实Gauss小波在三维测量中的应用进行深入讨论。理论分析了利用实小波函数经由Hilbert变换实现三维面形重建原理,完成了基于实Gauss小波的三维面形测量的模拟和实验。

Research on real Gauss wavelet in 3-D surface measurement

In 3-D surface measurement based on continuous wavelet transform(CWT),the choice of wavelet function plays a key role.Mexican hat wavelet,Morlet wavelet,DOG wavelet and Gabor wavelet generate from Gauss wavelet function,and Mexican hat wavelet is the second derivative of Gauss wavelet function.Because of few discussion about real Gauss wavelet,it can be used in 3-D measurement and will be deeply discussed in this paper.Based on theoretical analysis about the principle of phase reconstruction using real wavelet function via Hilbert transform,we can get the phase information from deformed grating image using real wavelet function.The simulation and experiment of 3D surface measurement based on real Gauss wavelet are carried out.