投影测量相位提取技术研究
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摘要
结构光投影三维轮廓测量广泛应用在国防安全,工业生产,柔性制造,太空探测,医疗检查等领域,其中只需要一幅调制图像就可以提取出被测物体三维轮廓的傅里叶轮廓术及其拓展方法具有数据点云密度大,精度高,环境友好,非接触,对被测物体无损伤,适合动态物体测量等优点,成为结构光投影三维轮廓测量的主流方法。
针对传统相位提取方法速度慢的问题,提出了基于离散Meyer小波的变形条纹相位提取方法,有效解决了相位提取的速度问题。研究了调频调幅信号的数学特征,并据此构造了一个代价函数,代价函数的最小值对应着变形条纹信号Meyer小波分解的最优层次。该方法的优势在于速度快,适用于背景较简单的条纹,能有效减少相位突变和频谱混叠带来的影响。
传统上,当被测物体表面高度变化较缓时,采用Mexican Hat小波可得到较高的处理速度和精度,但Mexican Hat小波采用固定的变换尺度,当载波频率和被测对象发生变化时,Mexican Hat小波的鲁棒性特别差。利用傅里叶变换的微分性质,文中重新构造了一个代价函数,和原有的代价函数相比较,新代价函数仅仅由一项构成,结构非常简单,数学原理清晰,运行结果稳定。基于新代价函数,提出了两种方法,第一种方法仍旧采用离散Meyer小波对变形条纹信号进行处理,其速度稍慢于前述方法,但对噪声的敏感程度下降,鲁棒性更强；第二种方法采用新的代价函数自适应的计算Mexican Hat小波的最优尺度,适用于被测物体表面高度梯度变化范围较小的变形条纹,进一步的研究还发现该代价函数可以自适应的从变形条纹的EMD分解中找到最优的载频分量。
为了提高相位提取的精度,基于OWT_SURE_LET方法,提出了一种改进的小波去噪方法,该方法采用冗余小波变换,无需假设小波系数服从某种先验分布,并且,文中从理论上详细推导了该改进算法的小波系数最优估计过程和步骤,并采用峰值信噪比(PSNR)和变形条纹相位提取均方根误差这两个性质指标,验证改进算法的有效性。
传统小波轮廓术采用动态规划和代价函数计算最优小波脊,在相位突变点处的误差比较大,为了克服这个问题,提出使用具有对数尺度间隔的二进小波进行变形条纹信号的相位提取,使用OTSU算法自适应的从二进小波脊及其邻域内,提取幅值较大的小波系数,并用其重构载波信号,当噪声较小时,该方法可以有效的克服相位突变引起的误差。
传统傅里叶变换轮廓术采用带通滤波的方法消除噪声和背景分量,但该方法中滤波器的中心频率和通带宽度难以确定。在二进小波变换的研究基础上,发现采用一定的小波子信号可以高精度的重构出载波分量,并提出了一个经验公式,可以自适应的选择需要的小波子信号,该方法等同于一个自适应带通小波滤波器,其带宽和中心频率完全由算法自适应的决定。当频谱混叠可以忽略时,算法可有效的解决傅里叶变换轮廓术中中心频率和通带宽度难以确定的难题,具有很好的鲁棒性,对噪声的抑制力较强,解相结果较平滑。
自适应性和鲁棒性是三维测量系统在实际应用中的基本要求,文中提出的所有相位提取方法均是自适应的,数据驱动的,工作过程中无需人工干预,即使对完全不同类型的测量对象,也无需预设任何参数,同时,这些方法的计算量都较小,适合动态物体测量的需要。
Fringe Projection Profilometry(FPP) successfully realized its application in many fields such as national security, industrial production, flexible manufacturing, space exploratory and medical examinations. Fourier Transform Profilometry (FTP)and its continuations, which can recover the instantaneous phase through only single fringe pattern, have becoming the main methods in FPP, as they have many merits such as large data density, high accuracy, friendly environment, non-contact, no-injury and suit for dynamic object measurement.
For the slow-rate of the phase recover problem, we proposed to use discrete Meyer wavelet in projection profilometry, which can increase the speed of phase retrieval. For the carrier wave component in distored fringe pattern, the inherent feature is detailed analyzed and then a cost function is constructed. The optimal discrete Meyer wavelet decomposition level is corresponding to the minimal value of the cost function. The main advantage of this method is it speedability, and also, which can avoid the detrimental effects of the phase jump and frequency overlap when the background component is sample enough.
Traditionally, Mexican Hat wavelet profilometry has high accuracy and speed for phase retrieval when the outline of the measure element is slow varying, but the robustness of the Mexican Hat wavelet profilometry is poor because the scale which used is fixed and invariant. Based on the differential property of the Fourier transform, a new cost function is constructed, which is robust and stable for signals with noises, has very sample expression and has a clear interpretation in theory. The optimal discrete Meyer decomposition level is corresponding to the minimal value of the new cost function, and the optimal continue Mexican Hat wavelet scale can be adaptive determined through the new cost function. The proposed method is very useful when the outline's gradient of the measurement object has a little vaiation range. And more study illustrates that the new cost function has ability to find the optimal carrier wave component form the Empirical Mode Decomposition (EMD) of the distorted fringe pattern.
To increase the accuracy of the phase retrieval, the pattern should be de-noised ahead of the processing of phase recover. In this paper, we lucubrate the wavelet de-noising methods, and, based on the Orthogonal Wavelet Transform Stein Unbiased error Estimate Linear Extend Transform(OWT_SURE_LET) wavelet de-noising method, we introduces an improved wavelet de-noising, which adopt redundancy wavelet transform and need no the knowledge of the wavelet coefficients prior distribution. The step and process of the noised pattern's wavelet coefficients optimal estimate for the improved method is made in detail in this manuscript. Peaks Signal Noise Radio (PSNR) and the Root Square Mean Error (RSME) of the phase retrieval for the distorted pattern are used to verify the effectiveness of the proposed improved wavelet de-noising method.
A large error will occur when phase jump exist for the traditional wavelet profilometry, for which use dynamic programming and cost funcition to find the optimal wavelet ridge. To overcome this problem, this paper proposed to use dynadic wavelet transform for phase recover, and this algorithm uses OTSU to adaptive choose the larger wavelet coefficients from the the wavelet ridge and its neighbourhood coefficients to reconstruct the carrier wave component. This method can decrease the effect of the phase jump when noise is very little and is ignored.
Band pass filter is offen used in fourier transform profilometry to eliminate the nosie and the back-component, but the center frequency and width of bandpass are hard to determine in practice. Bsed on the research of the dynadic wavelet transform, we found that the carrier wave compnent of the distorted fringe pattern can be reconstructed accurately using the dyadic wavelet sub-signal and its neighborhoods, and then an empirical formula is introduced in this algorithm to adaptive choose the child-signals form the results of the dyadic wavelet transform. Theory analysis show the new algorithm is an adaptive band-pass wavelet filter banks in essential, the band-width and center frequency are variant with types changing of the measurement objects,and this method is very useful when spectra overlap can be ignored.
Adaptability and robustness are very important for object3D measurement in practice. These phase retrieval algorithms presented in this paper are all self-adaptive, data driven, needing no manual intervation, and even for different types of measured object, all the proposed methods in this manuscript need not parameters adjusting at all and need not paremeters presetting at all. More important is that all the methods introduced in this paper are all realtime and have a little calculation, which guarantee that these methods can be used with high effective in3D measurement in practice.
针对传统相位提取方法速度慢的问题,提出了基于离散Meyer小波的变形条纹相位提取方法,有效解决了相位提取的速度问题。研究了调频调幅信号的数学特征,并据此构造了一个代价函数,代价函数的最小值对应着变形条纹信号Meyer小波分解的最优层次。该方法的优势在于速度快,适用于背景较简单的条纹,能有效减少相位突变和频谱混叠带来的影响。
传统上,当被测物体表面高度变化较缓时,采用Mexican Hat小波可得到较高的处理速度和精度,但Mexican Hat小波采用固定的变换尺度,当载波频率和被测对象发生变化时,Mexican Hat小波的鲁棒性特别差。利用傅里叶变换的微分性质,文中重新构造了一个代价函数,和原有的代价函数相比较,新代价函数仅仅由一项构成,结构非常简单,数学原理清晰,运行结果稳定。基于新代价函数,提出了两种方法,第一种方法仍旧采用离散Meyer小波对变形条纹信号进行处理,其速度稍慢于前述方法,但对噪声的敏感程度下降,鲁棒性更强；第二种方法采用新的代价函数自适应的计算Mexican Hat小波的最优尺度,适用于被测物体表面高度梯度变化范围较小的变形条纹,进一步的研究还发现该代价函数可以自适应的从变形条纹的EMD分解中找到最优的载频分量。
为了提高相位提取的精度,基于OWT_SURE_LET方法,提出了一种改进的小波去噪方法,该方法采用冗余小波变换,无需假设小波系数服从某种先验分布,并且,文中从理论上详细推导了该改进算法的小波系数最优估计过程和步骤,并采用峰值信噪比(PSNR)和变形条纹相位提取均方根误差这两个性质指标,验证改进算法的有效性。
传统小波轮廓术采用动态规划和代价函数计算最优小波脊,在相位突变点处的误差比较大,为了克服这个问题,提出使用具有对数尺度间隔的二进小波进行变形条纹信号的相位提取,使用OTSU算法自适应的从二进小波脊及其邻域内,提取幅值较大的小波系数,并用其重构载波信号,当噪声较小时,该方法可以有效的克服相位突变引起的误差。
传统傅里叶变换轮廓术采用带通滤波的方法消除噪声和背景分量,但该方法中滤波器的中心频率和通带宽度难以确定。在二进小波变换的研究基础上,发现采用一定的小波子信号可以高精度的重构出载波分量,并提出了一个经验公式,可以自适应的选择需要的小波子信号,该方法等同于一个自适应带通小波滤波器,其带宽和中心频率完全由算法自适应的决定。当频谱混叠可以忽略时,算法可有效的解决傅里叶变换轮廓术中中心频率和通带宽度难以确定的难题,具有很好的鲁棒性,对噪声的抑制力较强,解相结果较平滑。
自适应性和鲁棒性是三维测量系统在实际应用中的基本要求,文中提出的所有相位提取方法均是自适应的,数据驱动的,工作过程中无需人工干预,即使对完全不同类型的测量对象,也无需预设任何参数,同时,这些方法的计算量都较小,适合动态物体测量的需要。
Fringe Projection Profilometry(FPP) successfully realized its application in many fields such as national security, industrial production, flexible manufacturing, space exploratory and medical examinations. Fourier Transform Profilometry (FTP)and its continuations, which can recover the instantaneous phase through only single fringe pattern, have becoming the main methods in FPP, as they have many merits such as large data density, high accuracy, friendly environment, non-contact, no-injury and suit for dynamic object measurement.
For the slow-rate of the phase recover problem, we proposed to use discrete Meyer wavelet in projection profilometry, which can increase the speed of phase retrieval. For the carrier wave component in distored fringe pattern, the inherent feature is detailed analyzed and then a cost function is constructed. The optimal discrete Meyer wavelet decomposition level is corresponding to the minimal value of the cost function. The main advantage of this method is it speedability, and also, which can avoid the detrimental effects of the phase jump and frequency overlap when the background component is sample enough.
Traditionally, Mexican Hat wavelet profilometry has high accuracy and speed for phase retrieval when the outline of the measure element is slow varying, but the robustness of the Mexican Hat wavelet profilometry is poor because the scale which used is fixed and invariant. Based on the differential property of the Fourier transform, a new cost function is constructed, which is robust and stable for signals with noises, has very sample expression and has a clear interpretation in theory. The optimal discrete Meyer decomposition level is corresponding to the minimal value of the new cost function, and the optimal continue Mexican Hat wavelet scale can be adaptive determined through the new cost function. The proposed method is very useful when the outline's gradient of the measurement object has a little vaiation range. And more study illustrates that the new cost function has ability to find the optimal carrier wave component form the Empirical Mode Decomposition (EMD) of the distorted fringe pattern.
To increase the accuracy of the phase retrieval, the pattern should be de-noised ahead of the processing of phase recover. In this paper, we lucubrate the wavelet de-noising methods, and, based on the Orthogonal Wavelet Transform Stein Unbiased error Estimate Linear Extend Transform(OWT_SURE_LET) wavelet de-noising method, we introduces an improved wavelet de-noising, which adopt redundancy wavelet transform and need no the knowledge of the wavelet coefficients prior distribution. The step and process of the noised pattern's wavelet coefficients optimal estimate for the improved method is made in detail in this manuscript. Peaks Signal Noise Radio (PSNR) and the Root Square Mean Error (RSME) of the phase retrieval for the distorted pattern are used to verify the effectiveness of the proposed improved wavelet de-noising method.
A large error will occur when phase jump exist for the traditional wavelet profilometry, for which use dynamic programming and cost funcition to find the optimal wavelet ridge. To overcome this problem, this paper proposed to use dynadic wavelet transform for phase recover, and this algorithm uses OTSU to adaptive choose the larger wavelet coefficients from the the wavelet ridge and its neighbourhood coefficients to reconstruct the carrier wave component. This method can decrease the effect of the phase jump when noise is very little and is ignored.
Band pass filter is offen used in fourier transform profilometry to eliminate the nosie and the back-component, but the center frequency and width of bandpass are hard to determine in practice. Bsed on the research of the dynadic wavelet transform, we found that the carrier wave compnent of the distorted fringe pattern can be reconstructed accurately using the dyadic wavelet sub-signal and its neighborhoods, and then an empirical formula is introduced in this algorithm to adaptive choose the child-signals form the results of the dyadic wavelet transform. Theory analysis show the new algorithm is an adaptive band-pass wavelet filter banks in essential, the band-width and center frequency are variant with types changing of the measurement objects,and this method is very useful when spectra overlap can be ignored.
Adaptability and robustness are very important for object3D measurement in practice. These phase retrieval algorithms presented in this paper are all self-adaptive, data driven, needing no manual intervation, and even for different types of measured object, all the proposed methods in this manuscript need not parameters adjusting at all and need not paremeters presetting at all. More important is that all the methods introduced in this paper are all realtime and have a little calculation, which guarantee that these methods can be used with high effective in3D measurement in practice.
引文
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