CN104596443A - Light plane equation fitting locating calibration method based on inherent characteristics of three-line laser - Google Patents

Light plane equation fitting locating calibration method based on inherent characteristics of three-line laser Download PDF

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CN104596443A
CN104596443A CN201510038858.1A CN201510038858A CN104596443A CN 104596443 A CN104596443 A CN 104596443A CN 201510038858 A CN201510038858 A CN 201510038858A CN 104596443 A CN104596443 A CN 104596443A
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孙秋成
刘仁云
于繁华
王春艳
孙晔
刘成
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Changchun Normal University
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Abstract

本发明一种基于三线激光器固有特性的光平面方程拟合定位标定方法属于将三线激光器所发出的三个光平面的空间姿态方程均精确拟合于相机虚拟空间坐标系中的拟合标定方法领域,本发明的标定方法特别提出了将三个激光平面的邻近夹角量已知、三个激光平面均相交于同一交线、三个激光平面的投影光条均平行这三个真实的固有特性同时作为所述特殊三线激光器投影特征的数理模型的约束条件,由此获得能够整体反映这三个关键特征的目标函数及其约束条件,并为该目标函数的求解带来可能性,最终给出了一整套将真实世界中的三线激光器投射平面的一系列物理特征均同时精确移植到虚拟的相机坐标系的数学模型下的可行方法。

A light plane equation fitting, positioning and calibration method based on the inherent characteristics of a three-line laser belongs to the field of fitting and calibration methods for accurately fitting the spatial attitude equations of three light planes emitted by a three-line laser to a camera virtual space coordinate system. , the calibration method of the present invention specifically proposes the three true inherent characteristics that the adjacent angles of the three laser planes are known, the three laser planes all intersect on the same intersection line, and the projected light bars of the three laser planes are all parallel. At the same time, as the constraints of the mathematical model of the projection characteristics of the special three-line laser, the objective function and its constraints that can reflect the three key features as a whole are obtained, and it is possible to solve the objective function. Finally, It is a set of feasible methods to simultaneously and accurately transplant a series of physical characteristics of the three-line laser projection plane in the real world to the mathematical model of the virtual camera coordinate system.

Description

基于三线激光器固有特性的光平面方程拟合定位标定方法Optical Plane Equation Fitting Positioning Calibration Method Based on Inherent Characteristics of Three-Line Laser

技术领域technical field

本发明属于将三线激光器所发出的三个光平面的空间姿态方程均精确拟合于相机虚拟空间坐标系中的拟合标定方法领域,具体涉及一种基于三线激光器固有特性的光平面方程拟合定位标定方法。The invention belongs to the field of fitting and calibration methods for accurately fitting the spatial attitude equations of three light planes emitted by a three-line laser to a camera virtual space coordinate system, and specifically relates to a light plane equation fitting based on the inherent characteristics of a three-line laser positioning calibration method.

背景技术Background technique

视觉测量技术能很好地适应现代工业对工件外形尺寸检测所提出的新标准和要求,是一种兼备精度和效率的非接触式外形检测手段。视觉测量方法的基本思想是:用空间姿态已知的激光平面投射在被检测物体上,并用相机对激光平面在物体外形轮廓上的投影拍照,通过检测特征点图像坐标,根据已知相机内部参数和激光平面方程获得特征点在相机坐标系下对应的三维坐标,进而获得物体表面轮廓的三维信息。在使激光平面的空间姿态成为已知量的过程中,如何才能通过建模、标定等过程,使激光器在真实物理世界中所投射出的激光平面在相机的虚拟空间坐标系下映射成为已知的数学空间方程,始终是视觉测量技术领域研究的重点。Vision measurement technology can well adapt to the new standards and requirements of modern industry for the detection of workpiece shape and size. It is a non-contact shape detection method with both precision and efficiency. The basic idea of the visual measurement method is: use a laser plane with a known spatial attitude to project on the object to be detected, and use a camera to take pictures of the projection of the laser plane on the outline of the object. By detecting the image coordinates of feature points, according to the known internal parameters of the camera The three-dimensional coordinates corresponding to the feature points in the camera coordinate system are obtained with the laser plane equation, and then the three-dimensional information of the surface contour of the object is obtained. In the process of making the spatial attitude of the laser plane a known quantity, how can the laser plane projected by the laser in the real physical world be mapped in the virtual space coordinate system of the camera to become known through modeling, calibration and other processes The mathematical space equation has always been the focus of research in the field of visual measurement technology.

目前,用于求解和确定单一的线结构激光空间平面方程的方法已趋于成熟,其方法多样,它们的共性都是通过标定获得的相机内部参数和靶标三维信息,求解激光光条上的多个离散特征点对应的空间坐标(x、y、z)以作为拟合光平面的离散特征点,利用多个非共线的离散特征点可求出任意一个激光光平面的空间方程。At present, the methods for solving and determining the spatial plane equation of a single line-structured laser have become mature, and there are various methods. Their commonality is to obtain the internal parameters of the camera and the three-dimensional information of the target through calibration. The spatial coordinates (x, y, z) corresponding to each discrete feature point are used as discrete feature points for fitting the light plane, and the space equation of any laser light plane can be obtained by using multiple non-collinear discrete feature points.

比如,在专利申请号为201310352766.1的《多线结构光视觉传感器的快速标定方法》一文中,就在其公式(12)的求解方式中包含了所需的一组离散特征点空间坐标(x,y,z)的获取方法。For example, in the article "Quick Calibration Method for Multi-Line Structured Light Vision Sensor" with patent application number 201310352766.1, the solution method of formula (12) includes a set of discrete feature point space coordinates (x, y, z) acquisition method.

又如,本发明的发明人也在学术期刊Public Library of Science上所发表的Sun Q,Hou Y,Tan Q,Li G(2014)A Flexible Calibration Method Using the PlanarTarget with a Square Pattern for Line Structured Light Vision System.PLoS ONE9(9):e106911.doi:10.1371/journal.pone.0106911一文中,在其章节2.2Subpixelcenter localization of the light stripe中提出了求解激光光条中心点像素坐标(xp,yp)对应在相机坐标系下的坐标(Xc,Yc,Zc)的提取方法,按照该方法能获得连续且更为精确的光条中心点像素坐标,因此也可以作为获取激光光条上所需的一组离散特征点空间坐标(x,y,z)的方法,上述方法简称为离散特征点空间坐标提取方法B。As another example, Sun Q, Hou Y, Tan Q, Li G (2014) A Flexible Calibration Method Using the PlanarTarget with a Square Pattern for Line Structured Light Vision published by the inventor of the present invention on the academic journal Public Library of Science In the article System.PLoS ONE9(9):e106911.doi:10.1371/journal.pone.0106911, in its chapter 2.2Subpixelcenter localization of the light stripe, it is proposed to solve the pixel coordinates of the center point of the laser light stripe (x p , y p ) Corresponding to the extraction method of the coordinates (X c , Y c , Z c ) in the camera coordinate system, according to this method, continuous and more accurate pixel coordinates of the center point of the light strip can be obtained, so it can also be used as a method to obtain all the points on the laser light strip A set of discrete feature point space coordinates (x, y, z) method is required, the above method is referred to as discrete feature point space coordinate extraction method B.

借助上述任意一种已知的离散特征点空间坐标(x,y,z)的获取方法,我们均可以通过获得一组已知的离散特征点空间坐标来拟合求解出一个近似通过这些离散点的空间平面方程,由此在建立好的相机虚拟坐标系下,获得一个激光平面空间姿态方程,将真实物理世界中的激光器投射平面,移植到虚拟的相机坐标系下。重复上述过程,还可以进一步获得第二个、第三个,以至于更多新的虚拟的激光空间平面方程。通过该已知方法,还可以进一步实现:将真实物理世界中由多线激光器所投射出的多个激光平面均在相机的虚拟空间坐标系下粗略拼合映射成为已知数学空间方程的标定过程。With the help of any of the above methods for obtaining the spatial coordinates (x, y, z) of the known discrete feature points, we can obtain a set of known spatial coordinates of the discrete feature points to fit and solve an approximation through these discrete points The spatial plane equation of the laser plane is thus obtained in the established camera virtual coordinate system to obtain a laser plane space attitude equation, and the laser projection plane in the real physical world is transplanted into the virtual camera coordinate system. By repeating the above process, the second, third, and even more new virtual laser space plane equations can be further obtained. Through this known method, it can be further realized that multiple laser planes projected by multi-line lasers in the real physical world are roughly combined and mapped into a calibration process of known mathematical space equations under the virtual space coordinate system of the camera.

然而,这种粗略的在同一相机虚拟坐标系下拟合多个光平面的方式远远不能满足视觉测量对激光空间平面方程坐标定位的精度需求,简单地将针对单线激光器的激光空间平面方程拟合标定技术重复应用于多线激光器的光平面标定,以期实现多个光平面在同一坐标系下拼合的拟合方法存在明显的缺陷。现有由离散特征点拟合出的激光空间平面方程并不够精确,由于检测误差、算法误差等系统误差在所难免,因此所获得的激光空间平面方程与真实世界中的激光器投射平面并不能严格重合。因此,即便是在完全相同的光平面空间姿态方程标定条件下,若先将所获得的第一个和第二个激光空间平面方程在虚拟的相机坐标系下相交,并形成第一条交线的话,则按同样的方法,在将第三个激光空间平面方程也拟合到同一个虚拟的相机坐标系下时,则在误差干扰下,第三个激光空间平面方程可以分别与前两个激光平面分别相交于另外两条新的交线,而与第一和第二激光空间平面方程的交线并不重合。However, this rough method of fitting multiple light planes in the same camera virtual coordinate system is far from meeting the accuracy requirements of visual measurement for coordinate positioning of the laser space plane equation. Simply fitting the laser space plane equation for a single-line laser There are obvious defects in the fitting method that the combined calibration technology is repeatedly applied to the optical plane calibration of multi-line lasers in order to achieve the alignment of multiple optical planes in the same coordinate system. The existing laser space plane equation fitted by discrete feature points is not accurate enough. Due to the unavoidable system errors such as detection error and algorithm error, the obtained laser space plane equation cannot be strictly compared with the laser projection plane in the real world. coincide. Therefore, even under the same calibration conditions of the light plane space attitude equation, if the obtained first and second laser space plane equations are first intersected in the virtual camera coordinate system, and the first intersection line is formed Then, according to the same method, when the third laser space plane equation is also fitted to the same virtual camera coordinate system, then under the error interference, the third laser space plane equation can be compared with the first two The laser plane intersects with other two new intersection lines, but does not overlap with the intersection lines of the first and second laser space plane equations.

另一方面,最新的研究发现,如图1所示的多线结构光激光器是一种能从同一个线光源发出邻近夹角均相同的三个激光平面,且其三个激光平面能在同一投影平面形成三个平行光条的三线激光器,其在某些特殊的视觉测量方法中具有非同寻常的重要意义,由于三线激光器能从同一个线型光源按照相同的夹角α发出三个线结构激光平面,并且其各激光平面之间的夹角α均是真实对称的已知量,因此,若将三线激光器所发出的第一个激光平面a、第二个激光平面b以及第三个激光平面c的空间方程在相机坐标系中分别求解并将三者精确拟合,最终得到在相机的虚拟空间坐标系下,三个虚拟的激光平面空间方程均交于同一交线L,则可以将具有前述三线激光器其三个激光平面夹角α已知的固有真实物理特征移植至视觉测量成像系统的相机虚拟空间坐标系之中,并借助这一重要特性在后续的视觉测量过程中大幅提高测量的准确度和效率。而在前述发明201310352766.1《多线结构光视觉传感器的快速标定方法》一文中,也介绍了多线结构光视觉传感器在相机虚拟坐标系下的一种标定方法,从理论上来说,该方法可以直接用于能从同一个线光源发出邻近夹角均相同的三个激光平面,且其三个激光平面能在同一投影平面形成三个平行光条的三线激光器的标定过程。然而,其方法并未利用所需激光器从同一个线光源发出的三个激光平面中,相邻两个激光平面的夹角均相同这一真实且已知的固有物理特性,因此无法进一步修正和减小系统误差。此外,前述发明201310352766.1《多线结构光视觉传感器的快速标定方法》所介绍的标定方法还必须利用激光投影光条与方向性栅格标靶上的固有栅格线的交比不变性原理,才能辅助完成对离散特征点空间坐标(x,y,z)的获取和多个激光空间平面方程在同一相机坐标系下的标定。但由于方向性栅格上固有网格线条的数量有限,因此通过其与激光投影光条相交所能获得的离散特征点的数量也因此相对较少,而较少的离散特征点数量必然不利于所拟合出的激光空间平面方程在相机虚拟系中的坐标精度。On the other hand, the latest research has found that the multi-line structured light laser shown in Figure 1 is a kind of three laser planes that can emit three adjacent angles from the same line light source, and the three laser planes can be in the same A three-line laser whose projection plane forms three parallel light strips is of extraordinary significance in some special visual measurement methods, because a three-line laser can emit three lines from the same line light source at the same angle α structure laser plane, and the included angle α between each laser plane is a real and symmetrical known quantity, therefore, if the first laser plane a, the second laser plane b and the third laser plane b emitted by the three-line laser are The space equation of the laser plane c is solved separately in the camera coordinate system and the three are accurately fitted, and finally in the virtual space coordinate system of the camera, the three virtual laser plane space equations all intersect on the same intersection line L, then it can be Transplant the inherent real physical characteristics of the aforementioned three-line laser with known angles α between the three laser planes into the camera virtual space coordinate system of the visual measurement imaging system, and use this important feature to greatly improve the subsequent visual measurement process. Measurement accuracy and efficiency. In the aforementioned invention 201310352766.1 "Quick calibration method for multi-line structured light vision sensor", a calibration method for multi-line structured light vision sensor in the camera virtual coordinate system is also introduced. Theoretically speaking, this method can directly It is used for the calibration process of a three-line laser that can emit three laser planes with the same adjacent angles from the same line light source, and whose three laser planes can form three parallel light bars on the same projection plane. However, its method does not take advantage of the real and known inherent physical property that the angles between two adjacent laser planes are the same among the three laser planes emitted by the required laser from the same line source, so it cannot be further corrected and reduce system errors. In addition, the calibration method introduced in the aforementioned invention 201310352766.1 "Quick Calibration Method for Multi-Line Structured Light Vision Sensor" must also use the principle of cross-ratio invariance between the laser projection light strip and the inherent grid lines on the directional grid target. Assist in the acquisition of the space coordinates (x, y, z) of discrete feature points and the calibration of multiple laser space plane equations in the same camera coordinate system. However, due to the limited number of inherent grid lines on the directional grid, the number of discrete feature points that can be obtained by intersecting it with the laser projection light strip is relatively small, and the small number of discrete feature points is bound to be unfavorable. The coordinate accuracy of the fitted laser space plane equation in the camera virtual system.

此外,本发明的发明人在学术期刊Public Library of Science上公开发表的Sun Q,Hou Y,Tan Q,Li G(2014)A Flexible Calibration Method Using the PlanarTarget with a Square Pattern for Line Structured Light Vision System.PLoS ONE9(9):e106911.doi:10.1371/journal.pone.0106911一文中,在第一章Methods的章节1.Calibration ofcamera model还同时公开了一种对相机内部参数进行标定的方法,简称为相机内部参数标定方法A。In addition, the inventor of the present invention published Sun Q, Hou Y, Tan Q, Li G (2014) A Flexible Calibration Method Using the PlanarTarget with a Square Pattern for Line Structured Light Vision System in the academic journal Public Library of Science. In the article PLoS ONE9(9):e106911.doi:10.1371/journal.pone.0106911, in Chapter 1, Methods, Chapter 1.Calibration of camera model also discloses a method for calibrating the internal parameters of the camera, referred to as the camera Internal parameter calibration method A.

发明内容Contents of the invention

为了解决现有针对单线激光器的激光空间平面方程拟合标定技术,其用拼合的方式粗略地在同一相机虚拟坐标系下拟合多个光平面的方式远远不能满足视觉测量对激光空间平面方程坐标定位的精度需求,而现有针对多线结构光激光器的激光空间平面方程标定方法未能充分利用多线结构光激光器固有的重要物理特性,而且,还必须借助激光投影光条与方向性栅格标靶上的固有栅格线的交比不变性原理才能辅助完成离散特征点空间坐标的获取以及多个激光空间平面方程在同一相机坐标系下的标定。但由于方向性栅格上固有网格线条的数量有限,致使通过其与激光投影光条相交所能获得的离散特征点的数量也因此相对较少,因此无法修正和减小系统误差,不利于进一步提高激光空间平面方程在相机虚拟坐标系中的拟合标定精度的技术问题,本发明提供一种基于三线激光器固有特性的光平面方程拟合定位标定方法。In order to solve the existing laser space plane equation fitting and calibration technology for single-line lasers, the method of roughly fitting multiple light planes in the same camera virtual coordinate system by stitching is far from satisfying the requirements of visual measurement for laser space plane equations. Coordinate positioning accuracy requirements, while the existing laser space plane equation calibration method for multi-line structured light lasers fails to make full use of the inherent important physical characteristics of multi-line structured light lasers, and must also rely on laser projection light strips and directional gratings The cross-ratio invariance principle of the inherent grid lines on the grid target can assist in the acquisition of the spatial coordinates of discrete feature points and the calibration of multiple laser space plane equations in the same camera coordinate system. However, due to the limited number of inherent grid lines on the directional grid, the number of discrete feature points that can be obtained by intersecting the directional grid with the laser projection light strip is relatively small, so the system error cannot be corrected and reduced, which is not conducive to To further improve the technical problem of fitting and calibrating the laser space plane equation in the camera virtual coordinate system, the present invention provides a light plane equation fitting, positioning and calibrating method based on the inherent characteristics of the three-line laser.

本发明解决技术问题所采取的技术方案如下:The technical solution adopted by the present invention to solve the technical problems is as follows:

一种基于三线激光器固有特性的光平面方程拟合定位标定方法,其特征在于,该方法包括如下步骤:A light plane equation fitting positioning calibration method based on the inherent characteristics of three-line lasers, characterized in that the method comprises the following steps:

步骤一:选用一种能从同一个线光源发出邻近夹角均相同的三个激光平面,且其三个激光平面能在同一投影平面形成三个平行光条的三线激光器,并从该三线激光器固有的出厂性能指标参数中获取其邻近两个激光平面夹角的角度值参数α;Step 1: Select a three-line laser that can emit three laser planes with the same adjacent angles from the same line light source, and whose three laser planes can form three parallel light stripes on the same projection plane, and use the three-line laser The angle value parameter α of the angle between two adjacent laser planes is obtained from the inherent factory performance index parameters;

步骤二:按照相机内部参数标定方法A完成对相机内部参数进行的标定;Step 2: Complete the calibration of the internal parameters of the camera according to the calibration method A of the internal parameters of the camera;

步骤三:获取针对三线激光器中第一个激光平面(a)的N组离散特征点空间坐标值的集合R,其具体包括如下子步骤:Step 3: Obtain a set R of space coordinate values of N groups of discrete feature points for the first laser plane (a) in the three-line laser, which specifically includes the following sub-steps:

步骤3.1:按照离散特征点空间坐标提取方法B对步骤一所述三线激光器的第一个激光平面(a)在标靶平面(K)上的激光光条(a-1)进行所需的一组离散特征点空间坐标(x,y,z)的采样和提取,从而获得针对前述第一个激光平面(a)在初始姿态下的标靶平面(K)上投影所形成的激光光条(a-1)采样所获得的第一组离散特征点空间坐标:其中i=1,2,...,n,n表示在激光光条(a-1)上采样的离散特征点的数目,坐标值(x,y,z)各自的上角标(a)均表示该离散特征点隶属于第一个激光平面(a);Step 3.1: According to the discrete feature point spatial coordinate extraction method B, perform the required first laser light strip (a-1) on the target plane (K) of the first laser plane (a) of the three-line laser described in step 1. Sampling and extraction of the spatial coordinates (x, y, z) of a group of discrete feature points, so as to obtain the laser light bar ( a-1) The spatial coordinates of the first set of discrete feature points obtained by sampling: Where i=1,2,...,n, n represents the number of discrete feature points sampled on the laser light strip (a-1), and the respective superscripts (a) of the coordinate values (x, y, z) Both indicate that the discrete feature point belongs to the first laser plane (a);

步骤3.2:改变激光投影标靶平面(K)的倾角,并重复步骤3.1的过程,从而获得针对前述第一个激光平面(a)在新姿态下的标靶平面(K’)上投影所形成的激光光条(a-2)采样所获得的第二组离散特征点空间坐标:其中i=(n+1),(n+2),...,2n,n表示在激光光条(a-2)上采样的离散特征点的数目,坐标值(x,y,z)各自的上角标(a)均表示该离散特征点隶属于第一个激光平面(a);Step 3.2: Change the inclination angle of the laser projection target plane (K), and repeat the process of step 3.1 to obtain the projection of the first laser plane (a) on the target plane (K') in the new attitude. The second set of discrete feature point space coordinates obtained by sampling the laser light strip (a-2): Where i=(n+1),(n+2),...,2n, n represents the number of discrete feature points sampled on the laser light strip (a-2), coordinate value (x, y, z) Each superscript (a) indicates that the discrete feature point belongs to the first laser plane (a);

步骤3.3:通过N(N≥3,N是自然数)次改变激光投影靶标平面的倾角并重复步骤3.2的过程,直至获得针对前述第一个激光平面(a)在标靶平面(K)的第N个新姿态上投影所形成的激光光条(a-N)采样所获得的第N组离散特征点空间坐标值:其中i=((N-1)×n+1),((N-1)×n+2)...,N×n,n表示在激光光条(a-N)上采样的离散特征点的数目,坐标值(x,y,z)各自的上角标(a)均表示该离散特征点隶属于第一个激光平面(a);Step 3.3: Change the inclination of the laser projection target plane N times (N≥3, N is a natural number) and repeat the process of step 3.2 until the first laser plane (a) for the aforementioned first laser plane (a) on the target plane (K) is obtained. The spatial coordinate values of the Nth group of discrete feature points obtained by sampling the laser light bar (aN) formed by projection on N new attitudes: Where i=((N-1)×n+1),((N-1)×n+2)...,N×n, n represents the number of discrete feature points sampled on the laser light strip (aN) The superscript (a) of each coordinate value (x, y, z) indicates that the discrete feature point belongs to the first laser plane (a);

步骤3.4:将步骤3.1至步骤3.3分别获得的共计N组离散特征点统一合并成为一个非共线的离散特征点的集合R:Step 3.4: Merge a total of N sets of discrete feature points obtained from step 3.1 to step 3.3 into a set R of non-collinear discrete feature points:

RR == (( xx ii (( aa )) ,, ythe y ii (( aa )) ,, zz ii (( aa )) )) .. .. .. .. .. .. (( 11 )) ;;

式(1)中i=1,2,...,N×n,N×n表示在步骤3.1至步骤3.3中共计N次在激光光条(a-1)、(a-2)……(a-N)上采样的离散特征点的总数,坐标值(x,y,z)各自的上角标(a)均表示该离散特征点隶属于第一个激光平面(a);N表示靶标平面倾角的改变总次数;In the formula (1), i=1, 2,..., N×n, N×n means that a total of N times in the laser light strip (a-1), (a-2)... (a-N) The total number of discrete feature points upsampled, and the superscripts (a) of the coordinate values (x, y, z) indicate that the discrete feature points belong to the first laser plane (a); N indicates the target plane The total number of changes in inclination;

步骤四:采用与步骤三完全相同的方法,分别获取针对三线激光器中第二个激光平面(b)的、由共计N组离散特征点统一合并成为一个非共线的离散特征点的集合以及针对三线激光器中第三个激光平面(c)的、由共计N组离散特征点统一合并成为一个非共线的离散特征点的集合 T = ( x k ( c ) , y k ( c ) , z k ( c ) ) . . . . . . ( 3 ) ; Step 4: Using exactly the same method as Step 3, respectively obtain a set of discrete feature points for the second laser plane (b) in the three-line laser, which is unified and merged into a non-collinear discrete feature point by a total of N groups And for the third laser plane (c) in the three-line laser, a total of N sets of discrete feature points are unified into a set of non-collinear discrete feature points T = ( x k ( c ) , the y k ( c ) , z k ( c ) ) . . . . . . ( 3 ) ;

式(2)中j=1,2,...,N×n,N×n表示在步骤3.1至步骤3.3中共计N次在激光光条(b-1)、(b-2)……(b-N)上采样的离散特征点的总数,坐标值(x,y,z)各自的上角标(b)均表示该离散特征点隶属于第一个激光平面(b);N表示靶标平面倾角的改变总次数;In the formula (2), j=1, 2,..., N×n, N×n means that in step 3.1 to step 3.3, a total of N times in the laser light strip (b-1), (b-2)... (b-N) The total number of discrete feature points upsampled, and the superscripts (b) of the coordinate values (x, y, z) indicate that the discrete feature points belong to the first laser plane (b); N indicates the target plane The total number of changes in inclination;

式(3)中k=1,2,...,N×n,N×n表示在步骤3.1至步骤3.3中共计N次在激光光条(c-1)、(c-2)……(c-N)上采样的离散特征点的总数,坐标值(x,y,z)各自的上角标(c)均表示该离散特征点隶属于第一个激光平面(c);N表示靶标平面倾角的改变总次数;In the formula (3), k=1, 2,..., N×n, N×n means that in step 3.1 to step 3.3, a total of N times in the laser light bar (c-1), (c-2)... (c-N) The total number of discrete feature points upsampled, and the superscripts (c) of the coordinate values (x, y, z) indicate that the discrete feature points belong to the first laser plane (c); N indicates the target plane The total number of changes in inclination;

步骤五:根据多个空间平面方程在三维空间坐标系下的数学方程,定义一个表示三个空间平面均相交于同一交线的数学方程组表达式:Step 5: According to the mathematical equations of multiple space plane equations in the three-dimensional space coordinate system, define a mathematical equation expression that indicates that the three space planes all intersect on the same intersection line:

AA 11 xx ++ BB 11 ythe y ++ CC 11 zz ++ DD. 11 == 00 AA 22 xx ++ BB 22 ythe y ++ CC 22 zz ++ DD. 22 == 00 (( AA 11 ++ λAλA 22 )) xx ++ (( BB 11 ++ λBλB 22 )) ythe y ++ (( CC 11 ++ λCλ C 22 )) zz ++ (( DD. 11 ++ λDλD 22 )) == 00 .. .. .. .. .. .. (( 44 ))

式(4)中,(x,y,z)表示满足方程组的三个空间平面上的一组离散特征点的空间坐标值;In formula (4), (x, y, z) represent the spatial coordinate values of a group of discrete feature points on the three spatial planes satisfying the equation system;

待求解的多项式系数(A1,B1,C1,D1,A2,B2,C2,D2,λ)则共同定义了表示满足方程组(4)的三个空间平面各自的空间姿态系数;The polynomial coefficients to be solved (A 1 , B 1 , C 1 , D 1 , A 2 , B 2 , C 2 , D 2 , λ) jointly define the respective Space attitude coefficient;

式(4)中的第一个方程式是由步骤三所述式(1)所拟合出的、三线激光器的第一个激光平面(a)的激光空间平面方程;The first equation in the formula (4) is the laser space plane equation of the first laser plane (a) of the three-line laser fitted by the formula (1) described in step 3;

式(4)中的第二个方程式是由步骤四所述式(2)所拟合出的、三线激光器的第二个激光平面(b)的激光空间平面方程;The second equation in the formula (4) is the laser space plane equation of the second laser plane (b) of the three-line laser fitted by the formula (2) described in step 4;

式(4)中的第三个方程式是由步骤四所述式(3)所拟合出的、三线激光器的第三个激光平面(c)的激光空间平面方程;The third equation in the formula (4) is the laser space plane equation of the third laser plane (c) of the three-line laser fitted by the formula (3) described in step four;

式(4)中的第三个方程式同时表示第三个激光平面(c)严格通过式(4)中第一个激光平面(a)和第二个激光平面(b)的激光空间平面方程的交线;The third equation in formula (4) also expresses that the third laser plane (c) strictly passes through the laser space plane equations of the first laser plane (a) and the second laser plane (b) in formula (4). intersection line;

步骤六:利用由步骤三所获得的针对前述第一个激光平面(a)的一组非共线离散特征点空间坐标的集合i=1,2,...,(N×n);Step 6: Use the set of space coordinates of a set of non-collinear discrete feature points for the aforementioned first laser plane (a) obtained in step 3 i=1,2,...,(N×n);

由步骤四所获得的针对前述第二个激光平面(b)的一组非共线离散特征点空间坐标的集合j=1,2,...,(N×n);A set of space coordinates of a group of non-collinear discrete feature points for the aforementioned second laser plane (b) obtained in step 4 j=1,2,...,(N×n);

以及由步骤四所获得的针对前述第三个激光平面(c)的一组非共线离散特征点空间坐标的集合k=1,2,...,(N×n)共同作为拟合数据,将由步骤五所确定的表示三个空间平面均相交于同一交线的数学方程组表达式(4)作为拟合函数,并根据公知的最小二乘法建立统一的目标函数:And a set of space coordinates of a group of non-collinear discrete feature points for the aforementioned third laser plane (c) obtained in step 4 k=1,2,...,(N×n) are jointly used as the fitting data, and the expression (4) of the mathematical equation set representing that the three spatial planes all intersect at the same intersection line determined by step 5 is used as the fitting function , and establish a unified objective function according to the well-known least squares method:

MinMin (( ΔΔ )) == ΣΣ ii == 11 NN ×× nno (( AA 11 xx ii (( aa )) ++ BB 11 ythe y ii (( aa )) ++ CC 11 zz ii (( aa )) ++ DD. 11 )) 22 ++ ΣΣ jj == 11 NN ×× nno (( AA 22 xx jj (( bb )) ++ BB 22 ythe y jj (( bb )) ++ CC 22 zz jj (( bb )) ++ DD. 22 )) 22 ++ ΣΣ kk == 11 NN ×× nno (( (( AA 11 ++ λAλA 22 )) xx kk (( cc )) ++ (( BB 11 ++ λBλB 22 )) ythe y kk (( cc )) ++ (( CC 11 ++ λCλ C 22 )) zz kk (( cc )) ++ (( DD. 11 ++ λDλD 22 )) )) 22 .. .. .. .. .. .. (( 55 ))

步骤七:将步骤一所述三线激光器固有的出厂性能指标参数:邻近两个激光平面夹角的角度值参数α作为已知的约束条件,对步骤六所确定的目标函数(5)中的三个激光平面的各自的空间姿态多项式系数(A1,B1,C1,D1,A2,B2,C2,D2,λ)做进一步的数学限定,从而得到包含有角度限定条件的约束表达式:Step 7: Taking the inherent factory performance index parameters of the three-line laser described in step 1: the angle value parameter α of the angle between two adjacent laser planes as a known constraint condition, for the three in the objective function (5) determined in step 6 The respective spatial attitude polynomial coefficients (A 1 , B 1 , C 1 , D 1 , A 2 , B 2 , C 2 , D 2 , λ) of each laser plane are further mathematically limited, so as to obtain the angle limit condition Constraint expression for :

(( AA 11 ,, BB 11 ,, CC 11 )) (( AA 22 ,, BB 22 ,, CC 22 )) AA 11 22 ++ BB 11 22 ++ CC 11 22 AA 22 22 ++ BB 22 22 ++ CC 22 22 == coscos 22 αα (( AA 11 ,, BB 11 ,, CC 11 )) (( AA 11 ++ λAλA 22 ,, BB 11 ++ λBλB 22 ,, CC 11 ++ λCλ C 22 )) AA 11 22 ++ BB 11 22 ++ CC 11 22 (( AA 11 ++ λAλA 22 )) 22 ,, (( BB 11 ++ λBλB 22 )) 22 ,, (( CC 11 ++ λCλ C 22 )) 22 == coscos αα (( AA 22 ,, BB 22 ,, CC 22 )) (( AA 11 ++ λAλA 22 ,, BB 11 ++ λBλB 22 ,, CC 11 ++ λCλC 22 )) AA 22 22 ++ BB 22 22 ++ CC 22 22 (( AA 11 ++ λAλA 22 )) 22 ,, (( BB 11 ++ λBλB 22 )) 22 ,, (( CC 11 ++ λCλC 22 )) 22 == coscos αα .. .. .. .. .. .. (( 66 ))

步骤八:通过公知的Lenvenberg-Marquardt非线性优化算法对式(5)及其限定条件表达式(6)同时求解,从而解出(A1,B1,C1,D1,A2,B2,C2,D2,λ)的值,并完成利用一种能从同一个线光源发出邻近夹角均相同的三个激光平面,且其三个激光平面能在同一投影平面形成三个平行光条的三线激光器的固有特性,将三线激光器所发出的三个光平面的空间姿态方程均精确拟合于相机虚拟空间坐标系中的拟合标定过程。Step 8: Simultaneously solve formula (5) and its conditional expression (6) through the known Lenvenberg-Marquardt nonlinear optimization algorithm, so as to solve (A 1 , B 1 , C 1 , D 1 , A 2 , B 2 , C 2 , D 2 , λ), and complete the use of three laser planes that can emit three adjacent angles from the same line light source, and the three laser planes can form three laser planes on the same projection plane. The inherent characteristics of the three-line laser of the parallel light strips accurately fit the space attitude equations of the three light planes emitted by the three-line laser to the fitting and calibration process in the virtual space coordinate system of the camera.

本发明的有益效果是:本发明的标定方法特别提出了将三个激光平面的邻近夹角量已知、三个激光平面均相交于同一交线、三个激光平面的投影光条均平行这三个真实的固有特性同时作为所述特殊三线激光器投影特征的数理模型的约束条件,由此获得能够整体反映这三个关键特征的目标函数及其约束条件,并为该目标函数的求解带来可能性。最终给出了一整套将真实世界中的三线激光器投射平面的一系列物理特征均同时精确移植到虚拟的相机坐标系的数学模型下的可行方法。此外,本发明还克服了采用旧有用于求解和确定单一的线结构激光空间平面方程的方法直接向同一相机虚拟坐标系下拼合多个激光平面方程时,其粗略地在同一相机虚拟坐标系下拟合多个光平面的方式远远不能满足视觉测量对激光空间平面方程坐标定位的精度需求的问题,并提高了多线结构光拟合标定方法的误差,使得标定精度获得较大提高。The beneficial effects of the present invention are: the calibration method of the present invention specifically proposes that the adjacent angles of the three laser planes are known, the three laser planes all intersect on the same intersection line, and the projected light bars of the three laser planes are all parallel. The three real intrinsic characteristics are simultaneously used as the constraints of the mathematical model of the projection characteristics of the special three-line laser, thereby obtaining an objective function and its constraints that can reflect these three key features as a whole, and bringing new benefits to the solution of the objective function. possibility. Finally, a set of feasible methods are given to accurately transplant a series of physical characteristics of the three-line laser projection plane in the real world to the mathematical model of the virtual camera coordinate system at the same time. In addition, the present invention also overcomes the problem that when multiple laser plane equations are directly combined in the same camera virtual coordinate system using the old method for solving and determining a single line-structured laser space plane equation, it is roughly in the same camera virtual coordinate system. The method of fitting multiple light planes is far from meeting the accuracy requirements of visual measurement for coordinate positioning of the laser space plane equation, and increases the error of the multi-line structured light fitting calibration method, which greatly improves the calibration accuracy.

附图说明Description of drawings

图1是能从同一个线光源发出邻近夹角均相同的三个激光平面且其三个激光平面能在同一投影平面形成三个平行光条的三线激光器的三个激光平面的位置关系示意图。Figure 1 is a schematic diagram of the positional relationship of three laser planes of a three-line laser that can emit three adjacent laser planes with the same angle from the same line light source and can form three parallel light stripes on the same projection plane.

图2是图1所述三个激光平面在同一标靶平面上的三个投影光条的平行关系示意图。FIG. 2 is a schematic diagram of the parallel relationship of the three projected light stripes of the three laser planes in FIG. 1 on the same target plane.

图3是图2的俯视图。FIG. 3 is a top view of FIG. 2 .

图4是对图2中的三个激光平面分别简化并保留三个激光平面分别与标靶平面投影后所形成三条彼此平行的激光光条的示意图。FIG. 4 is a schematic diagram of three laser light stripes parallel to each other formed after the three laser planes in FIG. 2 are respectively simplified and retained after the three laser planes are respectively projected on the target plane.

图5是在图2基础上改变标靶平面的空间姿态和倾角并在其上新生成三个激光平面投影光条的位置关系示意图。FIG. 5 is a schematic diagram of the positional relationship of changing the spatial attitude and inclination of the target plane and generating three new laser plane projection light bars on the basis of FIG. 2 .

图6是图5的俯视图。FIG. 6 is a top view of FIG. 5 .

图7是对图5中的三个激光平面分别简化并保留三个激光平面分别与标靶平面投影后所形成三条彼此平行的激光光条的示意图。FIG. 7 is a schematic diagram of three laser light stripes parallel to each other formed by simplifying the three laser planes in FIG. 5 and retaining the three laser planes respectively projected on the target plane.

具体实施方式Detailed ways

下面结合附图对本发明做进一步详细说明。The present invention will be described in further detail below in conjunction with the accompanying drawings.

如图1所示的三线激光器能从同一个线光源发出邻近夹角均相同的三个激光平面,且其第一个激光平面a、第二个激光平面b以及第三个激光平面c能在同一投影标靶平面K上形成三个平行光条,即图2所示的激光光条a-1、激光光条b-1和激光光条c-1。该激光器选用COHERENT公司制造的STR-660-20-L01型三线结构光激光器。如图3所示,该激光器出厂时邻近两个激光平面固有夹角的角度值参数α为11.7°。The three-line laser shown in Figure 1 can emit three laser planes adjacent to the same angle from the same line source, and its first laser plane a, second laser plane b and third laser plane c can be in Three parallel light stripes are formed on the same projection target plane K, namely laser light stripe a-1, laser light stripe b-1 and laser light stripe c-1 shown in FIG. 2 . The laser is a STR-660-20-L01 three-line structured light laser manufactured by COHERENT. As shown in Figure 3, the angle value parameter α of the inherent angle between two adjacent laser planes when the laser leaves the factory is 11.7°.

图4是对图2中的三个激光平面分别简化并仅保留三个激光平面分别与标靶平面投影后所形成三条彼此平行的激光光条的示意图,而图5则是在图2基础上改变标靶平面K的空间姿态,并在倾角为K的新的标靶平面上新生成三个激光平面投影光条,即:激光光条a-2、激光光条b-2和激光光条c-2的位置关系示意图。保持三线激光器的位置和姿态均不变,而继续改变标靶平面K的空间倾角姿态,则还可以获得第N(N≥3,N是自然数)次改变标靶平面K的空间姿态时,由激光器的三个激光平面在该对应的标靶平面K的当前姿态下投影所新生成三个激光平面投影光条,即:激光光条a-N、激光光条b-N和激光光条c-N。Figure 4 is a schematic diagram of three laser light bars parallel to each other formed by simplifying the three laser planes in Figure 2 and only retaining the three laser planes respectively projected on the target plane, while Figure 5 is based on Figure 2 Change the spatial attitude of the target plane K, and generate three new laser plane projection light bars on the new target plane with an inclination angle of K ' , namely: laser light bar a-2, laser light bar b-2 and laser light bar Schematic diagram of the positional relationship of item c-2. Keeping the position and attitude of the three-line laser unchanged, and continuing to change the space inclination attitude of the target plane K, it is also possible to obtain the Nth (N ≥ 3, N is a natural number) when changing the space attitude of the target plane K, by The three laser planes of the laser project three newly generated laser plane projection light strips under the current attitude of the corresponding target plane K, namely: laser light strip aN, laser light strip bN and laser light strip cN.

本发明一种基于三线激光器固有特性的光平面方程拟合定位标定方法包括如下步骤:A light plane equation fitting positioning calibration method based on the inherent characteristics of the three-line laser of the present invention includes the following steps:

步骤一:选用一种能从同一个线光源发出邻近夹角均相同的三个激光平面,且其三个激光平面能在同一投影平面形成三个平行光条的三线激光器,比如选用COHERENT公司制造的STR-660-20-L01型三线结构光激光器,从该三线激光器固有的出厂性能指标参数中获取其邻近两个激光平面夹角的角度值参数α=11.7°;Step 1: Select a three-line laser that can emit three laser planes with the same adjacent angles from the same line light source, and whose three laser planes can form three parallel light bars on the same projection plane, such as COHERENT. For the STR-660-20-L01 three-line structured light laser, the angle value parameter α=11.7° of the angle between two adjacent laser planes is obtained from the inherent factory performance index parameters of the three-line laser;

步骤二:按照学术期刊PublicLibrary of Science上公开发表的Sun Q,Hou Y,Tan Q,Li G(2014)A Flexible Calibration Method Using the Planar Target with aSquare Pattern for Line Structured Light Vision System.PLoS ONE 9(9):e106911.doi:10.1371/journal.pone.0106911一文中,在第一章Methods的章节1.Calibrationof camera model所述方法完成对相机内部参数进行的标定;Step 2: According to Sun Q, Hou Y, Tan Q, Li G (2014) A Flexible Calibration Method Using the Planar Target with a Square Pattern for Line Structured Light Vision System.PLoS ONE 9(9) published on the academic journal Public Library of Science ):e106911.doi:10.1371/journal.pone.0106911, in the first chapter Methods, the method described in Chapter 1.Calibrationof camera model completes the calibration of the internal parameters of the camera;

步骤三:获取针对三线激光器中第一个激光平面a的N组离散特征点空间坐标值的集合R,其具体包括如下子步骤:Step 3: Obtain a set R of space coordinate values of N sets of discrete feature points for the first laser plane a in the three-line laser, which specifically includes the following sub-steps:

步骤3.1:按照步骤二所述学术期刊在其章节2.2Subpixel center localizationof the light stripe中所提出的求解激光光条中心点像素坐标(xp,yp)对应在相机坐标系下的坐标(Xc,Yc,Zc)的更精确方法,对步骤一所述三线激光器的第一个激光平面a在标靶平面K上的激光光条(a-1)进行所需的一组离散特征点空间坐标(x,y,z)的采样和提取,从而获得针对前述第一个激光平面a在初始姿态下的标靶平面K上投影所形成的激光光条(a-1)采样所获得的第一组离散特征点空间坐标:其中i=1,2,...,n,n表示在激光光条(a-1)上采样的离散特征点的数目,坐标值(x,y,z)各自的上角标(a)均表示该离散特征点隶属于第一个激光平面a;此处将i=1,...,n中的采样点数目的n值设为30,则可获得一组针对激光光条(a-1)且包含30个离散特征点空间坐标值i=1,2,...,30的点的集合;Step 3.1: Solve the pixel coordinates (x p , y p ) of the center point of the laser light stripe corresponding to the coordinates in the camera coordinate system (X c , Y c , Z c ), the more precise method is to carry out the required set of discrete feature points on the laser light strip (a-1) on the target plane K of the first laser plane a of the three-line laser described in step 1 Sampling and extraction of space coordinates (x, y, z), so as to obtain the laser light strip (a-1) obtained by sampling the first laser plane a projected on the target plane K at the initial attitude The first set of discrete feature point space coordinates: Where i=1,2,...,n, n represents the number of discrete feature points sampled on the laser light strip (a-1), and the respective superscripts (a) of the coordinate values (x, y, z) Both indicate that the discrete feature point belongs to the first laser plane a; here the The n value of the number of sampling points in i=1,...,n is set to 30, then a set of spatial coordinate values for the laser light strip (a-1) and containing 30 discrete feature points can be obtained A set of points with i=1,2,...,30;

步骤3.2:如图5至图7所示,改变激光投影标靶平面K的倾角,使激光投影标靶平面的空间姿态倾角变为K’,重复步骤3.1的过程,从而针对前述第一个激光平面a在新姿态下的标靶平面K’上投影所形成的激光光条(a-2)采样所获得的第二组离散特征点空间坐标:其中i=(n+1),(n+2),...,2n,n表示在激光光条(a-2)上采样的离散特征点的数目,坐标值(x,y,z)各自的上角标a均表示该离散特征点隶属于第一个激光平面a;Step 3.2: As shown in Figure 5 to Figure 7, change the inclination angle of the laser projection target plane K, so that the space attitude inclination angle of the laser projection target plane becomes K', repeat the process of step 3.1, so as to target the first laser projection The space coordinates of the second set of discrete feature points obtained by sampling the laser light strip (a-2) formed by the projection of plane a on the target plane K' under the new attitude: Where i=(n+1),(n+2),...,2n, n represents the number of discrete feature points sampled on the laser light strip (a-2), coordinate value (x, y, z) Each superscript a indicates that the discrete feature point belongs to the first laser plane a;

此处将i=(n+1),(n+2),...,2n中的采样点数目的n值依旧设为30,则可针对前述第一个激光平面a在新姿态下的标靶平面K’上的激光光条(a-2)进行第二组包含30个离散特征点空间坐标值的采样和提取:即可获得新的一组针对激光光条(a-2)且包含30个离散特征点空间坐标值:here will The n value of the number of sampling points in i=(n+1),(n+2),...,2n is still set to 30, then the target plane K in the new attitude of the aforementioned first laser plane a can be The second set of sampling and extraction of the spatial coordinate values of the laser light bar (a-2) containing 30 discrete feature points on the ' is obtained: a new set of laser light bar (a-2) containing 30 discrete feature points can be obtained Spatial coordinate values of feature points:

i=31,32...,60,的点的集合; i=31,32...,60, the set of points;

步骤3.3:通过N(N≥3,N是自然数)次改变激光投影靶标平面的倾角并重复步骤3.2的过程,直至获得针对前述第一个激光平面(a)在标靶平面(K)的第N个新姿态上投影所形成的激光光条(a-N)采样所获得的第N组离散特征点空间坐标值:其中i=((N-1)×n+1),((N-1)×n+2)...,N×n,n表示在激光光条(a-N)上采样的离散特征点的数目,坐标值(x,y,z)各自的上角标(a)均表示该离散特征点隶属于第一个激光平面(a);Step 3.3: Change the inclination of the laser projection target plane N times (N≥3, N is a natural number) and repeat the process of step 3.2 until the first laser plane (a) for the aforementioned first laser plane (a) on the target plane (K) is obtained. The spatial coordinate values of the Nth group of discrete feature points obtained by sampling the laser light bar (aN) formed by projection on N new attitudes: Where i=((N-1)×n+1),((N-1)×n+2)...,N×n, n represents the number of discrete feature points sampled on the laser light strip (aN) The superscript (a) of each coordinate value (x, y, z) indicates that the discrete feature point belongs to the first laser plane (a);

此处将i=((N-1)×n+1),((N-1)×n+2)...,N×n中的采样点数目的n值依旧设为30并令N=9,则可针对前述第一个激光平面a在标靶平面K的第九个姿态下投影所生成的激光光条(a-9)进行第九组包含30个离散特征点空间坐标值的采样和提取:即可获得新的一组针对激光光条(a-9)且包含30个离散特征点空间坐标值i=(8×30+1),(8×30+2),...,(9×30)的点的集合;here will i=((N-1)×n+1),((N-1)×n+2)..., the n value of the number of sampling points in N×n is still set to 30 and N=9, then The ninth group of sampling and extraction of the spatial coordinate values of 30 discrete feature points can be performed on the laser light bar (a-9) generated by the projection of the aforementioned first laser plane a at the ninth attitude of the target plane K: A new set of spatial coordinate values for the laser light bar (a-9) and containing 30 discrete feature points can be obtained i=(8×30+1),(8×30+2),...,(9×30) point set;

步骤3.4:将步骤3.1至步骤3.3分别获得的共计九组离散特征点统一合并成为一个非共线的离散特征点的集合R:Step 3.4: Merge a total of nine sets of discrete feature points obtained from step 3.1 to step 3.3 into a set R of non-collinear discrete feature points:

RR == (( xx ii (( aa )) ,, ythe y ii (( aa )) ,, zz ii (( aa )) )) ,, .. .. .. .. .. .. (( 11 )) ;;

式(1)中i=1,2,...,N×n,N×n表示在步骤3.1至步骤3.3中共计N次在激光光条(a-1)、(a-2)……(a-N)上采样的离散特征点的总数,坐标值(x,y,z)各自的上角标a均表示该离散特征点隶属于第一个激光平面a;N表示靶标平面倾角的改变总次数;In the formula (1), i=1, 2,..., N×n, N×n means that in step 3.1 to step 3.3, a total of N times in the laser light strip (a-1), (a-2)... (a-N) The total number of discrete feature points upsampled, and the superscript a of each coordinate value (x, y, z) indicates that the discrete feature point belongs to the first laser plane a; N represents the total change in the inclination angle of the target plane frequency;

即:当靶标平面K的倾角姿态先后改变N=9次,并把激光器的第一个激光平面a对应在靶标平面K的每一次姿态改变后投影所生成的激光光条(a-1)、(a-2)……(a-N)上的采样点数目n均设为30时,则可以将所获得的九组分别包含30个离散特征点的集合共同合并成为一个非共线的包含270个离散特征点空间坐标的集合i=1,2,...,(9×30);即可获得针对第一个激光平面a且包含有270个离散特征点的新集合R;That is: when the inclination attitude of the target plane K changes N=9 times successively, and the first laser plane a of the laser corresponds to the laser light bar (a-1) generated by projection after each attitude change of the target plane K, (a-2)...(aN) When the number n of sampling points on (aN) is set to 30, the obtained nine sets of discrete feature points each containing 30 discrete feature points can be merged into a non-collinear set containing 270 A collection of spatial coordinates of discrete feature points i=1,2,...,(9×30); A new set R containing 270 discrete feature points for the first laser plane a can be obtained;

步骤四:采用与步骤三完全相同的方法,获取并针对三线激光器中第二个激光平面b的、由共计九组离散特征点统一合并成为一个针对第二个激光平面b且包含有270个非共线的离散特征点的集合 Step 4: Using exactly the same method as Step 3, acquire and combine a total of nine sets of discrete feature points for the second laser plane b in the three-line laser into a unified and unified one for the second laser plane b that contains 270 non- A collection of collinear discrete feature points

在式(2)中j=1,2,...,N×n,N×n表示在步骤3.1至步骤3.3中共计九次在激光光条(b-1)、(b-2)……(b-N)上采样的离散特征点的总数,坐标值(x,y,z)各自的上角标(b)均表示该离散特征点隶属于第一个激光平面(b);N表示靶标平面倾角的改变总次数;即:当靶标平面K的倾角姿态先后改变N=9次,并把激光器的第一个激光平面b对应在靶标平面K的每一次姿态改变后投影所生成的激光光条(b-1)、(b-2)……(b-N)上的采样点数目n均设为30时,则可以将所获得的九组分别包含30个离散特征点的集合共同合并成为一个非共线的包含270个离散特征点空间坐标的集合:j=1,2,...,(9×30);In the formula (2), j=1, 2,..., N×n, N×n means that in the laser light bars (b-1), (b-2)... ...(bN) The total number of discrete feature points upsampled, and the superscripts (b) of the coordinate values (x, y, z) indicate that the discrete feature points belong to the first laser plane (b); N indicates the target The total number of changes in the plane inclination; that is: when the inclination attitude of the target plane K changes N=9 times successively, and the first laser plane b of the laser corresponds to the laser light generated by projection after each attitude change of the target plane K When the number of sampling points n on the bars (b-1), (b-2)...(bN) is set to 30, the obtained nine sets containing 30 discrete feature points can be combined into one A collection of 270 discrete feature point spatial coordinates that are non-collinear: j=1,2,...,(9×30);

即:当靶标平面K的倾角姿态先后改变N=9次,并把激光器的第二个激光平面b对应在靶标平面K的每一次姿态改变后投影所生成的激光光条(b-1)、(b-2)……(b-N)上的采样点数目n均设为30时,可获得针对第二个激光平面b且包含有270个离散特征点的新集合S;That is: when the inclination attitude of the target plane K changes N=9 times successively, and the second laser plane b of the laser corresponds to the laser light bar (b-1) generated by projection after each attitude change of the target plane K, (b-2)...(b-N) When the number of sampling points n is set to 30, a new set S containing 270 discrete feature points for the second laser plane b can be obtained;

采用与步骤三完全相同的方法,还可以获取并针对三线激光器中第三个激光平面c的、由共计九组离散特征点统一合并成为一个针对第三个激光平面c且包含有270个非共线的离散特征点的集合k=1,2...,(9×30)……(3);Using exactly the same method as Step 3, it is also possible to obtain and merge a total of nine sets of discrete feature points for the third laser plane c in the three-line laser into a single set of 270 non-common feature points for the third laser plane c. A collection of discrete feature points of a line k=1,2...,(9×30)...(3);

式(3)中k=1,2,...,N×n,N×n表示在步骤3.1至步骤3.3中共计九次在激光光条(c-1)、(c-2)……(c-N)上采样的离散特征点的总数,坐标值(x,y,z)各自的上角标(c)均表示该离散特征点隶属于第一个激光平面(c);N表示靶标平面倾角的改变总次数;即:当靶标平面K的倾角姿态先后改变N=9次,并把激光器的第三个激光平面c对应在靶标平面K的每一次姿态改变后投影所生成的激光光条(c-1)、(c-2)……(c-N)上的采样点数目n均设为30时,可获得针对第三个激光平面c且包含有270个离散特征点的新集合T;In the formula (3), k=1, 2,..., N×n, N×n means that in step 3.1 to step 3.3, a total of nine times in the laser light bar (c-1), (c-2)... (c-N) The total number of discrete feature points upsampled, and the superscripts (c) of the coordinate values (x, y, z) indicate that the discrete feature points belong to the first laser plane (c); N indicates the target plane The total number of changes in the inclination angle; that is: when the inclination attitude of the target plane K changes N=9 times successively, and the third laser plane c of the laser corresponds to the laser light bar generated by projection after each attitude change of the target plane K When the number n of sampling points on (c-1), (c-2)...(c-N) is set to 30, a new set T containing 270 discrete feature points for the third laser plane c can be obtained;

步骤五:根据多个空间平面方程在三维空间坐标系下的数学方程,定义一个表示三个空间平面均相交于同一交线的数学方程组表达式:Step 5: According to the mathematical equations of multiple space plane equations in the three-dimensional space coordinate system, define a mathematical equation expression that indicates that the three space planes all intersect on the same intersection line:

AA 11 xx ++ BB 11 ythe y ++ CC 11 zz ++ DD. 11 == 00 AA 22 xx ++ BB 22 ythe y ++ CC 22 zz ++ DD. 22 == 00 (( AA 11 ++ λAλA 22 )) xx ++ (( BB 11 ++ λBλB 22 )) ythe y ++ (( CC 11 ++ λCλ C 22 )) zz ++ (( DD. 11 ++ λDλD 22 )) == 00 .. .. .. .. .. .. (( 44 ))

式(4)中,(x,y,z)表示满足方程组的三个空间平面上的一组离散特征点的空间坐标值;In formula (4), (x, y, z) represent the spatial coordinate values of a group of discrete feature points on the three spatial planes satisfying the equation system;

待求解的多项式系数(A1,B1,C1,D1,A2,B2,C2,D2,λ)则共同定义了表示满足方程组(4)的三个空间平面各自的空间姿态系数;The polynomial coefficients to be solved (A 1 , B 1 , C 1 , D 1 , A 2 , B 2 , C 2 , D 2 , λ) jointly define the respective Space attitude coefficient;

式(4)中的第一个方程式是由步骤三所述式(1)所拟合出的、三线激光器的第一个激光平面a的激光空间平面方程;The first equation in the formula (4) is the laser space plane equation of the first laser plane a of the three-line laser fitted by the formula (1) described in step 3;

式(4)中的第二个方程式是由步骤四所述式(2)所拟合出的、三线激光器的第二个激光平面b的激光空间平面方程;The second equation in the formula (4) is the laser space plane equation of the second laser plane b of the three-line laser fitted by the formula (2) described in step 4;

式(4)中的第三个方程式是由步骤四所述式(3)所拟合出的、三线激光器的第三个激光平面c的激光空间平面方程;The third equation in formula (4) is the laser space plane equation of the third laser plane c of the three-line laser fitted by formula (3) described in step 4;

式(4)中的第三个方程式同时表示第三个激光平面c严格通过式(4)中第一个激光平面a和第二个激光平面b的激光空间平面方程的交线;The third equation in formula (4) represents simultaneously that the third laser plane c strictly passes through the intersection line of the laser space plane equation of the first laser plane a and the second laser plane b in formula (4);

步骤六:同时利用由步骤三所获得的针对前述第一个激光平面a的一组非共线的离散特征点空间坐标集合i=1,...,(9×30)和由步骤四所获得的针对前述第二个激光平面b的一组非共线的离散特征点空间坐标集合j=1,...,(9×30)以及由步骤四所获得的针对前述第三个激光平面c的一组非共线的离散特征点空间坐标集合k=1,...,(9×30)共同作为拟合数据,将由步骤五所确定的表示三个空间平面均相交于同一交线的数学方程组表达式(4)作为拟合函数,并根据公知的最小二乘法建立统一的目标函数:Step 6: Simultaneously use a set of non-collinear discrete feature point space coordinate sets for the first laser plane a obtained in step 3 i=1,...,(9×30) and a set of non-collinear discrete feature point space coordinates set for the second laser plane b obtained in step 4 j=1,...,(9×30) and a set of non-collinear discrete feature point space coordinates obtained in step 4 for the aforementioned third laser plane c k=1,...,(9×30) are jointly used as the fitting data, and the expression (4) of the mathematical equation system that represents that the three spatial planes all intersect at the same intersection line determined by step 5 is used as the fitting function, and Establish a unified objective function according to the well-known least squares method:

MinMin (( ΔΔ )) == ΣΣ ii == 11 99 ×× 3030 (( AA 11 xx ii (( aa )) ++ BB 11 ythe y ii (( aa )) ++ CC 11 zz ii (( aa )) ++ DD. 11 )) 22 ++ ΣΣ jj == 11 99 ×× 3030 (( AA 22 xx jj (( bb )) ++ BB 22 ythe y jj (( bb )) ++ CC 22 zz jj (( bb )) ++ DD. 22 )) 22 ++ ΣΣ kk == 11 99 ×× 3030 (( (( AA 11 ++ λAλA 22 )) xx kk (( cc )) ++ (( BB 11 ++ λBλB 22 )) ythe y kk (( cc )) ++ (( CC 11 ++ λCλ C 22 )) zz kk (( cc )) ++ (( DD. 11 ++ λDλD 22 )) )) 22 .. .. .. .. .. .. (( 55 ))

步骤七:将步骤一所述三线激光器固有的出厂性能指标参数:邻近两个激光平面夹角的角度值参数α=11.7°作为已知的约束条件,对步骤六所确定的目标函数(5)中的三个激光平面的各自的空间姿态多项式系数(A1,B1,C1,D1,A2,B2,C2,D2,λ)做进一步的数学限定,从而得到包含有角度限定条件的约束表达式:Step 7: The inherent factory performance index parameter of the three-line laser described in step 1: the angle value parameter α=11.7° of the angle between two adjacent laser planes is used as a known constraint condition, and the objective function (5) determined in step 6 The respective spatial attitude polynomial coefficients (A 1 , B 1 , C 1 , D 1 , A 2 , B 2 , C 2 , D 2 , λ) of the three laser planes in , are further defined mathematically, so as to obtain the Constraint expression for angle qualification:

(( AA 11 ,, BB 11 ,, CC 11 )) (( AA 22 ,, BB 22 ,, CC 22 )) AA 11 22 ++ BB 11 22 ++ CC 11 22 AA 22 22 ++ BB 22 22 ++ CC 22 22 == coscos 22 αα (( AA 11 ,, BB 11 ,, CC 11 )) (( AA 11 ++ λAλA 22 ,, BB 11 ++ λBλB 22 ,, CC 11 ++ λCλ C 22 )) AA 11 22 ++ BB 11 22 ++ CC 11 22 (( AA 11 ++ λAλA 22 )) 22 ,, (( BB 11 ++ λBλB 22 )) 22 ,, (( CC 11 ++ λCλC 22 )) 22 == coscos αα (( AA 22 ,, BB 22 ,, CC 22 )) (( AA 11 ++ λAλA 22 ,, BB 11 ++ λBλB 22 ,, CC 11 ++ λCλ C 22 )) AA 22 22 ++ BB 22 22 ++ CC 22 22 (( AA 11 ++ λAλA 22 )) 22 ,, (( BB 11 ++ λBλB 22 )) 22 ,, (( CC 11 ++ λCλC 22 )) 22 == coscos αα .. .. .. .. .. .. (( 66 ))

步骤八:通过公知的Lenvenberg-Marquardt非线性优化算法对式(5)及其限定条件表达式(6)同时求解,从而解出(A1,B1,C1,D1,A2,B2,C2,D2,λ)的值,并完成利用一种能从同一个线光源发出邻近夹角均相同的三个激光平面,且其三个激光平面能在同一投影平面形成三个平行光条的三线激光器的固有特性,将三线激光器所发出的三个光平面的空间姿态方程均精确拟合于相机虚拟空间坐标系中的拟合标定过程。Step 8: Simultaneously solve formula (5) and its conditional expression (6) through the known Lenvenberg-Marquardt nonlinear optimization algorithm, so as to solve (A 1 , B 1 , C 1 , D 1 , A 2 , B 2 , C 2 , D 2 , λ), and complete the use of three laser planes that can emit three adjacent angles from the same line light source, and the three laser planes can form three laser planes on the same projection plane. The inherent characteristics of the three-line laser of the parallel light strips accurately fit the space attitude equations of the three light planes emitted by the three-line laser to the fitting and calibration process in the virtual space coordinate system of the camera.

通过对式(5)及其限定条件表达式(6)的同时求解,所获得的方程的解必然精确地、同时表达了如下含义:By simultaneously solving formula (5) and its limiting condition expression (6), the solution of the obtained equation must express the following meanings precisely and simultaneously:

第一:求得解之后的平面方程组所表示的三个已知平面,必然能够形成如图3或图6所示的a、b、c三条射线;其三条射线在同一靶标平面上的三条投影线段必然彼此平行;First: the three known planes represented by the plane equations after the solution must be able to form three rays a, b, and c as shown in Figure 3 or Figure 6; three rays on the same target plane The projected line segments must be parallel to each other;

第二:求得解之后的平面方程组所表示的三个已知平面,必然同时精确相交于同一交线L;Second: The three known planes represented by the plane equations after the solution must intersect precisely at the same intersection line L at the same time;

第三:求得解之后的平面方程组所表示的三个已知平面,其邻近两平面之间的夹角必然等于已知量α;Third: For the three known planes represented by the plane equations after the solution is obtained, the angle between two adjacent planes must be equal to the known quantity α;

由此可知,求得解之后的平面方程组所表示的三个已知平面必然是前述能从同一个线光源发出邻近夹角均相同的三个激光平面且其三个激光平面能在同一投影平面形成三个平行光条的三线激光器的理想数理模型,即实现了将真实世界中的三线激光器投射平面的一系列物理特征均同时精确移植到虚拟的相机坐标系的数学模型下。It can be seen from this that the three known planes represented by the plane equations after the solution must be the aforementioned three laser planes with the same adjacent angles that can be emitted from the same line light source, and the three laser planes can be projected on the same plane. The ideal mathematical model of a three-line laser that forms three parallel light strips on a plane, that is, a series of physical characteristics of the three-line laser projection plane in the real world are simultaneously and accurately transplanted to the mathematical model of the virtual camera coordinate system.

本发明的光平面方程拟合定位标定方法直接按照本发明人在学术期刊Public Library of Science上公开的求解激光光条中心点像素坐标(xp,yp)对应在相机坐标系下的坐标(Xc,Yc,Zc)的更精确方法对激光平面在相机照片中的投影光条图案的中心点像素坐标进行提取,所获得的光条中心是连续光条图案上的每一个像素点的中心点,通过该成熟方法所能取得的离散特征点的数据量和精度均远远高于采用固有网格线条数量极为有限的方向性栅格的方法所获得的离散特征点的数据量和坐标精确度,从而从数据来源的角度为进一步修正和减小系统误差提供了可靠保障。The optical plane equation fitting positioning calibration method of the present invention is directly according to the inventor's disclosure on the academic journal Public Library of Science to solve the pixel coordinates (x p , y p ) of the center point of the laser light bar corresponding to the coordinates in the camera coordinate system ( The more accurate method of X c , Y c , Z c ) extracts the pixel coordinates of the center point of the projected light strip pattern of the laser plane in the camera photo, and the obtained light strip center is each pixel point on the continuous light strip pattern The data volume and accuracy of the discrete feature points obtained by this mature method are much higher than those obtained by using the directional grid method with a very limited number of inherent grid lines. Coordinate accuracy, thus providing a reliable guarantee for further correction and reduction of system errors from the perspective of data sources.

另一方面,本发明充分利用了一种能从同一个线光源发出邻近夹角均相同的三个激光平面且其三个激光平面能在同一投影平面形成三个平行光条的三线激光器的固有特性:其高精度的邻近激光平面夹角是其出厂指标给出的已知量,而该激光器所发出的三个激光平面又是真实地从同一个精确的线光源所投射出的。On the other hand, the present invention makes full use of the inherent characteristics of a three-line laser that can emit three adjacent laser planes with the same included angle from the same line light source, and whose three laser planes can form three parallel light bars on the same projection plane. Features: Its high-precision adjacent laser plane angle is a known quantity given by its factory index, and the three laser planes emitted by the laser are actually projected from the same precise line light source.

最重要的是,本发明的标定方法特别提出了将三个激光平面的邻近夹角量已知、三个激光平面均相交于同一交线、三个激光平面的投影光条均平行这三个真实的固有特性同时作为所述特殊三线激光器投影特征的数理模型的约束条件,由此才能获得能够整体反映这三个关键特征的目标函数及其约束条件,并为该目标函数的求解带来可能性。最终给出了一整套将真实世界中的三线激光器投射平面的一系列物理特征均同时精确移植到虚拟的相机坐标系的数学模型下的可行方法。The most important thing is that the calibration method of the present invention specifically proposes that the adjacent angles of the three laser planes are known, the three laser planes all intersect on the same intersection line, and the projection light bars of the three laser planes are all parallel. The real inherent characteristics are also used as the constraints of the mathematical model of the projection characteristics of the special three-line laser, so that the objective function and its constraints that can reflect these three key features as a whole can be obtained, and it is possible to solve the objective function sex. Finally, a set of feasible methods are given to accurately transplant a series of physical characteristics of the three-line laser projection plane in the real world to the mathematical model of the virtual camera coordinate system at the same time.

此外,本发明还克服了采用旧有用于求解和确定单一的线结构激光空间平面方程的方法直接向同一相机虚拟坐标系下拼合多个激光平面方程时,其粗略地在同一相机虚拟坐标系下拟合多个光平面的方式远远不能满足视觉测量对激光空间平面方程坐标定位的精度需求的问题,并提高了多线结构光拟合标定方法的误差,使得标定精度获得较大提高。In addition, the present invention also overcomes the problem that when multiple laser plane equations are directly combined in the same camera virtual coordinate system using the old method for solving and determining a single line-structured laser space plane equation, it is roughly in the same camera virtual coordinate system. The method of fitting multiple light planes is far from meeting the accuracy requirements of visual measurement for coordinate positioning of the laser space plane equation, and increases the error of the multi-line structured light fitting calibration method, which greatly improves the calibration accuracy.

Claims (1)

1.基于三线激光器固有特性的光平面方程拟合定位标定方法,其特征在于,该方法包括如下步骤:1. The optical plane equation fitting positioning calibration method based on the inherent characteristics of the three-line laser is characterized in that the method comprises the following steps: 步骤一:选用一种能从同一个线光源发出邻近夹角均相同的三个激光平面,且其三个激光平面能在同一投影平面形成三个平行光条的三线激光器,并从该三线激光器固有的出厂性能指标参数中获取其邻近两个激光平面夹角的角度值参数α;Step 1: Select a three-line laser that can emit three laser planes with the same adjacent angles from the same line light source, and whose three laser planes can form three parallel light stripes on the same projection plane, and use the three-line laser The angle value parameter α of the angle between two adjacent laser planes is obtained from the inherent factory performance index parameters; 步骤二:按照相机内部参数标定方法A完成对相机内部参数的标定;Step 2: Complete the calibration of the internal parameters of the camera according to the calibration method A of the internal parameters of the camera; 步骤三:获取针对三线激光器中第一个激光平面(a)的N组离散特征点空间坐标值的集合R,其具体包括如下子步骤:Step 3: Obtain a set R of space coordinate values of N groups of discrete feature points for the first laser plane (a) in the three-line laser, which specifically includes the following sub-steps: 步骤3.1:按照离散特征点空间坐标提取方法B对步骤一所述三线激光器的第一个激光平面(a)在标靶平面(K)上的激光光条(a-1)进行所需的一组离散特征点空间坐标(x,y,z)的采样和提取,从而获得针对前述第一个激光平面(a)在初始姿态下的标靶平面(K)上投影所形成的激光光条(a-1)采样所获得的第一组离散特征点空间坐标:其中i=1,2,...,n,n表示在激光光条(a-1)上采样的离散特征点的数目,坐标值(x,y,z)各自的上角标(a)均表示该离散特征点隶属于第一个激光平面(a);Step 3.1: According to the discrete feature point spatial coordinate extraction method B, perform the required first laser light strip (a-1) on the target plane (K) of the first laser plane (a) of the three-line laser described in step 1. Sampling and extraction of the spatial coordinates (x, y, z) of a group of discrete feature points, so as to obtain the laser light bar ( a-1) The spatial coordinates of the first set of discrete feature points obtained by sampling: Where i=1,2,...,n, n represents the number of discrete feature points sampled on the laser light strip (a-1), and the respective superscripts (a) of the coordinate values (x, y, z) Both indicate that the discrete feature point belongs to the first laser plane (a); 步骤3.2:改变激光投影标靶平面(K)的倾角,并重复步骤3.1的过程,从而获得针对前述第一个激光平面(a)在新姿态下的标靶平面(K’)上投影所形成的激光光条(a-2)采样所获得的第二组离散特征点空间坐标:其中i=(n+1),(n+2),...,2n,n表示在激光光条(a-2)上采样的离散特征点的数目,坐标值(x,y,z)各自的上角标(a)均表示该离散特征点隶属于第一个激光平面(a);Step 3.2: Change the inclination angle of the laser projection target plane (K), and repeat the process of step 3.1 to obtain the projection of the first laser plane (a) on the target plane (K') in the new attitude. The second set of discrete feature point space coordinates obtained by sampling the laser light strip (a-2): Where i=(n+1),(n+2),...,2n, n represents the number of discrete feature points sampled on the laser light strip (a-2), coordinate value (x, y, z) Each superscript (a) indicates that the discrete feature point belongs to the first laser plane (a); 步骤3.3:通过N(N≥3,N是自然数)次改变激光投影靶标平面的倾角并重复步骤3.2的过程,直至获得针对前述第一个激光平面(a)在标靶平面(K)的第N个新姿态上投影所形成的激光光条(a-N)采样所获得的第N组离散特征点空间坐标值:其中i=((N-1)×n+1),((N-1)×n+2)...,N×n,n表示在激光光条(a-N)上采样的离散特征点的数目,坐标值(x,y,z)各自的上角标(a)均表示该离散特征点隶属于第一个激光平面(a);Step 3.3: Change the inclination of the laser projection target plane N times (N≥3, N is a natural number) and repeat the process of step 3.2 until the first laser plane (a) for the aforementioned first laser plane (a) on the target plane (K) is obtained. The spatial coordinate values of the Nth group of discrete feature points obtained by sampling the laser light bar (aN) formed by projection on N new attitudes: Where i=((N-1)×n+1),((N-1)×n+2)...,N×n, n represents the number of discrete feature points sampled on the laser light strip (aN) The superscript (a) of each coordinate value (x, y, z) indicates that the discrete feature point belongs to the first laser plane (a); 步骤3.4:将步骤3.1至步骤3.3分别获得的共计N组离散特征点统一合并成为一个非共线的离散特征点的集合R:Step 3.4: Merge a total of N sets of discrete feature points obtained from step 3.1 to step 3.3 into a set R of non-collinear discrete feature points: RR == (( xx ii (( aa )) ,, ythe y ii (( aa )) ,, zz ii (( aa )) )) ,, .. .. .. .. .. .. (( 11 )) ;; 式(1)中i=1,2,...,N×n,N×n表示在步骤3.1至步骤3.3中共计N次在激光光条(a-1)、(a-2)……(a-N)上采样的离散特征点的总数,坐标值(x,y,z)各自的上角标(a)均表示该离散特征点隶属于第一个激光平面(a);N表示靶标平面倾角的改变总次数;In the formula (1), i=1, 2,..., N×n, N×n means that a total of N times in the laser light strip (a-1), (a-2)... (a-N) The total number of discrete feature points upsampled, and the superscripts (a) of the coordinate values (x, y, z) indicate that the discrete feature points belong to the first laser plane (a); N indicates the target plane The total number of changes in inclination; 步骤四:采用与步骤三完全相同的方法,分别获取针对三线激光器中第二个激光平面(b)的、由共计N组离散特征点统一合并成为一个非共线的离散特征点的集合以及针对三线激光器中第三个激光平面(c)的、由共计N组离散特征点统一合并成为一个非共线的离散特征点的集合 T = ( x k ( c ) , y k ( c ) , z k ( c ) ) . . . . . . ( 3 ) ; Step 4: Using exactly the same method as Step 3, respectively obtain a set of discrete feature points for the second laser plane (b) in the three-line laser, which is unified and merged into a non-collinear discrete feature point by a total of N groups And for the third laser plane (c) in the three-line laser, a total of N sets of discrete feature points are unified into a set of non-collinear discrete feature points T = ( x k ( c ) , the y k ( c ) , z k ( c ) ) . . . . . . ( 3 ) ; 式(2)中j=1,2,...,N×n,N×n表示在步骤3.1至步骤3.3中共计N次在激光光条(b-1)、(b-2)……(b-N)上采样的离散特征点的总数,坐标值(x,y,z)各自的上角标(b)均表示该离散特征点隶属于第一个激光平面(b);N表示靶标平面倾角的改变总次数;In the formula (2), j=1, 2,..., N×n, N×n means that in step 3.1 to step 3.3, a total of N times in the laser light strip (b-1), (b-2)... (b-N) The total number of discrete feature points upsampled, and the superscripts (b) of the coordinate values (x, y, z) indicate that the discrete feature points belong to the first laser plane (b); N indicates the target plane The total number of changes in inclination; 式(3)中k=1,2,...,N×n,N×n表示在步骤3.1至步骤3.3中共计N次在激光光条(c-1)、(c-2)……(c-N)上采样的离散特征点的总数,坐标值(x,y,z)各自的上角标(c)均表示该离散特征点隶属于第一个激光平面(c);N表示靶标平面倾角的改变总次数;In the formula (3), k=1, 2,..., N×n, N×n means that in step 3.1 to step 3.3, a total of N times in the laser light bar (c-1), (c-2)... (c-N) The total number of discrete feature points upsampled, and the superscripts (c) of the coordinate values (x, y, z) indicate that the discrete feature points belong to the first laser plane (c); N indicates the target plane The total number of changes in inclination; 步骤五:根据多个空间平面方程在三维空间坐标系下的数学方程,定义一个表示三个空间平面均相交于同一交线的数学方程组表达式:Step 5: According to the mathematical equations of multiple space plane equations in the three-dimensional space coordinate system, define a mathematical equation expression that indicates that the three space planes all intersect on the same intersection line: AA 11 xx ++ BB 11 ythe y ++ CC 11 zz ++ DD. 11 == 00 AA 22 xx ++ BB 22 ythe y ++ CC 22 zz ++ DD. 22 == 00 (( AA 11 ++ λλ AA 22 )) xx ++ (( BB 11 ++ λλ BB 22 )) ythe y ++ (( CC 11 ++ λλ CC 22 )) zz ++ (( DD. 11 ++ λλ DD. 22 )) == 00 .. .. .. .. .. .. (( 44 )) 式(4)中,(x,y,z)表示满足方程组的三个空间平面上的一组离散特征点的空间坐标值;In formula (4), (x, y, z) represent the spatial coordinate values of a group of discrete feature points on the three spatial planes satisfying the equation system; 待求解的多项式系数(A1,B1,C1,D1,A2,B2,C2,D2,λ)则共同定义了表示满足方程组(4)的三个空间平面各自的空间姿态系数;The polynomial coefficients to be solved (A 1 , B 1 , C 1 , D 1 , A 2 , B 2 , C 2 , D 2 , λ) jointly define the respective Space attitude coefficient; 式(4)中的第一个方程式是由步骤三所述式(1)所拟合出的、三线激光器的第一个激光平面(a)的激光空间平面方程;The first equation in the formula (4) is the laser space plane equation of the first laser plane (a) of the three-line laser fitted by the formula (1) described in step 3; 式(4)中的第二个方程式是由步骤四所述式(2)所拟合出的、三线激光器的第二个激光平面(b)的激光空间平面方程;The second equation in the formula (4) is the laser space plane equation of the second laser plane (b) of the three-line laser fitted by the formula (2) described in step 4; 式(4)中的第三个方程式是由步骤四所述式(3)所拟合出的、三线激光器的第三个激光平面(c)的激光空间平面方程;The third equation in the formula (4) is the laser space plane equation of the third laser plane (c) of the three-line laser fitted by the formula (3) described in step four; 式(4)中的第三个方程式同时表示第三个激光平面(c)严格通过式(4)中第一个激光平面(a)和第二个激光平面(b)的激光空间平面方程的交线;The third equation in formula (4) also expresses that the third laser plane (c) strictly passes through the laser space plane equations of the first laser plane (a) and the second laser plane (b) in formula (4). intersection line; 步骤六:利用由步骤三所获得的针对前述第一个激光平面(a)的一组非共线离散特征点空间坐标的集合i=1,2,...,(N×n);Step 6: Use the set of space coordinates of a set of non-collinear discrete feature points for the aforementioned first laser plane (a) obtained in step 3 i=1,2,...,(N×n); 由步骤四所获得的针对前述第二个激光平面(b)的一组非共线离散特征点空间坐标的集合j=1,2,...,(N×n);A set of space coordinates of a group of non-collinear discrete feature points for the aforementioned second laser plane (b) obtained in step 4 j=1,2,...,(N×n); 以及由步骤四所获得的针对前述第三个激光平面(c)的一组非共线离散特征点空间坐标的集合k=1,2,...,(N×n)共同作为拟合数据,将由步骤五所确定的表示三个空间平面均相交于同一交线的数学方程组表达式(4)作为拟合函数,并根据公知的最小二乘法建立统一的目标函数:And a set of space coordinates of a group of non-collinear discrete feature points for the aforementioned third laser plane (c) obtained in step 4 k=1,2,...,(N×n) are jointly used as the fitting data, and the expression (4) of the mathematical equation set representing that the three spatial planes all intersect at the same intersection line determined by step 5 is used as the fitting function , and establish a unified objective function according to the well-known least squares method: MinMin (( ΔΔ )) == ΣΣ ii == 11 NN ×× nno (( AA 11 xx ii (( aa )) ++ BB 11 ythe y ii (( aa )) ++ CC 11 zz ii (( aa )) ++ DD. 11 )) 22 ++ ΣΣ jj == 11 NN ×× nno (( AA 22 xx jj (( bb )) ++ BB 22 ythe y jj (( bb )) ++ CC 22 zz jj (( bb )) ++ DD. 22 )) 22 ++ ΣΣ kk == 11 NN ×× nno (( (( AA 11 ++ λλ AA 22 )) xx kk (( cc )) ++ (( BB 11 ++ λλ BB 22 )) ythe y kk (( cc )) ++ (( CC 11 ++ λλ CC 22 )) zz kk (( cc )) ++ (( DD. 11 ++ λλ DD. 22 )) )) 22 .. .. .. .. .. .. (( 55 )) 步骤七:将步骤一所述三线激光器固有的出厂性能指标参数:邻近两个激光平面夹角的角度值参数α作为已知的约束条件,对步骤六所确定的目标函数(5)中的三个激光平面的各自的空间姿态多项式系数(A1,B1,C1,D1,A2,B2,C2,D2,λ)做进一步的数学限定,从而得到包含有角度限定条件的约束表达式:Step 7: Taking the inherent factory performance index parameters of the three-line laser described in step 1: the angle value parameter α of the angle between two adjacent laser planes as a known constraint condition, for the three in the objective function (5) determined in step 6 The respective spatial attitude polynomial coefficients (A 1 , B 1 , C 1 , D 1 , A 2 , B 2 , C 2 , D 2 , λ) of each laser plane are further mathematically limited, so as to obtain the angle limit condition Constraint expression for : (( AA 11 ,, BB 11 ,, CC 11 )) (( AA 22 ,, BB 22 ,, CC 22 )) AA 11 22 ++ BB 11 22 ++ CC 11 22 AA 22 22 ++ BB 22 22 ++ CC 22 22 == coscos 22 αα (( AA 11 ,, BB 11 ,, CC 11 )) (( AA 11 ++ λλ AA 22 ,, BB 11 ++ λλ BB 22 ,, CC 11 ++ λλ CC 22 )) AA 11 22 ++ BB 11 22 ++ CC 11 22 (( AA 11 ++ λλ AA 22 )) 22 ,, (( BB 11 ++ λλ BB 22 )) 22 ,, (( CC 11 ++ λλ CC 22 )) 22 == coscos αα (( AA 22 ,, BB 22 ,, CC 22 )) (( AA 11 ++ λλ AA 22 ,, BB 11 ++ λλ BB 22 ,, CC 11 ++ λλ CC 22 )) AA 22 22 ++ BB 22 22 ++ CC 22 22 (( AA 11 ++ λλ AA 22 )) 22 ,, (( BB 11 ++ λλ BB 22 )) 22 ,, (( CC 11 ++ λλ CC 22 )) 22 == coscos αα .. .. .. .. .. .. (( 66 )) 步骤八:通过公知的Lenvenberg-Marquardt非线性优化算法对式(5)及其限定条件表达式(6)同时求解,从而解出(A1,B1,C1,D1,A2,B2,C2,D2,λ)的值,并完成利用一种能从同一个线光源发出邻近夹角均相同的三个激光平面,且其三个激光平面能在同一投影平面形成三个平行光条的三线激光器的固有特性,将三线激光器所发出的三个光平面的空间姿态方程均精确拟合于相机虚拟空间坐标系中的拟合标定过程。Step 8: Simultaneously solve formula (5) and its conditional expression (6) through the known Lenvenberg-Marquardt nonlinear optimization algorithm, so as to solve (A 1 , B 1 , C 1 , D 1 , A 2 , B 2 , C 2 , D 2 , λ), and complete the use of three laser planes that can emit three adjacent angles from the same line light source, and the three laser planes can form three laser planes on the same projection plane. The inherent characteristics of the three-line laser of the parallel light strips accurately fit the space attitude equations of the three light planes emitted by the three-line laser to the fitting and calibration process in the virtual space coordinate system of the camera.
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