WO2022198974A1 - 面向正弦条纹的非线性自矫正结构光三维测量方法及系统 - Google Patents

面向正弦条纹的非线性自矫正结构光三维测量方法及系统 Download PDF

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WO2022198974A1
WO2022198974A1 PCT/CN2021/121524 CN2021121524W WO2022198974A1 WO 2022198974 A1 WO2022198974 A1 WO 2022198974A1 CN 2021121524 W CN2021121524 W CN 2021121524W WO 2022198974 A1 WO2022198974 A1 WO 2022198974A1
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fringe
nonlinear response
nonlinear
formula
groups
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PCT/CN2021/121524
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French (fr)
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郑卓鋆
高健
张揽宇
莫健华
陈云
张凯
张昱
贺云波
陈新
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广东工业大学
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    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01B—MEASURING LENGTH, THICKNESS OR SIMILAR LINEAR DIMENSIONS; MEASURING ANGLES; MEASURING AREAS; MEASURING IRREGULARITIES OF SURFACES OR CONTOURS
    • G01B11/00—Measuring arrangements characterised by the use of optical techniques
    • G01B11/24—Measuring arrangements characterised by the use of optical techniques for measuring contours or curvatures
    • G01B11/25—Measuring arrangements characterised by the use of optical techniques for measuring contours or curvatures by projecting a pattern, e.g. one or more lines, moiré fringes on the object
    • G01B11/254—Projection of a pattern, viewing through a pattern, e.g. moiré

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  • the invention relates to the technical field of optical three-dimensional measurement, in particular to a nonlinear self-correcting structured light three-dimensional measurement method and system for sinusoidal stripes.
  • phase-shift profilometry is the most representative method in structured light methods. Through the modulation and decoding of the phase, the pixel correspondence between the camera and the projector can be effectively established, thereby realizing high-precision three-dimensional measurement.
  • the most widely used method in phase-shift profilometry is sinusoidal fringe phase-shift profilometry.
  • sinusoidal fringes Compared with other fringes, sinusoidal fringes have better anti-random noise and anti-defocus ability, and higher robustness.
  • the sinusoidal fringe phase-shift profilometry can eliminate the nonlinear phase error and improve the measurement accuracy by increasing the number of phase shifts. This feature enables the method to achieve high-precision measurement in different scenarios.
  • a large number of projections will undoubtedly consume a lot of measurement time, making it difficult to achieve high-speed and high-precision 3D measurement. Therefore, in order to achieve high-speed and high-precision 3D measurement, eliminating the phase nonlinearity error without increasing the number of projections has always been the focus of research on sinusoidal fringe phase-shift profilometry.
  • the purpose of the present invention is to propose a non-linear self-correcting structured light three-dimensional measurement method and system for sinusoidal fringes to solve the above problems.
  • the nonlinear self-correcting structured light 3D measurement method for sinusoidal fringes includes the following steps:
  • Step A Projecting three groups of sinusoidal fringes with different mean intensities and modulation intensities onto the object to be measured, and taking pictures to obtain fringe images;
  • Step B Calculate the DC components of fringe images of different frequencies
  • Step C using the DC components of different groups of fringe images to identify the nonlinear response parameters of the system to obtain a nonlinear response function
  • Step D use the inverse function of the nonlinear response function to correct the grayscale of the fringe image
  • Step E use the corrected fringe image to calculate the three groups of wrapping phases, and use the multi-frequency heterodyne method to unwrap to obtain the absolute phase;
  • Step F Reconstructing a three-dimensional point cloud according to triangulation ranging to build a three-dimensional model of the object to be measured.
  • the projected three groups of fringe images I h , I m , and I l are represented by formula one, formula two and formula three respectively:
  • I h (x, y, n), I m (x, y, n), I l (x, y, n) are the three groups of fringe images projected respectively, and (x, y) is the sinusoidal fringe image
  • the horizontal and vertical coordinates of , is the phase
  • a 1 , A 2 , and A 3 are the mean intensity of stripes at different frequencies
  • B 1 , B 2 , and B 3 are the modulation intensities of stripes at different frequencies
  • n is the serial number of the amplitude.
  • the average value of the high-frequency fringe image, the intermediate-frequency fringe image and the low-frequency fringe image obtained by taking pictures is calculated to obtain the DC component;
  • I' h (x, y, n), I' m (x, y, n), I' l (x, y, n) are the three groups of fringe images obtained by taking pictures;
  • I sh (x, y ), I sm (x, y), and I sl (x, y) correspond to the DC components obtained by accumulating the high-frequency fringe image, the intermediate-frequency fringe image, and the low-frequency fringe image respectively.
  • step C the nonlinear response parameters of the system are identified, and the method for obtaining the nonlinear response function is:
  • the matrix Q is a known constant coefficient matrix
  • the matrix M is the nonlinear response parameter matrix to be solved
  • a 0 , a 1 , and a 2 are the nonlinear response parameters of the system
  • the matrix P is the DC component matrix calculated in step B;
  • step D use formula nine to correct the grayscale of the fringe image
  • I(x,y,n) is the projected fringe image
  • I'(x,y,n) is the fringe image obtained by taking pictures
  • f -1 is the inverse function of the nonlinear response function
  • step E use formula ten to calculate and obtain three groups of wrapping phases
  • the invention also provides a non-linear self-correcting structured light three-dimensional measurement system oriented to sinusoidal stripes, including a projection module, a photographing module, a DC component calculation module, an identification module, a correction module, a phase calculation module and a modeling module;
  • the projection module is used for projecting three groups of sinusoidal fringes with different mean intensities and modulation intensities to the object to be measured;
  • the photographing module is used for photographing to obtain striped images
  • the DC component calculation module is used to calculate the DC components of fringe images of different frequencies
  • the identification module is used to identify the nonlinear response parameters of the system by utilizing the DC components of different groups of fringe images, and obtain the nonlinear response function;
  • the correction module is used to correct the grayscale of the fringe image using the inverse function of the nonlinear response function
  • the phase calculation module is used to calculate three groups of wrapped phases using the corrected fringe images, and to use the multi-frequency heterodyne method to unwrap to obtain absolute phases;
  • the modeling module is used for reconstructing a three-dimensional point cloud according to triangulation ranging to build a three-dimensional model of the object to be measured.
  • the invention proposes a new mathematical model of the DC component. Based on the DC component model, the modulation intensity and the mean intensity of the three groups of sinusoidal fringes are adjusted, and the nonlinear response equation is established to calculate each pixel. Then use the inverse function of the nonlinear response equation to correct the grayscale of the fringe image, calculate the wrapped phase and the unwrapped phase of the corrected fringe image, and finally reconstruct the three-dimensional point cloud according to the triangulation ranging, and build it to be tested.
  • the three-dimensional model of the object completes the three-dimensional measurement of the object to be measured.
  • the advantage is that the nonlinear self-correcting structured light three-dimensional measurement method and system for sinusoidal stripes provided by the present invention can reduce the nonlinear errors of different frequencies and phases without increasing the projection time and the time-consuming calculation of the huge matrix inversion.
  • the precision of the wrapping method is based on the fringe phase precision of each frequency, so the present invention can simultaneously improve the wrapping phase precision and the unwrapping precision, and realize high-speed and high-precision three-dimensional measurement.
  • the mathematical model adopted in the present invention is more reasonable and followable. Under the premise of known mathematical model, it is only necessary to establish an equation to solve the model parameters. Compared with the previous fitting method based on statistics, more data is required to ensure the fitting. The accuracy of the fitting method solves the large amount of calculation and the problem of overfitting.
  • Fig. 1 is a schematic flow diagram of one embodiment of the present invention
  • Figure 2 is a schematic diagram of the evolution of one of the embodiments of the present invention.
  • the present invention derives the mathematical model of the DC component of the actual fringe by deriving the following formula.
  • the projected fringe image is: in is the phase, A is the mean intensity, B is the modulation intensity, and n is the sequence number of the amplitude.
  • the DC component of the actual fringe can be obtained by accumulating the expression for the actual light intensity, so the expression for the DC component is obtained: Is is denoted as the DC component of the actual fringe. It can be known that the DC signal strength of the actual fringe is jointly determined by the mean intensity A of the ideal fringe and the modulation amount B.
  • Step A Projecting three groups of sinusoidal fringes with different mean intensities and modulation intensities onto the object to be measured, and taking pictures to obtain fringe images;
  • Step B Calculate the DC components of fringe images of different frequencies
  • Step C using the DC components of different groups of fringe images to identify the nonlinear response parameters of the system to obtain a nonlinear response function
  • Step D use the inverse function of the nonlinear response function to correct the grayscale of the fringe image
  • Step E use the corrected fringe image to calculate the three groups of wrapping phases, and use the multi-frequency heterodyne method to unwrap to obtain the absolute phase;
  • Step F Reconstructing a three-dimensional point cloud according to triangulation ranging to build a three-dimensional model of the object to be measured.
  • this method proposes a new mathematical model of the DC component. Based on the DC component model, the modulation intensity and the mean intensity of the three groups of sinusoidal fringes are adjusted, and the nonlinear response equation is established. Then use the inverse function of the nonlinear response equation to correct the grayscale of the fringe image, calculate the wrapped phase and the unwrapped phase of the corrected fringe image, and finally reconstruct the three-dimensional point cloud according to the triangulation ranging. The three-dimensional model of the object to be measured is completed, and the three-dimensional measurement of the object to be measured is completed.
  • the non-linear self-correcting structured light three-dimensional measurement method for sinusoidal stripes provided by the present invention can reduce the nonlinear error of different frequency phases without increasing the projection time and the huge time-consuming calculation of matrix inversion.
  • the accuracy is based on the fringe phase accuracy of each frequency, so the present invention can simultaneously improve the wrapping phase accuracy and the unwrapping accuracy, and realize high-speed and high-precision three-dimensional measurement.
  • the mathematical model adopted in the present invention is more reasonable and followable. Under the premise of known mathematical model, it is only necessary to establish an equation to solve the model parameters. Compared with the previous fitting method based on statistics, more data is required to ensure the fitting. The accuracy of the fitting method solves the large amount of calculation and the problem of overfitting.
  • the projected three groups of fringe images I h , I m , and I l are represented by formula 1, formula 2 and formula 3 respectively:
  • I h (x, y, n), I m (x, y, n), I l (x, y, n) are the three groups of fringe images projected respectively, and (x, y) is the sinusoidal fringe image
  • the horizontal and vertical coordinates of , is the phase
  • a 1 , A 2 , and A 3 are the mean intensity of stripes at different frequencies
  • B 1 , B 2 , and B 3 are the modulation intensities of stripes at different frequencies
  • n is the serial number of the amplitude.
  • the projected pixel coordinates are modulated into the phase of the fringe pattern according to the above formula 1, formula 2 and formula 3, and then the corresponding relationship between the projected pixels of the camera is obtained by decoding according to the fringe image.
  • the average value of the high-frequency fringe image, the intermediate-frequency fringe image and the low-frequency fringe image obtained by taking pictures is calculated to obtain the DC component;
  • I' h (x, y, n), I' m (x, y, n), I' l (x, y, n) are the three groups of fringe images obtained by taking pictures;
  • I sh (x, y ), I sm (x, y), and I sl (x, y) correspond to the DC components obtained by accumulating the high-frequency fringe image, the intermediate-frequency fringe image, and the low-frequency fringe image respectively.
  • the calculated high-frequency fringe images, the intermediate-frequency fringe images, and the low-frequency fringe images are respectively accumulated to obtain the DC components, which are used for the subsequent identification of the nonlinear response parameters of the system.
  • step C the method for identifying the nonlinear response parameters of the system and obtaining the nonlinear response function is:
  • the matrix Q is the known constant coefficient matrix
  • the matrix M is the nonlinear response parameter matrix to be solved
  • a 0 , a 1 , a 2 are the nonlinear response parameters of the system
  • the matrix P is the DC component matrix calculated in step B. ;
  • the grayscale of the fringe image is corrected using Formula 9;
  • I(x,y,n) is the projected fringe image
  • I'(x,y,n) is the fringe image obtained by taking pictures
  • f -1 is the inverse function of the nonlinear response function
  • f -1 is the nonlinear The inverse of the response function. In this way, the grayscale of the fringe image is corrected.
  • step E use formula ten to calculate and obtain three groups of wrapping phases
  • the corrected fringe image is substituted into Formula 10, and the phase without nonlinear error is calculated, so as to obtain the corrected low, medium and high frequency fringes, and three groups of wrapped phases are calculated.
  • the invention also provides a non-linear self-correcting structured light three-dimensional measurement system oriented to sinusoidal stripes, including a projection module, a photographing module, a DC component calculation module, an identification module, a correction module, a phase calculation module and a modeling module;
  • the projection module is used for projecting three groups of sinusoidal fringes with different mean intensities and modulation intensities to the object to be measured;
  • the photographing module is used for photographing to obtain striped images
  • the DC component calculation module is used to calculate the DC components of fringe images of different frequencies
  • the identification module is used to identify the nonlinear response parameters of the system by utilizing the DC components of different groups of fringe images, and obtain the nonlinear response function;
  • the correction module is used to correct the grayscale of the fringe image using the inverse function of the nonlinear response function
  • the phase calculation module is used to calculate three groups of wrapped phases using the corrected fringe images, and to use the multi-frequency heterodyne method to unwrap to obtain absolute phases;
  • the modeling module is used for reconstructing a three-dimensional point cloud according to triangulation ranging to build a three-dimensional model of the object to be measured.
  • the measurement system provided by the present invention proposes a new mathematical model of the DC component according to the nonlinear response of the system. Based on the DC component model, the modulation intensity and the mean intensity of the three groups of sinusoidal fringes are adjusted to establish the nonlinear response equation, Calculate the respective nonlinear parameters of each pixel, then use the inverse function of the nonlinear response equation to correct the grayscale of the fringe image, calculate the wrapped phase and the unwrapped phase of the corrected fringe image, and finally reconstruct the three-dimensional point according to the triangulation ranging. Cloud, build a three-dimensional model of the object to be measured, and complete the three-dimensional measurement of the object to be measured.
  • the non-linear self-correcting structured light three-dimensional measurement system provided by the present invention can reduce the nonlinear error of different frequency phases without increasing the projection time and the huge matrix inversion calculation time.
  • the accuracy is based on the fringe phase accuracy of each frequency, so the present invention can simultaneously improve the wrapping phase accuracy and the unwrapping accuracy, and realize high-speed and high-precision three-dimensional measurement.
  • the mathematical model is more reasonable and followable in the present invention.
  • the accuracy of the fitting method solves the large amount of calculation and the problem of overfitting.

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Abstract

一种面向正弦条纹的非线性自矫正结构光三维测量方法及系统。该方法根据系统非线性响应，提出一种新的直流分量的数学模型，基于该直流分量模型，调整三组正弦条纹各自的调制强度以及均值强度，建立关于非线性响应方程，计算得到每个像素各自的非线性相应参数，再利用非线性响应方程的反函数矫正条纹图像的灰度，将矫正后的条纹图像计算出包裹相位和解包裹相位，最后根据三角测距重建三维点云，建成待测物体的三维模型，完成待测物体的三维测量。该方法无需增加投影时间以及庞大的矩阵求逆计算耗时，减少不同频率相位的非线性误差，同时提高包裹相位精度以及解包裹精度，实现高速、高精度的三维测量。

Description

面向正弦条纹的非线性自矫正结构光三维测量方法及系统 技术领域
本发明涉及光学三维测量技术领域，尤其是面向正弦条纹的非线性自矫正结构光三维测量方法及系统。
背景技术
三维测量一直是测量领域的发展重点。随着数据处理能力的发展，三维数据的普及度也越来越高。三维测量广泛应用于逆向工程，文物测量，工业检测。基于投影与成像技术的高速发展，结构光测量方法具有高速，高精度，适用范围广的特点，是广泛应用的非接触式三维测量方法之一。相移轮廓术是结构光方法中最具有代表性的方法。通过相位的调制与解码，能有效建立相机与投影仪之间的像素对应关系，从而实现高精度三维测量。相移轮廓术中应用最广泛的方法就是正弦条纹相移轮廓术。与其他条纹相比，正弦条纹具有更好的抗随机噪声以及抗离焦能力，鲁棒性更高。然而投影系统与成像系统存在非线性响应，这使得解码得到得相位存在相位误差。正弦条纹相移轮廓术可以通过增加相移次数从而消除非线性相位误差提高测量精度，这一特点使得该方法在不同场景下均能实现高精度测量。然而大量的投影数量无疑会消耗大量测量时间，使得高速高精度的三维测量难以实现。因此，为了实现高速高精度的三维测量，在不增加投影数量的前提下，消除相位非线性误差一直是正弦条纹相移轮廓术的研究重点。
发明内容
本发明的目的在于提出面向正弦条纹的非线性自矫正结构光三维测量方法及系统，以解决上述问题。
为达此目的，本发明采用以下技术方案：
面向正弦条纹的非线性自矫正结构光三维测量方法，包括以下步骤：
步骤A：投影三组不同均值强度以及调制强度的正弦条纹到待测物体，拍照获取条纹图像；
步骤B：计算不同频率的条纹图像的直流分量；
步骤C：利用不同组的条纹图像的直流分量，辨识系统非线性响应参数，得到非线性响应函数；
步骤D：使用非线性响应函数的反函数矫正条纹图像的灰度；
步骤E：使用矫正后的条纹图像计算三组包裹相位，并使用多频外差法解包裹得到绝对相位；
步骤F：根据三角测距重建三维点云，建成待测物体的三维模型。
进一步，所述步骤A中，投影的三组条纹图像I h,I m,I l分别使用公式一、公式二和公式三表示：
Figure PCTCN2021121524-appb-000001
Figure PCTCN2021121524-appb-000002
Figure PCTCN2021121524-appb-000003
其中，I h(x,y,n),I m(x,y,n),I l(x,y,n)分别是投影出的三组条纹图像，(x,y)为正弦条纹图像的横纵坐标，
Figure PCTCN2021121524-appb-000004
是相位，A 1、A 2、A 3是不同频率条纹的均值强度，B 1、B 2、B 3是不同频率条纹的调制强度，n是幅数的序号。
进一步，所述步骤B中，按照公式四、公式五以及公式六对拍照获取的高频条纹图像、中频条纹图像以及低频条纹图像进行均值计算，得到直流分量；
Figure PCTCN2021121524-appb-000005
Figure PCTCN2021121524-appb-000006
Figure PCTCN2021121524-appb-000007
其中I’ h(x,y,n),I’ m(x,y,n),I’ l(x,y,n)分别是拍照获取到的三组条纹图像；I sh(x,y)，I sm(x,y)，I sl(x,y)分别对应高频条纹图像、中频条纹图像以及低频条纹图像各自累加得到的直流分量。
进一步，所述步骤C中，辨识系统非线性响应参数，得到非线性响应函数的方法是：
先根据公式四、公式五以及公式六建立方程组求解，得到公式七：
Figure PCTCN2021121524-appb-000008
其中矩阵Q为已知的常量系数矩阵，矩阵M为待求解的非线性响应参数矩阵，a 0，a 1，a 2是系统非线性响应参数，矩阵P为步骤B计算得到的直流分量矩阵；
基于公式七中矩阵Q为已知的常量矩阵，变换公式七得到求解系统非线性响应参数的非线性响应函数：
Figure PCTCN2021121524-appb-000009
其中，Q -1是矩阵Q的逆矩阵。
进一步，所述步骤D中，使用公式九矫正条纹图像的灰度；
Figure PCTCN2021121524-appb-000010
I(x,y,n)表示为投影出的条纹图像，I’(x,y,n)表示为拍照获取到的条纹图像，f -1是非线性响应函数的反函数。
进一步，所述步骤E中，使用公式十计算得到三组包裹相位；
Figure PCTCN2021121524-appb-000011
其中，
Figure PCTCN2021121524-appb-000012
表示为条纹图像的包裹相位。
本发明还提供面向正弦条纹的非线性自矫正结构光三维测量系统，包括投影模块、拍照模块、直流分量计算模块、辨识模块、矫正模块、相位计算模块和建模模块；
所述投影模块用于投影三组不同均值强度以及调制强度的正弦条纹到待测物体；
所述拍照模块用于拍照获取条纹图像；
所述直流分量计算模块用于计算不同频率的条纹图像的直流分量；
所述辨识模块用于利用不同组的条纹图像的直流分量，辨识系统非线性响应参数，得到非线性响应函数；
所述矫正模块用于使用非线性响应函数的反函数矫正条纹图像的灰度；
所述相位计算模块用于使用矫正后的条纹图像计算三组包裹相位，并用于使用多频外差法解包裹得到绝对相位；
所述建模模块用于根据三角测距重建三维点云，建成待测物体的三维模型。
本发明根据系统非线性响应，提出一种新的直流分量的数学模型，基于该直流分量模型，调整三组正弦条纹各自的调制强度以及均值强度，建立关于非 线性响应方程，计算得到每个像素各自的非线性相应参数，再利用非线性响应方程的反函数矫正条纹图像的灰度，将矫正后的条纹图像计算出包裹相位和解包裹相位，最后根据三角测距重建三维点云，建成待测物体的三维模型，完成待测物体的三维测量。
优点在于：本发明提供的面向正弦条纹的非线性自矫正结构光三维测量方法及系统，无需增加投影时间以及庞大的矩阵求逆计算耗时，即可减少不同频率相位的非线性误差，由于解包裹方法的精度是基于各个频率的条纹相位精度，因此本发明能同时提高包裹相位精度以及解包裹精度，实现高速、高精度的三维测量。其中，本发明采用数学模型更加有理可循，在已知数学模型的前提下，只需要建立方程求解模型参数即可，相对于以往基于统计学的拟合方法需要更多的数据以保证拟合的准确性，解决了拟合方法存在的计算量大，以及容易出现过拟合的问题。
附图说明
附图对本发明做进一步说明，但附图中的内容不构成对本发明的任何限制。
图1是本发明其中一个实施例的流程示意图；
图2是本发明其中一个实施例的演变示意图。
具体实施方式
首先，本发明通过以下的公式推导，得到实际条纹的直流分量数学模型。
在测量中，由于相机实际获取的光强可以被投影仪的理想光强的多项式形式表达，因此投影的条纹图像为：
Figure PCTCN2021121524-appb-000013
其中
Figure PCTCN2021121524-appb-000014
是相位，A是均值强度，B是调制强度，n是幅数的序号。
进一步，由于三步相移法的误差来源主要来源于二次谐波，因此本方法假定系统的光强响应是一个二阶多项式：I′ n＝f(I n)≈a 0+a 1I n+a 2I n 2。经过系统响应，推算得到实际光强的表达式为：
Figure PCTCN2021121524-appb-000015
即：
Figure PCTCN2021121524-appb-000016
其中a 0，a 1，a 2是系统非线性响应的系统参数。
通过累加实际光强的表达式可以得到实际条纹的直流分量，因此得到直流分量的表达式：
Figure PCTCN2021121524-appb-000017
I s表示为实际条纹的直流分量。可得知，实际条纹的直流信号强度是由理想条纹的均值强度A与调制量B共同决定的。
以上为本方法的理论基础。下面结合具体实施方式来进一步说明本发明的技术方案。
本实施例的面向正弦条纹的非线性自矫正结构光三维测量方法，包括以下步骤：
步骤A：投影三组不同均值强度以及调制强度的正弦条纹到待测物体，拍照获取条纹图像；
步骤B：计算不同频率的条纹图像的直流分量；
步骤C：利用不同组的条纹图像的直流分量，辨识系统非线性响应参数，得到非线性响应函数；
步骤D：使用非线性响应函数的反函数矫正条纹图像的灰度；
步骤E：使用矫正后的条纹图像计算三组包裹相位，并使用多频外差法解包 裹得到绝对相位；
步骤F：根据三角测距重建三维点云，建成待测物体的三维模型。
本方法根据系统非线性响应，提出了一种新的直流分量的数学模型，基于该直流分量模型，调整三组正弦条纹各自的调制强度以及均值强度，建立关于非线性响应方程，计算得到每个像素各自的非线性相应参数，再利用非线性响应方程的反函数矫正条纹图像的灰度，将矫正后的条纹图像计算出包裹相位和解包裹相位，最后根据三角测距重建三维点云，建成待测物体的三维模型，完成待测物体的三维测量。
本发明提供的一种面向正弦条纹的非线性自矫正结构光三维测量方法，无需增加投影时间以及庞大的矩阵求逆计算耗时，即可减少不同频率相位的非线性误差，由于解包裹方法的精度是基于各个频率的条纹相位精度，因此本发明能同时提高包裹相位精度以及解包裹精度，实现高速、高精度的三维测量。其中，本发明采用数学模型更加有理可循，在已知数学模型的前提下，只需要建立方程求解模型参数即可，相对于以往基于统计学的拟合方法需要更多的数据以保证拟合的准确性，解决了拟合方法存在的计算量大，以及容易出现过拟合的问题。
具体地，所述步骤A中，投影的三组条纹图像I h,I m,I l分别使用公式一、公式二和公式三表示：
Figure PCTCN2021121524-appb-000018
Figure PCTCN2021121524-appb-000019
Figure PCTCN2021121524-appb-000020
其中，I h(x,y,n),I m(x,y,n),I l(x,y,n)分别是投影出的三组条纹图像，(x,y)为正弦条纹图像的横纵坐标，
Figure PCTCN2021121524-appb-000021
是相位，A 1、A 2、A 3是不同频率条纹的均值强度，B 1、B 2、B 3是不同频率条纹的调制强度，n是幅数的序号。
如此，本实施例通过上述公式一、公式二和公式三把投影的像素坐标调制到了条纹图案的相位中，后续根据条纹图像进行解码从而获得相机投影像素的对应关系。
进一步，所述步骤B中，按照公式四、公式五以及公式六对拍照获取的高频条纹图像、中频条纹图像以及低频条纹图像进行均值计算，得到直流分量；
Figure PCTCN2021121524-appb-000022
Figure PCTCN2021121524-appb-000023
Figure PCTCN2021121524-appb-000024
其中I’ h(x,y,n),I’ m(x,y,n),I’ l(x,y,n)分别是拍照获取到的三组条纹图像；I sh(x,y)，I sm(x,y)，I sl(x,y)分别对应高频条纹图像、中频条纹图像以及低频条纹图像各自累加得到的直流分量。如此，计算得到的高频条纹图像、中频条纹图像以及低频条纹图像各自累加得到的直流分量，以用于后续的系统非线性响应参数辨识。
值得说明的是，所述步骤C中，辨识系统非线性响应参数，得到非线性响应函数的方法是：
先根据公式四、公式五以及公式六建立方程组求解，得到公式七：
Figure PCTCN2021121524-appb-000025
其中，矩阵Q为已知的常量系数矩阵，矩阵M为待求解的非线性响应参数矩阵，a 0，a 1，a 2是系统非线性响应参数，矩阵P为步骤B计算得到的直流分量矩阵；
基于公式七中矩阵Q为已知的常量矩阵，变换公式七得到求解系统非线性响应参数的非线性响应函数：
Figure PCTCN2021121524-appb-000026
其中，Q -1是矩阵Q的逆矩阵。
如此，通过公式八计算出系统非线性响应的系统参数a 0，a 1，a 2，从而得到非线性响应函数。
具体地，所述步骤D中，使用公式九矫正条纹图像的灰度；
Figure PCTCN2021121524-appb-000027
I(x,y,n)表示为投影出的条纹图像，I’(x,y,n)表示为拍照获取到的条纹图像，f -1是非线性响应函数的反函数，f -1是非线性响应函数的反函数。如此，实现矫正条纹图像的灰度。
进一步，所述步骤E中，使用公式十计算得到三组包裹相位；
Figure PCTCN2021121524-appb-000028
其中，
Figure PCTCN2021121524-appb-000029
表示为条纹图像的包裹相位。
如此，将矫正条纹图像代入公式十中，计算得到没有非线性误差的相位，从而得到矫正后的低中高频率条纹计算得到三组包裹相位。
本发明还提供面向正弦条纹的非线性自矫正结构光三维测量系统，包括投影模块、拍照模块、直流分量计算模块、辨识模块、矫正模块、相位计算模块和建模模块；
所述投影模块用于投影三组不同均值强度以及调制强度的正弦条纹到待测物体；
所述拍照模块用于拍照获取条纹图像；
所述直流分量计算模块用于计算不同频率的条纹图像的直流分量；
所述辨识模块用于利用不同组的条纹图像的直流分量，辨识系统非线性响应参数，得到非线性响应函数；
所述矫正模块用于使用非线性响应函数的反函数矫正条纹图像的灰度；
所述相位计算模块用于使用矫正后的条纹图像计算三组包裹相位，并用于使用多频外差法解包裹得到绝对相位；
所述建模模块用于根据三角测距重建三维点云，建成待测物体的三维模型。
本发明提供的测量系统根据系统非线性响应，提出了一种新的直流分量的数学模型，基于该直流分量模型，调整三组正弦条纹各自的调制强度以及均值强度，建立关于非线性响应方程，计算得到每个像素各自的非线性相应参数，再利用非线性响应方程的反函数矫正条纹图像的灰度，将矫正后的条纹图像计算出包裹相位和解包裹相位，最后根据三角测距重建三维点云，建成待测物体的三维模型，完成待测物体的三维测量。
本发明提供的一种面向正弦条纹的非线性自矫正结构光三维测量系统，无需增加投影时间以及庞大的矩阵求逆计算耗时，即可减少不同频率相位的非线性误差，由于解包裹方法的精度是基于各个频率的条纹相位精度，因此本发明能同时提高包裹相位精度以及解包裹精度，实现高速、高精度的三维测量。其 中，本发明采用数学模型更加有理可循，在已知数学模型的前提下，只需要建立方程求解模型参数即可，相对于以往基于统计学的拟合系统需要更多的数据以保证拟合的准确性，解决了拟合方法存在的计算量大，以及容易出现过拟合的问题。
以上结合具体实施例描述了本发明的技术原理。这些描述只是为了解释本发明的原理，而不能以任何方式解释为对本发明保护范围的限制。基于此处的解释，本领域的技术人员不需要付出创造性的劳动即可联想到本发明的其它具体实施方式，这些等同的变型或替换均包含在本申请权利要求所限定的范围内。

Claims (2)

  1. 面向正弦条纹的非线性自矫正结构光三维测量方法，其特征在于：包括以下步骤：
    步骤A：投影三组不同均值强度以及调制强度的正弦条纹到待测物体，拍照获取条纹图像；其中，所述步骤A中，投影的三组条纹图像I h,I m,I l分别使用公式一、公式二和公式三表示：
    Figure PCTCN2021121524-appb-100001
    Figure PCTCN2021121524-appb-100002
    Figure PCTCN2021121524-appb-100003
    其中，I h(x,y,n),I m(x,y,n),I l(x,y,n)分别是投影出的三组条纹图像，(x,y)为正弦条纹图像的横纵坐标，
    Figure PCTCN2021121524-appb-100004
    是相位，A 1、A 2、A 3是不同频率条纹的均值强度，B 1、B 2、B 3是不同频率条纹的调制强度，n是幅数的序号；
    步骤B：计算不同频率的条纹图像的直流分量；其中，所述步骤B中，按照公式四、公式五以及公式六对拍照获取的高频条纹图像、中频条纹图像以及低频条纹图像进行均值计算，得到直流分量；
    Figure PCTCN2021121524-appb-100005
    Figure PCTCN2021121524-appb-100006
    Figure PCTCN2021121524-appb-100007
    其中I’ h(x,y,n),I’ m(x,y,n),I’ l(x,y,n)分别是拍照获取到的三组条纹图像；
    I sh(x,y)，I sm(x,y)，I sl(x,y)分别对应高频条纹图像、中频条纹图像以及低频条纹图像各自累加得到的直流分量；
    步骤C：利用不同组的条纹图像的直流分量，辨识系统非线性响应参数，得到非线性响应函数；其中，所述步骤C中，辨识系统非线性响应参数，得到非线性响应函数的方法是：
    先根据公式四、公式五以及公式六建立方程组求解，得到公式七：
    Figure PCTCN2021121524-appb-100008
    其中矩阵Q为已知的常量系数矩阵，矩阵M为待求解的非线性响应参数矩阵，a 0，a 1，a 2是系统非线性响应参数，矩阵P为步骤B计算得到的直流分量矩阵；
    基于公式七中矩阵Q为已知的常量矩阵，变换公式七得到求解系统非线性响应参数的非线性响应函数：
    Figure PCTCN2021121524-appb-100009
    其中，Q -1是矩阵Q的逆矩阵；
    步骤D：使用非线性响应函数的反函数矫正条纹图像的灰度；其中，所述步骤D中，使用公式九矫正条纹图像的灰度；
    Figure PCTCN2021121524-appb-100010
    I(x,y,n)表示为投影出的条纹图像，I’(x,y,n)表示为拍照获取到的条纹图像，f -1是非线性响应函数的反函数；
    步骤E：使用矫正后的条纹图像计算三组包裹相位，并使用多频外差法解包裹得到绝对相位；其中，所述步骤E中，使用公式十计算得到三组包裹相位；
    Figure PCTCN2021121524-appb-100011
    其中，
    Figure PCTCN2021121524-appb-100012
    表示为条纹图像的包裹相位；
    步骤F：根据三角测距重建三维点云，建成待测物体的三维模型。
  2. 面向正弦条纹的非线性自矫正结构光三维测量系统，其特征在于：应用在权利要求1所述的面向正弦条纹的非线性自矫正结构光三维测量方法，所述系统包括投影模块、拍照模块、直流分量计算模块、辨识模块、矫正模块、相位计算模块和建模模块；
    所述投影模块用于投影三组不同均值强度以及调制强度的正弦条纹到待测物体；
    所述拍照模块用于拍照获取条纹图像；
    所述直流分量计算模块用于计算不同频率的条纹图像的直流分量；
    所述辨识模块用于利用不同组的条纹图像的直流分量，辨识系统非线性响应参数，得到非线性响应函数；
    所述矫正模块用于使用非线性响应函数的反函数矫正条纹图像的灰度；
    所述相位计算模块用于使用矫正后的条纹图像计算三组包裹相位，并用于使用多频外差法解包裹得到绝对相位；
    所述建模模块用于根据三角测距重建三维点云，建成待测物体的三维模型。
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