基于价值函数的二维小波变换小波脊提取算法
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摘要
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。
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 2 D Cauchy wavelet has better directivity and higher accuracy by applying different mother wavelets to the proposed method.
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 2 D Cauchy wavelet has better directivity and higher accuracy by applying different mother wavelets to the proposed method.
引文
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[20]LI CH H,HUANG D X,DAI H SH.Applications of adaptive elastic net procedure for logistic regression model[J].Chinese Journal of Engineering Mathematics,2015,32(5):759-771.
[21]ITON K.Analysis of the phase unwrapping algorithm[J].Applied Optics,1982,21(14):2470-2471.
[22]许罗鹏,陈文静,赵玥,等.选择小波函数的方法研究[J].四川大学学报:自然科学版,2010,47(4):785-790.XU L P,CHEN W J,ZHAO Y,et al.Study on selecting wavelet function[J].Journal of Sichuan University:Natural Science Edition,2010,47(4):785-790.
[2]CHEN F,BROWN G M,SONG M M.Overview of three-dimensional shape measurement using optical methods[J].Optical Engineering,2000,39(1):10-22.
[3]刘常杰,杨学友,叶声华.采用LCD投影实现三维曲面测量技术研究[J].电子测量与仪器学报,2005,19(2):41-44.LIU CH J,YANG X Y,YE SH H.A new visual technology of 3-D measurement using LCD projection[J].Journal of Electronic Measurement and Instrument,2005,19(2):41-44.
[4]赵庆祥,曾丹,张之江.编码结构光技术在人脸建模中的应用[J].电子测量技术,2010,33(1):114-118.ZHAO Q X,ZENG D,ZHANG ZH J.Coded structured light for face modeling[J].Electronic Measurement Technology,2010,33(1):114-118.
[5]占栋,于龙,肖建,等.多摄像机结构光大视场测量中全局标定方法研究[J].仪器仪表学报,2015,36(4):904-910.ZHAN D,YU L,XIAO J,et al.Study on multi-cameras and structured-light vision system calibration approach study in large field view measurement[J].Chinese Journal of Scientific Instrument,2015,36(4):904-910.
[6]刘今越,刘佳斌,郭志红,等.一种基于面结构光的刀具三维测量系统[J].电子测量与仪器学报,2016,30(12):1884-1891.LIU J Y,LIU J B,GUO ZH H,et al.A three dimensional tool measurement system based on surface structured light[J].Journal of Electronic Measurement and Instrumentation,2016,30(12):1884-1891.
[7]ZHONG K,LI ZH W,SHI Y SH,et al.Fast phase measurement profilometry for arbitrary shape objects without phase unwrapping[J].Optics and Lasers in Engineering,2013,51(11):1213-1222.
[8]FU Y J,LUO Q.Fringe projection profilometry based on a novel phase shift method[J].Optics Express,2011,19(22):21739-21747.
[9]TAKEDA M,MUTOH K.Fourier transform profilometry for the automatic measurement of 3-D object shapes[J].Applied Optics,1983,22(24):3977-3982.
[10]ZHONG M,CHEN F,XIAO CH,et al.3-D surface profilometry based on modulation measurement by applying wavelet transform method[J].Optics and Lasers in Engineering,2017,88(1):243-254.
[11]ZHONG J,WENG J.Phase retrieval of optical fringe patterns from the ridge of a wavelet transform[J].Optics Letters,2005,30(19):2560-2562.
[12]LIU H,CARTWRIGHT A,BASARAN C.Moiréinterferogram phase extraction:A ridge detection algorithm for continuous wavelet transform[J].Applied Optics,2004,43(4):850-857.
[13]王勇,饶勤菲,闫河,等.改进的基于代价函数的小波脊相位提取算法[J].光电子·激光,2016,27(7):761-766.WANG Y,RAO Q F,YAN H,et al.Improved wavelet ridge phase extraction algorithm based on cost function[J].Journal of Optoelectronics·Laser,2016,27(7):761-766.
[14]WANG ZH Y,MA J,VO M.Recent progress in two-dimensional continuous wavelet transform technique for fringe pattern analysis[J].Optics and Lasers in Engineering,2012,50(8):1052-1058.
[15]黄昊,达飞鹏.小波变换轮廓术中快速相位展开方法研究[J].仪器仪表学报,2012,33(2):397-404.HUANG H,DA F P.Novel phase unwrapping method for wavelet profilometry[J].Chinese Journal of Scientific Instrument,2012,33(2):397-404.
[16]GDEISAT M A,BURTON D R,LABOR M J.Spatialcarrier fringe pattern demodulation by use of a two-dimensional continuous wavelet transform[J].Applied Optics,2006,45(34):8722-8732.
[17]ZHANG Z B,ZHONG J G.Applicability analysis of wavelet-transform profilometry[J].Optics Express,2013,21(16):18777-18796.
[18]CHEN W J,LI S K,CAI Y X,et al.Analysis on fringe pattern demodulation by use of 2-D CWT[J].Optik,2011,122(19):1039-1746.
[19]NIU H,QUAN C,TAY C.Phase retrieval of speckle fringe pattern with carriers using 2D wavelet transform[J].Optics and Lasers in Engineering,2009,47(12):1334-1339.
[20]LI CH H,HUANG D X,DAI H SH.Applications of adaptive elastic net procedure for logistic regression model[J].Chinese Journal of Engineering Mathematics,2015,32(5):759-771.
[21]ITON K.Analysis of the phase unwrapping algorithm[J].Applied Optics,1982,21(14):2470-2471.
[22]许罗鹏,陈文静,赵玥,等.选择小波函数的方法研究[J].四川大学学报:自然科学版,2010,47(4):785-790.XU L P,CHEN W J,ZHAO Y,et al.Study on selecting wavelet function[J].Journal of Sichuan University:Natural Science Edition,2010,47(4):785-790.