基于改进价值函数和三维相位展开的动态三维测量方法研究
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摘要
针对物体连续变化过程的三维测量,提出了一种有效的动态三维测量方法。该方法采用基于改进价值函数的二维小波变换解包裹相位、三维相位展开方法得到实际相位。其突出优势在于3个方面,首先仅需一幅光栅条纹图案即可重建物体三维面形,可实现高速动态三维测量;其次相较于基于直接最大模和基于价值函数的二维小波变换小波脊提取算法,基于改进价值函数的小波脊提取算法具有更好的抑噪能力;最后,提出了一种三维相位展开方法,在二维相位展开路径上引入了时间轴方向,从而实现了大梯度物体的相位展开,同时说明了三维相位展开的适用条件。仿真对比了直接最大模的二维小波变换法、基于价值函数的二维小波变换法和基于改进价值函数的二维小波变换法的解包裹相位效果,同时对多种二维相位展开方法、所提三维展开方法进行仿真对比与分析,最后对连续凸起曲面进行了实验比较,证明所提方法可用于物体连续变化过程的动态三维测量。
An effective dynamic three-dimensional measurement method is proposed for the process of continuous change of object. The two-dimensional wavelet transform employing an improved value function is used to obtain the wrapped phase and three-dimensional phase unwrapping method is used to obtain the actual phase. The first advantage of the proposed method is that only one grating pattern is needed to reconstruct the three-dimensional shape of the object,and the high speed dynamic three-dimensional measurement can be realized. The second is that,compared with wavelet ridge extraction algorithm in two-dimensional wavelet transform based on direct maximum modulus and cost function,wavelet ridge extraction algorithm based on an improved value function has better noise suppression ability. The third is that a three-dimensional phase unwrapping method is proposed,and the phase unwrapping of a large gradient object is realized by introducing the direction of the time axis on the two-dimensional phase unwrapping path. In addition,the applicable conditions of the three dimensional phase unwrapping method are explained. The simulation comparison of the unwrapping phase effect between two-dimensional wavelet transform based on direct maximum modulus,cost function,and an improved cost function is conducted. Meanwhile,the simulation comparison and analysis of various two-dimensional phase unwrapping methods and the proposed three-dimensional phase unwrapping method is implemented. Finally,the experimental comparison of the continuous convex surface is carried out,and the results prove that the proposed method can be used for dynamic three-dimensional measurement of the process of continuous change of object.
An effective dynamic three-dimensional measurement method is proposed for the process of continuous change of object. The two-dimensional wavelet transform employing an improved value function is used to obtain the wrapped phase and three-dimensional phase unwrapping method is used to obtain the actual phase. The first advantage of the proposed method is that only one grating pattern is needed to reconstruct the three-dimensional shape of the object,and the high speed dynamic three-dimensional measurement can be realized. The second is that,compared with wavelet ridge extraction algorithm in two-dimensional wavelet transform based on direct maximum modulus and cost function,wavelet ridge extraction algorithm based on an improved value function has better noise suppression ability. The third is that a three-dimensional phase unwrapping method is proposed,and the phase unwrapping of a large gradient object is realized by introducing the direction of the time axis on the two-dimensional phase unwrapping path. In addition,the applicable conditions of the three dimensional phase unwrapping method are explained. The simulation comparison of the unwrapping phase effect between two-dimensional wavelet transform based on direct maximum modulus,cost function,and an improved cost function is conducted. Meanwhile,the simulation comparison and analysis of various two-dimensional phase unwrapping methods and the proposed three-dimensional phase unwrapping method is implemented. Finally,the experimental comparison of the continuous convex surface is carried out,and the results prove that the proposed method can be used for dynamic three-dimensional measurement of the process of continuous change of object.
引文
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[18]刘永久.基于结构光投影的运动物体高速实时三维测量方法研究[D].合肥:中国科技大学,2014:3-5.LIU Y J.Research on High-speed,real-time 3-D measurement of moving object based on structured light projection[D].Hefei:University of Science and Technology of China,2014:3-5.
[19]李中伟.基于数字光栅投影的结构光三维测量技术与系统研究[D].武汉:华中科技大学,2009:14-23.Li ZH W.Research on structured light 3D measuring technology and system based on digital fringe projection[D].Wuhan:Huazhong University of Science and Technology,2009:14-23.
[20]ABID A.Fringe pattern demodulation using the onedimensional continuous wavelet transform:fieldprogrammable gate array implementation[J].Applied Optics,2013,52(7):1468-1471.
[21]ZHANG Z B,ZHONG J G.Applicability analysis of wavelet-transform profilometry[J].Optics Express,2013,21(16):18777-18796.
[22]WANG ZH Y,MA J,MINH V.Recent progress in twodimensional continuous wavelet transform technique for fringe pattern analysis[J].Optics and Lasers in Engineering,2012,50(8):1052-1058.
[23]ZHONG M,CHEN F,XIAO CH,WEI Y CH.3-D surface profilometry based on modulation measure-ment by applying wavelet transform method[J].Optics and Lasers in Engineering,2017(1):243-254.
[24]ITON K.Analysis of the phase unwrapping algorithm[J].Applied Optics,1982,21(14):2470-2471.
[25]吴明云.二维相位展开算法的研究[D].天津:天津大学,2012:16-23.WU M Y.Research on the two dimensional phase unwrapping algorithms[D].Tianjin:Tianjin University,2012:16-23.
[26]DENNIS D C,ROMERO L A.Robust two-dimensional weighted and unweighted phase unwrapping that uses fast transforms and iterative methods[J].Journal of the Optical Society of America A,1994,11(1):107-117.
[27]GUO Y,CHEN X T,ZHANG T.Robust phase unwrapping algorithm based on least squares[J].Optics and Lasers in Engineering,2014,63(4):25-29.
[2]ZHANG S,YAU S T.High-resolution,real-time 3d absolute coordinate measurement based on a phaseshifting method[J].Optics Express,2006,14(7):2644-2649.
[3]GAI SH Y,DA F P.A novel phase-shifting method based on strip marker[J].Optics and Laser in Engineering,2010,48(2):205-211.
[4]HUANG P S,ZHANG S.Fast three-step phase-shifting algorithm[J].Applied Optics,2006,45(21):5086-5091.
[5]HUNTLEY J M,SALDNER H.Temporal phaseunwrapping algorithm for automated interferogram analysis[J].Applied Optics,1993,32(17):3047-3052.
[6]TIAN J D,PENG X,ZHAN X B.A generalized temporal phase unwrapping algorithm for threedimensional profilometry[J].Optics and Laser in Engineering,2008,46(4):336-342.
[7]赵文静,陈文静,苏显渝.几种时间相位展开方法的比较[J].四川大学学报(自然科学版),2010,47(4):785-790.ZHAO W J,CHEN W J,SU X Y.The comparison of several time phase unwrapping methods[J].Journal of Sichuan University(Natural Science Edition),2010,47(4):785-790.
[8]艾佳,刘守起,刘元坤,等.利用三频外差实现的小视场三维测量系统[J].光电工程,2016,43(9):39-43.AI J,LIU SH Q,LIU Y K,et al.Three-dimensional small-field measurement system based on tri-frequency heterodyne fringe analysis[J].Opto-Electronic Engineering,2016,43(9):39-43.
[9]王长波,谢明红.格雷码与相移结合的双目三维重构[J].计算机工程,2013,39(5):178-182.WANG CH B,XIE M H.Binocular three-dimensional reconstruction combined with gray coding and phaseshift[J].Computer Engineering,2013,39(5):178-182.
[10]石爱军,白瑞林,田青华.Gray码结合线移的结构光三维测量[J].光电工程,2016,43(11):26-32.SHI AI J,BAI R L,TIAN Q H.3D measurement based on structured light using a combination of gray code and line-shift patterns[J].Opto-Electronic Engineering,2016,43(11):26-32.
[11]岳慧敏.基于时间相位展开的三维轮廓测量研究[D].成都:四川大学,2005:25-28.YUE H M.Research on Three-dimensional profilometry based on temporal phase unwrapping[D].Chengdu:Sichuan University,2005:25-28.
[12]TAKEDA M,MUTOH K.Fourier transform profilometry for the automatic measurement of 3-D object shapes[J].Applied Optics,1983,22(24):3977-3982.
[13]ZHONG J.Phase retrieval of optical fringe patterns from the ridge of a wavelet transform[J].Optics Letters,2005,30(19):2560-2562.
[14]WATKINS L R.Phase recovery from fringe patterns using the continuous wavelet transform[J].Optics and Lasers in Engineering,2007,45(2):298-303.
[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]王建华,杨延西,马晨.基于价值函数的二维小波变换小波脊提取算法[J].仪器仪表学报,2017,38(12):2915-2923.WANG J H,YANG Y X,MA CH.Wavelet ridge extraction algorithm employing a cost function in twodimensional wavelet transform[J].Chinese Journal of Scientific Instrument,2017,38(12):2915-2923.
[17]张启灿,苏显渝.动态三维面形测量的研究进展[J].激光与光电子学进展,2013,50(1):1-14.ZHANG Q C,SU X Y.Research progress of dynamic three-dimensional shape measurement[J].Laser&Optoelectronics Progress,2013,50(1):1-14.
[18]刘永久.基于结构光投影的运动物体高速实时三维测量方法研究[D].合肥:中国科技大学,2014:3-5.LIU Y J.Research on High-speed,real-time 3-D measurement of moving object based on structured light projection[D].Hefei:University of Science and Technology of China,2014:3-5.
[19]李中伟.基于数字光栅投影的结构光三维测量技术与系统研究[D].武汉:华中科技大学,2009:14-23.Li ZH W.Research on structured light 3D measuring technology and system based on digital fringe projection[D].Wuhan:Huazhong University of Science and Technology,2009:14-23.
[20]ABID A.Fringe pattern demodulation using the onedimensional continuous wavelet transform:fieldprogrammable gate array implementation[J].Applied Optics,2013,52(7):1468-1471.
[21]ZHANG Z B,ZHONG J G.Applicability analysis of wavelet-transform profilometry[J].Optics Express,2013,21(16):18777-18796.
[22]WANG ZH Y,MA J,MINH V.Recent progress in twodimensional continuous wavelet transform technique for fringe pattern analysis[J].Optics and Lasers in Engineering,2012,50(8):1052-1058.
[23]ZHONG M,CHEN F,XIAO CH,WEI Y CH.3-D surface profilometry based on modulation measure-ment by applying wavelet transform method[J].Optics and Lasers in Engineering,2017(1):243-254.
[24]ITON K.Analysis of the phase unwrapping algorithm[J].Applied Optics,1982,21(14):2470-2471.
[25]吴明云.二维相位展开算法的研究[D].天津:天津大学,2012:16-23.WU M Y.Research on the two dimensional phase unwrapping algorithms[D].Tianjin:Tianjin University,2012:16-23.
[26]DENNIS D C,ROMERO L A.Robust two-dimensional weighted and unweighted phase unwrapping that uses fast transforms and iterative methods[J].Journal of the Optical Society of America A,1994,11(1):107-117.
[27]GUO Y,CHEN X T,ZHANG T.Robust phase unwrapping algorithm based on least squares[J].Optics and Lasers in Engineering,2014,63(4):25-29.