基于价值函数的二维小波变换小波脊提取算法

条纹图存在噪声干扰时,将二维小波变换系数模的最大值作为小波脊,会产生较大误差。针对这一问题,提出了基于价值函数的二维小波变换小波脊提取算法。首先,提取二维小波变换系数模的最大值点,并将最大值90%的局部极值点提取出来,共同作为小波脊候选点;其次,在模上引入尺度因子的梯度,建立价值函数进而评估所有候选点的价值,利用对数Logistic模型进行权值调整改进,从而得到更加合理的价值估计;最后,使用动态规划思想准确找出最优的小波脊线,提取脊线处的相位即可得到包裹相位。其优势在于能准确解调信噪比较低的条纹图案,抗噪性能优于直接最大模的小波脊提取;并且只需投影一幅条纹图案即可重建物体形貌,可用于恶劣环境下的动态三维测量。计算机仿真和实验结果表明,对于含有噪声污染的条纹图,所提算法相较于最大模的小波脊提取算法,三维形貌恢复精度明显提高;而相较于全部局部极值点提取,其运算时间缩短了46.9%。同时,应用不同母小波于所提方法,仿真结果表明二维Cauchy小波具有更好的方向性和更高的精度。

Wavelet ridge extraction algorithm using a cost function in two dimensional wavelet transform

Using the maximum of two dimensional wavelet transform coefficient modulus as wavelet ridge will produce large error for the fringe image with noise interference. In view of this problem, wavelet ridge extraction algorithm utilizing a cost function in two dimensional wavelet transform is proposed. Firstly, the maximum point is extracted from two dimensional wavelet transform coefficient modulus, and the local maximum points exceeded 90% of maximum point are also obtained, these points are selected as wavelet ridge candidates. Then, the gradient of scale factor is introduced into the modulus, the cost function is established to evaluate the value of all candidate points. The logarithmic Logistic model is used to adjust the weights to improve the estimator. Finally, the dynamic programming is applied to accurately identify the optimal wavelet ridge, and the wrapped phase can be obtained by extracting the phase at the ridge. Consequently, the fringe pattern with low signal to noise ratio can be demodulated accurately, and its noise immunity is better than wavelet ridge extraction from direct maximum modulus. At the same time, only one fringe pattern can be projected to reconstruct the shape of object, which can be used for dynamic 3D measurement in harsh environment. Simulation and experimental results show that, for the fringe pattern with noise, the accuracy of 3D surface recovery by the proposed algorithm is increased, compared with the maximum modulus of the wavelet ridge extraction algorithm. And the computation time is shortened by 46.9% compared with the extraction of the whole local extreme points. In addition, , simulation results show that the 2D Cauchy wavelet has better directivity and higher accuracy by applying different mother wavelets to the proposed method.