CN103162622A - Monocular vision system, portable ball target used by monocular vision system and measuring method of monocular vision system - Google Patents

Abstract

Translated fromChinese

本发明提供一种单目视觉系统及其使用的便携式球靶标及其测量方法，球靶标由球体、连接块和一系列不同形状和长度的探针组成，探针由接长杆和测头组成，连接块用于支撑每个球体以及连接探针，球形连接块表面打有均匀的14个螺纹孔，与接长杆和球之间采用螺杆连接。设计不同的连接杆以适应不同的测量场合。球体部分由三个以上非共面圆球组成，单个相机拍摄一幅图像即可快速标定摄像机内部参数、确定球心位置，从而得到待测点的三维坐标，为单目测量系统下的深度信息获取提供了一种可行途径。相机移动后，根据球靶标的球体部分单幅图像即可快速标定相机移动外参，实现空间数据拼接，有效扩大测量范围和测量速度。

The invention provides a monocular vision system and its portable ball target and its measurement method. The ball target is composed of a sphere, a connecting block and a series of probes of different shapes and lengths. The probe is composed of an extension rod and a measuring head. , The connection block is used to support each sphere and connect the probe. The surface of the spherical connection block is uniformly punched with 14 threaded holes, and the connection between the extension rod and the ball is connected by a screw. Different connecting rods are designed to suit different measurement occasions. The sphere part is composed of more than three non-coplanar spheres. A single camera can quickly calibrate the internal parameters of the camera and determine the position of the sphere center by taking an image, so as to obtain the three-dimensional coordinates of the point to be measured, which is the depth information under the monocular measurement system. Acquisition provides a viable path. After the camera moves, the external parameters of the camera movement can be quickly calibrated according to a single image of the spherical part of the ball target, realizing spatial data splicing, and effectively expanding the measurement range and measurement speed.

Description

Translated fromChinese

单目视觉系统及其使用的便携式球靶标及其测量方法Monocular vision system and portable ball target used therefor and its measuring method

【技术领域】【Technical field】

本发明属于视觉测量技术领域，涉及一种可用于单目视觉测量系统快速标定、测量和数据拼接的便携式球靶标。The invention belongs to the technical field of visual measurement and relates to a portable ball target that can be used for rapid calibration, measurement and data splicing of a monocular visual measurement system.

【背景技术】【Background technique】

随着工件外形检测需求的增多，视觉测量技术得到越来越多的应用。较之需要多台摄像机的立体视觉系统，单摄像机无需摄像机同步设备和保持摄像机相对位置的机械装置，因此使用方便、价格低廉、便于实现。然而单纯利用单目视觉系统进行测量时无法恢复三维物体的深度信息，往往需要借助线激光等额外条件构成三角约束、约束测量物体在特定的位置成像或者使用标记点或标定面约束待测量面等方法来确定三维深度信息，测量过程十分复杂，应用受限。同时标定相机内、外部参数的过程费时费力，不利于工件快速测量。另外，单目视觉系统测量范围有限，在测量大型工件时往往只能测量局部信息，采用拼接靶标进行三维数据拼接成为扩大测量范围的有效途径。目前常用的拼接靶标主要是平面靶标，存在相机移动视角过大时畸变过大甚至观测不到的不足。With the increasing demand for workpiece shape inspection, visual measurement technology has been applied more and more. Compared with a stereo vision system that requires multiple cameras, a single camera does not require a camera synchronization device and a mechanical device for maintaining the relative positions of the cameras, so it is easy to use, low in price, and easy to implement. However, the depth information of a three-dimensional object cannot be recovered simply by using a monocular vision system for measurement. It is often necessary to use additional conditions such as line lasers to form a triangle constraint, constrain the measurement object to be imaged at a specific position, or use marker points or calibration surfaces to constrain the surface to be measured, etc. method to determine the three-dimensional depth information, the measurement process is very complicated, and the application is limited. At the same time, the process of calibrating the internal and external parameters of the camera is time-consuming and laborious, which is not conducive to the rapid measurement of the workpiece. In addition, the monocular vision system has a limited measurement range. When measuring large workpieces, it can only measure local information. Using stitching targets for 3D data stitching has become an effective way to expand the measurement range. At present, the commonly used splicing targets are mainly planar targets, which have the disadvantage that the distortion is too large or even invisible when the camera movement angle is too large.

【发明内容】【Content of invention】

针对上述现有单目测量系统的缺陷或不足，本发明的目的在于提供一种更加灵活简便、且视角不受靶标单面约束的单目视觉系统及其使用的便携式球靶标及其测量方法，实现单目测量系统快速标定、测量和数据拼接。由于球具有外轮廓连续性好等优点，可以实现360度空间视场无视角限制、便捷标定，消除了平面靶标在摄像机移动视角太大时畸变过大甚至观测不到的不足。本发明采用球体作为拼接靶标和标定靶标，将标定过程和拼接过程使用球靶标同步完成。Aiming at the defects or deficiencies of the existing monocular measurement system mentioned above, the object of the present invention is to provide a more flexible and simple monocular vision system whose viewing angle is not restricted by one side of the target and the portable ball target and its measurement method used therefor. Realize rapid calibration, measurement and data stitching of the monocular measurement system. Because the ball has the advantages of good continuity of the outer contour, it can realize 360-degree spatial field of view without viewing angle limitation, convenient calibration, and eliminates the problem that the plane target is too distorted or even unobservable when the camera moves too much. The present invention adopts spheres as splicing targets and calibration targets, and the calibration process and splicing process are completed synchronously by using the spherical targets.

为了实现上述目的，本发明采用如下技术方案：In order to achieve the above object, the present invention adopts the following technical solutions:

一种用于单目视觉系统快速标定和测量的便携式球靶标，主要由球体、连接块和一系列不同形状和长度的探针组成；所述连接块用于支撑每个球体以及连接探针，所述探针由连接长杆和测头组成，设计不同的连接杆以适应不同的测量场合；所述球体部分由三个以上非共面圆球组成，所述球体通过螺杆与连接块连接。A portable ball target for rapid calibration and measurement of a monocular vision system, mainly composed of a sphere, a connecting block and a series of probes of different shapes and lengths; the connecting block is used to support each sphere and connect the probes, The probe is composed of a connecting long rod and a measuring head, and different connecting rods are designed to adapt to different measurement occasions; the sphere part is composed of more than three non-coplanar spheres, and the spheres are connected to the connecting block through a screw.

作为本发明的优选实施例，所述连接块为球体形状。As a preferred embodiment of the present invention, the connecting block is in the shape of a sphere.

一种基于所述的便携式球靶标的单目视觉系统，所述单目视觉系统包括便携式球靶标及摄像机，所述摄像机能看见完整的球靶标球体部分。A monocular vision system based on the portable ball target, the monocular vision system includes a portable ball target and a camera, and the camera can see the complete spherical part of the ball target.

一种基于所述的单目视觉系统的测量方法，（1）由单目视觉系统拍摄一幅球靶标图像，根据摄像机透视成像模型和球体投影模型基于绝对二次曲线成像几何标定摄像机内部参数K，所述摄像机内部参数K包括摄像机光心(u₀,v₀)，焦距f以及倾斜因子s；（2）利用标定的摄像机内部参数和球透视成像几何模型确定各个球心在摄像机坐标系下的三维坐标；（3）求取球靶标中每个圆球球心到测头的距离；（4）根据球靶标圆球和测头的位置关系确定测头的位置，即待测点的三维坐标。A measurement method based on the monocular vision system, (1) A spherical target image is captured by the monocular vision system, and the internal parameter K of the camera is calibrated based on the absolute conic imaging geometry according to the camera perspective imaging model and the spherical projection model , the camera internal parameters K include camera optical center (u₀ , v₀ ), focal length f and tilt factor s; (2) use the calibrated camera internal parameters and spherical perspective imaging geometric model to determine the position of each spherical center in the camera coordinate system (3) Calculate the distance from the center of each sphere in the ball target to the probe; (4) Determine the position of the probe according to the positional relationship between the ball of the ball target and the probe, that is, the three-dimensional position of the point to be measured coordinate.

作为本发明的优选实施例，上述步骤（1）的具体方法包括以下步骤：As a preferred embodiment of the present invention, the specific method of the above step (1) includes the following steps:

（5.1）采用图像处理方法和边缘检测算子提取每个圆球在摄像机内所成的椭圆轮廓，然后采用最小二乘法拟合对应椭圆轮廓的曲线方程C_i，其中，i为圆球的个数；(5.1) Use image processing methods and edge detection operators to extract the elliptical contour formed by each sphere in the camera, and then use the least squares method to fit the curve equation C_i corresponding to the elliptical contour, where i is the number of spheres number;

（5.2）根据球体透视投影成像模型，摄像机坐标系O_cX_cY_cZ_c与第i个圆球的球坐标系O_siX_siY_siZ_si之间的单应性矩阵为：H_i=KR_idiag{1,1,Λ_i}，其中，Λ_i=Z_i0/r_i，Z_i0为第i个圆球的球心到摄像机光心之间的距离，r_i为第i个圆球的半径，圆球在摄像机内成像椭圆的二次曲线方程C_i在对偶空间中表示形式为：(5.2) According to the spherical perspective projection imaging model, the homography matrix between the camera coordinate system O_c X_c Y_c Z_c and the spherical coordinate system O_si X_si Y_si Z_si of the i-th sphere is: H_i =KR_i diag{1,1,Λ_i }, where, Λ_i =Z_i0 /r_i , Z_i0 is the distance from the center of the i-th sphere to the optical center of the camera, r_i is the i-th The radius of the sphere, the quadratic curve equation C_i of the ellipse imaged by the sphere in the camera is expressed in the dual space as:

$C_i^{*}=H_i{C}_{\mathrm{ui}}^{*}{H}_i^T=K{R}_i\mathrm{diag}(\mathrm{1,1}-{\mathrm{\Λ}}_i^2)R_i^T{K}^T={\mathrm{KK}}^T-o_i{o}_i^T,$公式（5.1）$C_i^{*}=h_i{C}_{\mathrm{ui}}^{*}{h}_i^T=K{R}_i\mathrm{diag}(\mathrm{1,1}-{\mathrm{\Λ}}_i^2)R_i^T{K}^T={\mathrm{KK}}^T-o_i{o}_i^T,$ Formula (5.1)

其中，

是第i个圆球的球心成像坐标，r_3i为相应的旋转矩阵R_i的第3列，R_i为旋转矩阵，K为摄像机内部参数形成的矩阵。in,

is the imaging coordinate of the center of the i-th sphere, r_3i is the third column of the corresponding rotation matrix R_i , R_i is the rotation matrix, and K is the matrix formed by the internal parameters of the camera.

作为本发明的优选实施例，所述步骤（5.2）中，求解摄像机内部参数K时，引入绝对二次曲线，该绝对二次曲线在单应性矩阵下的图像为w=(KK^T)^-1，在对偶空间中表示为：w^*=KK^T；球靶标中的每两个圆球的成像椭圆曲线方程之间的单应性矩阵为

A,B=1,2,3且A≠B，其中，

为圆球A的成像椭圆曲线方程C_A在对偶空间中的表示形式，C_B为圆球B的成像椭圆无线方程；根据视图几何理论，每一对成像椭圆的单应性矩阵均包括一个穿过相应的椭圆对的特征向量，称为单应性矩阵的极线，表示为l_AB，其中，A,B=1,2,3且A≠B，每个特征向量对应的特征值称为极点，表示为v_AB，A,B=1,2,3且A≠B.l_AB、v_AB以及w满足[l_AB]×wv_AB=0，根据奇异值分解得到w，进而根据公式w^*=KK^T正交分解即得摄像机内部参数K。As a preferred embodiment of the present invention, in the step (5.2), when solving the internal parameter K of the camera, an absolute conic curve is introduced, and the image of the absolute conic curve under the homography matrix is w=(KK^T )^{− 1} , expressed in the dual space as: w^* =KK^T ; the homography matrix between the imaging elliptic curve equations of every two spheres in the spherical target is

A, B=1,2,3 and A≠B, where,

is the expression form of the imaging elliptic curve equation C_A of the sphere A in the dual space, and C_B is the wireless equation of the imaging ellipse of the sphere B; according to the theory of view geometry, the homography matrix of each pair of imaging ellipses includes a wear The eigenvector passing through the corresponding ellipse pair is called the epipolar line of the homography matrix, expressed as l_AB , where A, B=1, 2, 3 and A≠B, and the eigenvalue corresponding to each eigenvector is called Pole, expressed as v_AB , A, B=1,2,3 and A≠Bl_AB , v_AB and w satisfy [l_AB ]×wv_AB =0, obtain w according to singular value decomposition, and then according to the formula w^* = The KK^T is orthogonally decomposed to obtain the internal parameter K of the camera.

作为本发明的优选实施例，步骤（2）的具体方法为：对步骤（5.2）中的公式（5.1）进行变形得到：${\mathrm{\β}}_i{K}^{-1}{C}_i^{*}{K}^{-T}=R_i\mathrm{diag}(\mathrm{1,1},-{\mathrm{\Λ}}_i^2)R_i^T,$其中，β_i为第i个圆球的成像比例因子；将等式左边的表达式通过奇异值分解得到与等式右边一致的形式，从而，得到旋转矩阵R_i和Λ_i，得到各个球心的三维坐标。As a preferred embodiment of the present invention, the specific method of step (2) is: transform the formula (5.1) in step (5.2) to obtain:${\mathrm{\β}}_i{K}^{-1}{C}_i^{*}{K}^{-T}=R_i\mathrm{diag}(\mathrm{1,1},-{\mathrm{\Λ}}_i^2)R_i^T,$ Among them, β_i is the imaging scale factor of the i-th sphere; the expression on the left side of the equation is decomposed into a form consistent with the right side of the equation through singular value decomposition, thus, the rotation matrices R_i and Λ_i are obtained, and the center of each sphere is obtained three-dimensional coordinates.

作为本发明的优选实施例，所述待测点的位置坐标(x,y,z)根据以下计算：As a preferred embodiment of the present invention, the position coordinates (x, y, z) of the point to be measured are calculated according to the following:

(x_i-x)²+(y_i-y)²+(z_i-z)²=(d_i)²，     公式（8.1）(x_i -x)² +(y_i -y)² +(z_i -z)² =(d_i )² , formula (8.1)

其中，i为圆球的个数，(x_i,y_i,z_i)为第i个圆球球心坐标，d_i为圆球与测头之间的距离，i个圆球即得i个公式（8.1），联合即得待测点的位置坐标(x,y,z)。Among them, i is the number of spheres, (x_i , y_i , zi₎ is the coordinates of the center of the i-th sphere, d_i is the distance between the sphere and the probe, i Combined with formula (8.1), the position coordinates (x, y, z) of the point to be measured can be obtained.

作为本发明的优选实施例，测量之前，首先对球靶标进行自标定，得到圆球与测头之间的距离，自标定的方法为：令测头固定在一点不动，球靶标绕测头旋转多个角度拍摄m幅图像，利用同心圆半径不变的约束联合所有球心建立误差最小化函数，通过最小化总距离误差得到待测点空间位置，最后即得得到每个圆球的球心与待测点之间的距离。As a preferred embodiment of the present invention, before the measurement, the ball target is first self-calibrated to obtain the distance between the ball and the probe. The method of self-calibration is: the probe is fixed at one point, and the ball target is around the probe. Rotate multiple angles to shoot m images, use the constraint of constant radius of concentric circles to combine all sphere centers to establish an error minimization function, and obtain the spatial position of the point to be measured by minimizing the total distance error, and finally get the sphere of each sphere The distance between the center and the point to be measured.

一种基于所述的单目视觉系统进行移动标定和数据拼接的方法，（10.1）首先将球靶标放置在合适的位置，保证摄像机能够看到球靶标球体部分；（10.2）建立世界坐标系O_wX_wY_wZ_w，按照顺序选取球靶标的三个圆球，其中，世界坐标系的原点O_w为第一个圆球的球心，世界坐标系的X_w轴为第二个圆球的球心到第一个圆球的球心的向量

世界坐标系的Z_w轴为：$\stackrel{\‾}{O_w{Z}_w}=\stackrel{\‾}{O_2{O}_1}\×\stackrel{\‾}{O_3{O}_1},$世界坐标系的Y_w轴为$\stackrel{\‾}{O_w{Y}_w}=\stackrel{\‾}{O_w{Z}_w}\×\stackrel{\‾}{O_2{O}_1};$（10.3）由步骤（10.2）即得摄像机坐标系和世界坐标系之间的关系[R_w-1,T_w-1]，当摄像机移动到其他非第一位置时，摄像机在该位置的坐标系与世界系之间的关系为[R_w-i,T_w-i]，设定摄像机在第一位置时的坐标系为参考坐标系，将其他所有位置时测量的数据统一到参考坐标系下实现数据的拼接。A method for mobile calibration and data splicing based on the monocular vision system, (10.1) first place the ball target in a suitable position to ensure that the camera can see the spherical part of the ball target; (10.2) establish a world coordinate system O_w X_w Y_w Z_w , select three spheres of the spherical target in order, where the origin O_w of the world coordinate system is the center of the first sphere, and the X_w axis of the world coordinate system is the second circle Vector from the center of the ball to the center of the first sphere

The Z_w axis of the world coordinate system is:$\stackrel{\‾}{o_w{Z}_w}=\stackrel{\‾}{o_2{o}_1}\×\stackrel{\‾}{o_3{o}_1},$ The Y_w axis of the world coordinate system is$\stackrel{\‾}{o_w{Y}_w}=\stackrel{\‾}{o_w{Z}_w}\×\stackrel{\‾}{o_2{o}_1};$ (10.3) From the step (10.2), the relationship between the camera coordinate system and the world coordinate system [R_w-1 , T_w-1 ] is obtained. When the camera moves to other non-first positions, the coordinates of the camera at this position The relationship between the world system and the world system is [R_wi , T_wi ], set the coordinate system of the camera at the first position as the reference coordinate system, and unify the measured data at all other positions into the reference coordinate system to achieve data integration. stitching.

与现有技术相比，本发明具有以下有益效果：本发明测量时，对球靶标中的不同圆球进行拍摄，从而得到待测点的位置坐标。由于球具有外轮廓连续性好等优点，可以实现360度空间视场无视角限制、便捷标定，消除了平面靶标在摄像机移动视角太大时畸变过大甚至观测不到的不足。Compared with the prior art, the present invention has the following beneficial effects: when the present invention is measuring, different spheres in the ball target are photographed, so as to obtain the position coordinates of the points to be measured. Because the ball has the advantages of good continuity of the outer contour, it can realize 360-degree spatial field of view without viewing angle limitation, convenient calibration, and eliminates the problem that the plane target is too distorted or even unobservable when the camera moves too much.

【附图说明】【Description of drawings】

图1为本发明球靶标结构及摄像机透视成像模型示意图；Fig. 1 is the schematic diagram of ball target structure and camera perspective imaging model of the present invention;

图2为本发明球靶标球体部分透视成像模型示意图；Fig. 2 is a schematic diagram of a partial perspective imaging model of a ball target sphere of the present invention;

图3为本发明球靶标自标定及测头位置计算原理示意图；Fig. 3 is a schematic diagram of the self-calibration of the ball target and the calculation principle of the probe position of the present invention;

图4为本发明球靶标的摄像机移动位置标定示意图。Fig. 4 is a schematic diagram of camera movement position calibration of the ball target of the present invention.

【具体实施方式】【Detailed ways】

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

图1为本发明球靶标结构及摄像机透视成像模型示意图。其中的标号分别表示：1、测头，2、接长杆，3、圆球，4、螺杆，5、球形连接块。O_cX_cY_cZ_c为摄像机坐标系，O_c为摄像机光心，Z_c轴与摄像机光轴方向重合。O_s1、O_s2、O_s3分别为用于建立靶标坐标系的三个球的球心，O_sX_sY_sZ_s为靶标坐标系。uv表示图像像素坐标系（即实物在摄像机内成像的图像坐标系），(u₀,v₀)表示图像中心。Fig. 1 is a schematic diagram of the ball target structure and camera perspective imaging model of the present invention. The labels therein represent respectively: 1. measuring head, 2. extension rod, 3. ball, 4. screw rod, 5. spherical connection block. O_c X_c Y_c Z_c is the camera coordinate system, O_c is the optical center of the camera, and the Z_c axis coincides with the direction of the camera optical axis. O_s1 , O_s2 , and O_s3 are the centers of three spheres used to establish the target coordinate system, respectively, and O_s X_s Y_s Z_s is the target coordinate system. uv represents the image pixel coordinate system (that is, the image coordinate system in which the object is imaged in the camera), and (u₀ , v₀ ) represents the image center.

本发明以由4个圆球组成的球靶标为例进行具体说明。球靶标的探针由测头1和接长杆2组成，测头1通过接长杆2连接到球形连接块5上，球形连接块5表面打有均布的14个螺纹孔，与接长杆2和圆球3之间采用螺杆连接，螺纹孔的数量保证了可以根据需要确定需要安装的球体数量。每两个移动位置的摄像机要求有重叠的视场。本方法先根据空间球成像和绝对二次曲线的关系标定摄像机内部参数，然后根据球透视成像模型和矩阵分解法求得各个球的球心位置，由此计算测头的空间三维坐标。最后利用球靶标作为拼接靶标，标定摄像机移动位置关系，实现不同位置的数据拼接。The present invention is specifically described by taking a ball target composed of 4 spheres as an example. The probe of the ball target is composed of aprobe 1 and an extension rod 2. Theprobe 1 is connected to the spherical connection block 5 through the extension rod 2. The surface of the spherical connection block 5 is punched with 14 threaded holes evenly distributed. The rod 2 and the ball 3 are connected by a screw, and the number of threaded holes ensures that the number of spheres to be installed can be determined as required. Every two cameras in the mobile position require overlapping fields of view. In this method, the internal parameters of the camera are calibrated according to the relationship between the spatial spherical imaging and the absolute quadratic curve, and then the center position of each ball is obtained according to the spherical perspective imaging model and the matrix decomposition method, thereby calculating the three-dimensional coordinates of the measuring head. Finally, the spherical target is used as the splicing target to calibrate the moving position relationship of the camera to realize data splicing at different positions.

图2为球靶标球体部分透视成像模型示意图。O_cX_cY_cZ_c为摄像机坐标系，O_siX_siY_siZ_si为以摄像机光心为原点、光心与球心连线为Z轴建立的第i个球的球坐标系。球心O_i到摄像机光心O_c的距离为Z_i0，球的半径为r_i，根据射线跟踪，由出射的射线与球相切的点组成一个圆，即轮廓生成元

（轮廓生成元即每一个圆球实际的轮廓），

在摄像机像平面上的成像椭圆表示为C_i，uv表示图像像素坐标系。Fig. 2 is a schematic diagram of a perspective imaging model of a spherical part of a spherical target. O_c X_c Y_c Z_c is the camera coordinate system, O_si X_si Y_si Z_si is the spherical coordinate system of the i-th ball established with the optical center of the camera as the origin and the line connecting the optical center and the center of the sphere as the Z axis. The distance from the center of the sphere O_i to the optical center of the camera O_c is Z_i0 , and the radius of the sphere is r_i . According to ray tracing, a circle is formed by the point where the outgoing ray is tangent to the sphere, that is, the contour generating element

(The contour generator is the actual contour of each sphere),

The imaging ellipse on the camera image plane is represented as C_i , and uv represents the image pixel coordinate system.

图3为球靶标自标定及测头位置计算原理示意图。其中的标号分别表示：P₀表示待测点三维坐标，也即靶标测头所在位置，O_sX_sY_sZ_s表示靶标坐标系，d₁～d₄表示四个球的球心到测头的距离。Figure 3 is a schematic diagram of the principle of ball target self-calibration and probe position calculation. The labels in it respectively indicate: P₀ indicates the three-dimensional coordinates of the point to be measured, that is, the position of the target probe, O_s X_s Y_s Z_s indicates the target coordinate system, and d₁ ~ d₄ indicate the four balls from the center to the measuring point. head distance.

图4为能同时覆盖球靶标的摄像机移动位置标定示意图。其中的标号分别表示：O_ciX_ciY_ciZ_ci表示摄像机在第i个位置构建的摄像机坐标系，O_sX_sY_sZ_s表示靶标坐标系，Pos(i)代表摄像机移动位置，[R_ab,T_ab]代表坐标系a到坐标系b的转换关系，脚标a、b代表各个位置的摄像机坐标系和靶标坐标系。Fig. 4 is a schematic diagram of camera movement position calibration capable of simultaneously covering a ball target. The labels in it represent respectively: O_ci X_ci Y_ci Z_ci represents the camera coordinate system constructed by the camera at the i-th position, O_s X_s Y_s Z_s represents the target coordinate system, Pos(i) represents the moving position of the camera, [ R_ab , T_ab ] represents the transformation relationship from coordinate system a to coordinate system b, and subscripts a and b represent the camera coordinate system and target coordinate system at each position.

下面，对各步骤进行具体介绍。Each step is described in detail below.

第一阶段：硬件的建立Phase 1: Establishment of the hardware

参见图1，搭建单目视觉测量系统，建立摄像机透视成像模型。球靶标的球体部分包括三个以上由球形连接块5连接的圆球3，所述圆球3通过螺杆4连接在球形连接件5上，圆球半径r_i可以不一样，根据测量视场确定球的数量和大小；探针的接长杆2连接在球形连接块5上，其长度和形状根据实际的测量场合确定；测头1设置在接长杆的末端，圆球与测头1的位置可以通过球靶标自标定确定。球靶标置于摄像机视场内合适位置，测头1与被测点接触。拍摄一幅图像。Referring to Figure 1, build a monocular vision measurement system and establish a camera perspective imaging model. The spherical part of the ball target includes more than three balls 3 connected by a spherical connection block 5, and the balls 3 are connected to the spherical connection part 5 through a screw 4. The radius r_i of the ball can be different, and it is determined according to the measurement field of view The number and size of the balls; the extension rod 2 of the probe is connected to the spherical connection block 5, and its length and shape are determined according to the actual measurement occasion; theprobe 1 is arranged at the end of the extension rod, and the ball and theprobe 1 The position can be determined by ball target self-calibration. The ball target is placed at a proper position in the field of view of the camera, and theprobe 1 is in contact with the measured point. Take an image.

第二阶段：基于球靶标和绝对二次曲线的摄像机内部参数K的单幅图像标定。The second stage: a single image calibration based on the spherical target and the camera internal parameter K of the absolute conic curve.

参见图2，球体部分透视成像，每个圆球在像平面上成像为椭圆。所述像平面即实际圆球在摄像机内的成像所在的平面。摄像机内部参数K主要是由摄像机光心和焦距形成的矩阵，标定过程如下：Referring to Fig. 2, the sphere is partly imaged in perspective, and each sphere is imaged as an ellipse on the image plane. The image plane is the plane where the image of the actual sphere in the camera is located. The camera internal parameter K is mainly a matrix formed by the camera optical center and focal length, and the calibration process is as follows:

2.1、采用二值化、膨胀、阈值等图像处理方法和边缘检测算子提取球体所成椭圆轮廓，采用最小二乘法拟合椭圆曲线方程C_i(i=1～4)，i为球靶标中圆球的个数。将每个圆球的投影二次曲线C_i按一定的顺序保存待用。2.1. Use binarization, expansion, threshold and other image processing methods and edge detection operators to extract the ellipse contour formed by the sphere, and use the least square method to fit the elliptic curve equation C_i (i=1～4), where i is the center of the spherical target The number of balls. Save the projected quadratic curve C_i of each sphere in a certain order for later use.

2.2、根据球体透视投影成像模型，摄像机坐标系O_cX_cY_cZ_c与第i个圆球的球坐标系O_siX_siY_siZ_si之间只存在一个旋转，因此两者之间的单应性矩阵H_i=KR_idiag{1,1,Λ_i}，其中，Λ_i=Z_i0/r_i，Z_i0为第i个圆球的球心到摄像机光心之间的距离，r_i为第i个圆球的半径，R_i为旋转矩阵，球的轮廓生成元在像平面上的成像椭圆二次曲线方程为$C_i={H_i}^{-T}\stackrel{\‾}{C_i}{H}_i^{-1}=H_i^{-T}\mathrm{diag}(\mathrm{1,1},-1)H_i^{-1}.$在对偶空间中表示形式为：2.2. According to the spherical perspective projection imaging model, there is only one rotation between the camera coordinate system O_c X_c Y_c Z_c and the spherical coordinate system O_si X_si Y_si Z_si of the i-th sphere, so there is only one rotation between the two The homography matrix H_i =KR_i diag{1,1,Λ_i }, where, Λ_i =Z_i0 /r_i , Z_i0 is the distance from the center of the ith sphere to the optical center of the camera ,_ri is the radius of the i-th sphere, R_i is the rotation matrix, and the imaging ellipse quadratic curve equation of the contour generator of the sphere on the image plane is$C_i={h_i}^{-T}\stackrel{\‾}{C_i}{h}_i^{-1}=h_i^{-T}\mathrm{diag}(\mathrm{1,1},-1)h_i^{-1}.$ The representation in the dual space is:

${\mathrm{<span><span>C</span>C</span>}}_{\mathrm{<span><span>i</span>i</span>}}^{<span><span>*</span>*</span>}<span><span>=</span>=</span>{\mathrm{<span><span>H</span>h</span>}}_{\mathrm{<span><span>i</span>i</span>}}{\mathrm{<span><span>C</span>C</span>}}_{\mathrm{<span><span>ui</span>ui</span>}}^{<span><span>*</span>*</span>}{\mathrm{<span><span>H</span>h</span>}}_{\mathrm{<span><span>i</span>i</span>}}^{\mathrm{<span><span>T</span>T</span>}}<span><span>=</span>=</span>\mathrm{<span><span>K</span>K</span>}{\mathrm{<span><span>R</span>R</span>}}_{\mathrm{<span><span>i</span>i</span>}}\mathrm{<span><span>diag</span>diag</span>}<span><span>(</span>(</span>\mathrm{<span><span>1,1</span>1,1</span>}<span><span>-</span>-</span>{\mathrm{<span><span>\&Lambda;</span>\&Lambda;</span>}}_{\mathrm{<span><span>i</span>i</span>}}^{\mathrm{<span><span>2</span>2</span>}}<span><span>)</span>)</span>{\mathrm{<span><span>R</span>R</span>}}_{\mathrm{<span><span>i</span>i</span>}}^{\mathrm{<span><span>T</span>T</span>}}{\mathrm{<span><span>K</span>K</span>}}^{\mathrm{<span><span>T</span>T</span>}}<span><span>=</span>=</span>{\mathrm{<span><span>KK</span>KK</span>}}^{\mathrm{<span><span>T</span>T</span>}}<span><span>-</span>-</span>{\mathrm{<span><span>o</span>o</span>}}_{\mathrm{<span><span>i</span>i</span>}}{\mathrm{<span><span>o</span>o</span>}}_{\mathrm{<span><span>i</span>i</span>}}^{\mathrm{<span><span>T</span>T</span>}}<span><span>-</span>-</span><span><span>-</span>-</span><span><span>-</span>-</span><span><span>(</span>(</span>\mathrm{<span><span>1</span>1</span>}<span><span>)</span>)</span>$

其中

是第i个圆球的球心所成像坐标，r_3i为相应的旋转矩阵R_i的第3列。in

is the imaging coordinate of the center of the i-th sphere, and r_3i is the third column of the corresponding rotation matrix R_i .

绝对二次曲线IAC是无穷远平面π_∞=(0,0,0,1)^T上的二次曲线，在单应性矩阵H=KR下的图像w=(KK^T)^-1其在对偶空间中可表示为The absolute conic IAC is a conic on the infinite plane π_∞ =(0,0,0,1)^T , the image w=(KK^T )^-1 under the homography matrix H=KR is in the dual in space can be expressed as

w^*=KK^T  (2)w^* =KK^T (2)

由空间三个球体成像可以得到如（3）所示的三个方程。计算每两个成像椭圆曲线方程之间的单应性矩阵

为C_A在对偶空间中的表示形式。根据视图几何理论，每一对成像椭圆的单应性矩阵均包括一个穿过相应的椭圆对的特征向量，称为单应性矩阵的极线，表示为l_AB(A,B=1,2,3且A≠B)，每个特征向量对应的特征值称为极点，表示为v_AB(A,B=1,2,3且A≠B).l_AB、v_AB以及w满足方程（3）：The three equations shown in (3) can be obtained by imaging three spheres in space. Compute the homography matrix between every two imaging elliptic curve equations

is the representation of C_A in the dual space. According to the theory of view geometry, the homography matrix of each pair of imaging ellipses includes an eigenvector passing through the corresponding pair of ellipses, called the epipolar line of the homography matrix, expressed as l_AB (A, B=1,2 ,3 and A≠B), the eigenvalue corresponding to each eigenvector is called a pole, expressed as v_AB (A,B=1,2,3 and A≠B).l_AB , v_AB and w satisfy the equation ( 3):

[l_AB]×wv_AB=0  (3)[l_AB ]×wv_AB =0 (3)

,根据奇异值分解可以得到w，进而根据式（2）正交分解得到摄像机内部参数K。进而可求取。, according to the singular value decomposition, w can be obtained, and then the internal parameter K of the camera can be obtained according to the orthogonal decomposition of formula (2). and thus obtainable.

第三阶段：基于球靶标成像模型利用矩阵奇异值分解获得每个球心位置O_i，通过球靶标自标定确定球心与测头之间的位置关系；位置参数一旦标定，可以作为已知量，在球靶标在不拆斜（增减球或换测头接长杆等）的情况下用于接下来的工件表面测量。The third stage: Based on the spherical target imaging model, the matrix singular value decomposition is used to obtain the position O_i of each spherical center, and the positional relationship between the spherical center and the probe is determined through the spherical target self-calibration; once the position parameter is calibrated, it can be used as a known quantity , the ball target is used for the next workpiece surface measurement without dismantling the skew (increase or decrease the ball or change the probe extension rod, etc.).

3.1、对步骤2中的公式(1)进行简单变形可得到3.1. Simple deformation of the formula (1) in step 2 can be obtained

${\mathrm{<span><span>\&beta;</span>\&beta;</span>}}_{\mathrm{<span><span>i</span>i</span>}}{\mathrm{<span><span>K</span>K</span>}}^{<span><span>-</span>-</span>\mathrm{<span><span>1</span>1</span>}}{\mathrm{<span><span>C</span>C</span>}}_{\mathrm{<span><span>i</span>i</span>}}^{<span><span>*</span>*</span>}{\mathrm{<span><span>K</span>K</span>}}^{<span><span>-</span>-</span>\mathrm{<span><span>T</span>T</span>}}<span><span>=</span>=</span>{\mathrm{<span><span>R</span>R</span>}}_{\mathrm{<span><span>i</span>i</span>}}\mathrm{<span><span>diag</span>diag</span>}<span><span>(</span>(</span>\mathrm{<span><span>1,1</span>1,1</span>}<span><span>,</span>,</span><span><span>-</span>-</span>{\mathrm{<span><span>\&Lambda;</span>\&Lambda;</span>}}_{\mathrm{<span><span>i</span>i</span>}}^{\mathrm{<span><span>2</span>2</span>}}<span><span>)</span>)</span>{\mathrm{<span><span>R</span>R</span>}}_{\mathrm{<span><span>i</span>i</span>}}^{\mathrm{<span><span>T</span>T</span>}}<span><span>-</span>-</span><span><span>-</span>-</span><span><span>-</span>-</span><span><span>(</span>(</span>\mathrm{<span><span>4</span>4</span>}<span><span>)</span>)</span>$

其中，β_i为第i个圆球的成像比例因子；Among them, β_i is the imaging scale factor of the i-th sphere;

等式左边为对称阵，通过奇异值分解可以得到与等式右边一致的形式，从而得到旋转矩阵R_i和Λ_i，得到各个球心的三维坐标。The left side of the equation is a symmetric matrix, and the form consistent with the right side of the equation can be obtained through singular value decomposition, so that the rotation matrices R_i and Λ_i can be obtained, and the three-dimensional coordinates of each sphere center can be obtained.

3.2、参见图3，由步骤3.1中的计算可以得到球心的三维坐标，为了得到准确的球心和测头之间的位置关系，在使用靶标进行三维测量之前，对球靶标进行自标定。令测头固定在一点不动，球靶标绕测头旋转多个角度拍摄m幅图像，球靶标中使用的圆球个数n=4，设第j幅图像中球心O_i(i=1～n)的坐标为利用步骤3.1可以确定该坐标。第i个球在第j个位置时到测头的距离和测头位置(x,y,z)为未知量，3.2. Referring to Figure 3, the three-dimensional coordinates of the center of the ball can be obtained from the calculation in step 3.1. In order to obtain an accurate positional relationship between the center of the ball and the probe, the ball target is self-calibrated before using the target for three-dimensional measurement. Let the measuring head stay fixed at one point, and the ball target rotates around the measuring head at multiple angles to shoot m images, the number of balls used in the ball target is n=4, and the center of the j-th image is O_i (i=1 ~n) coordinates are This coordinate can be determined using step 3.1. The distance from the i-th ball to the probe when it is at the j-th position and probe position (x, y, z) are unknown quantities,

${<span><span>(</span>(</span>{\mathrm{<span><span>x</span>x</span>}}_{\mathrm{<span><span>i</span>i</span>}}^{\mathrm{<span><span>j</span>j</span>}}<span><span>-</span>-</span>\mathrm{<span><span>x</span>x</span>}<span><span>)</span>)</span>}^{\mathrm{<span><span>2</span>2</span>}}<span><span>+</span>+</span>{<span><span>(</span>(</span>{\mathrm{<span><span>y</span>the\; y</span>}}_{\mathrm{<span><span>i</span>i</span>}}^{\mathrm{<span><span>j</span>j</span>}}<span><span>-</span>-</span>\mathrm{<span><span>y</span>the\; y</span>}<span><span>)</span>)</span>}^{\mathrm{<span><span>2</span>2</span>}}<span><span>+</span>+</span>{<span><span>(</span>(</span>{\mathrm{<span><span>z</span>z</span>}}_{\mathrm{<span><span>i</span>i</span>}}^{\mathrm{<span><span>j</span>j</span>}}<span><span>-</span>-</span>\mathrm{<span><span>z</span>z</span>}<span><span>)</span>)</span>}^{\mathrm{<span><span>2</span>2</span>}}<span><span>=</span>=</span>{<span><span>(</span>(</span>{\mathrm{<span><span>d</span>d</span>}}_{\mathrm{<span><span>i</span>i</span>}}^{\mathrm{<span><span>j</span>j</span>}}<span><span>)</span>)</span>}^{\mathrm{<span><span>2</span>2</span>}}<span><span>,</span>,</span><span><span>-</span>-</span><span><span>-</span>-</span><span><span>-</span>-</span><span><span>(</span>(</span>\mathrm{<span><span>5</span>5</span>}<span><span>)</span>)</span>$

对每一个球，均可以利用同心圆半径不变的约束得到m-1个约束方程，联合所有球心建立误差最小化函数For each sphere, m-1 constraint equations can be obtained by using the constraint that the radius of the concentric circle is constant, and the error minimization function can be established by combining all sphere centers

$\mathrm{<span><span>min</span>min</span>}\underset{\mathrm{<span><span>i</span>i</span>}<span><span>=</span>=</span>\mathrm{<span><span>1</span>1</span>}}{\overset{\mathrm{<span><span>n</span>no</span>}}{\mathrm{<span><span>\&Sigma;</span>\&Sigma;</span>}}}\underset{\mathrm{<span><span>j</span>j</span>}<span><span>=</span>=</span>\mathrm{<span><span>1</span>1</span>}}{\overset{\mathrm{<span><span>m</span>m</span>}}{\mathrm{<span><span>\&Sigma;</span>\&Sigma;</span>}}}<span><span>(</span>(</span>{\mathrm{<span><span>d</span>d</span>}}_{\mathrm{<span><span>i</span>i</span>}}^{\mathrm{<span><span>j</span>j</span>}}<span><span>-</span>-</span>{\mathrm{<span><span>d</span>d</span>}}_{\mathrm{<span><span>i</span>i</span>}}<span><span>)</span>)</span><span><span>-</span>-</span><span><span>-</span>-</span><span><span>-</span>-</span><span><span>(</span>(</span>\mathrm{<span><span>6</span>6</span>}<span><span>)</span>)</span>$

通过最小化总距离误差得到优化的待测点空间位置，然后将该空间位置作为已知量带入(5)，每个球的球心与待测点之间距离利用

求得。将得到的距离值作为已知量用于后续测量过程中。因为自标定过程只需要一次，后续测量过程只需拍摄单幅图像即可得到待测点三维坐标。The optimized spatial position of the point to be measured is obtained by minimizing the total distance error, and then the spatial position is brought into (5) as a known quantity, and the distance between the center of each ball and the point to be measured is used

Get it. The obtained distance value is used as a known quantity in the subsequent measurement process. Because the self-calibration process only needs one time, the subsequent measurement process only needs to take a single image to obtain the three-dimensional coordinates of the point to be measured.

第四阶段：基于球靶标的单目测量系统移动标定和数据拼接The fourth stage: mobile calibration and data splicing of monocular measurement system based on ball target

参见图4，首先基于向量标准正交法以空间球为基准建立世界坐标系O_wX_wY_wZ_w作为拼接坐标系，然后利用拼接坐标系实现摄像机在不同位置的坐标转化。Referring to Fig. 4, the world coordinate system O_w X_w Y_w Z_w is established as the splicing coordinate system based on the vector orthonormal method and the space sphere as the reference, and then the coordinate transformation of the camera at different positions is realized by using the splicing coordinate system.

4.1、将球靶标放置在视场中合适的位置，摄像机在位置1拍摄一幅图像，然后移动摄像机到位置i，要求两个位置的摄像机均可以看到球靶标球体部分。若需要更多的位置以实现大型工件表面测量，则要求每个位置均可以看到球靶标球体部分。要求每个位置拍摄的球按相同顺利排列，保证世界坐标系的统一性。4.1. Place the ball target at a suitable position in the field of view. The camera takes an image atposition 1, and then moves the camera to position i. It is required that the cameras at both positions can see the spherical part of the ball target. If more positions are required for large workpiece surface measurements, each position must be able to see the spherical part of the ball target. The balls shot at each position are required to be arranged in the same smooth manner to ensure the unity of the world coordinate system.

4.2、以不动的空间球为基准建立世界坐标系，三个球即可根据标准正交法建立笛卡尔直角坐标系。选取特定的三个球，如序号1～3的球。首先将世界坐标系原点O_w置于球1的球心位置，确定球2、球3的球心到球心1的向量

定义为X_w轴方向，由此可确定Z_w轴，$\stackrel{\&OverBar;}{O_w{Z}_w}=\stackrel{\&OverBar;}{O_2{O}_1}\&times;\stackrel{\&OverBar;}{O_3{O}_1},$最后确定Y_w轴：$\stackrel{\&OverBar;}{O_w{Y}_w}=\stackrel{\&OverBar;}{O_w{Z}_w}\&times;\stackrel{\&OverBar;}{O_2{O}_1}.$将坐标轴向量方向确定出来后，将各个方向向量单位化，即完成了世界坐标系的建立。4.2. Establish the world coordinate system based on the fixed space sphere, and the three spheres can establish the Cartesian Cartesian coordinate system according to the standard orthogonal method. Select specific three balls, such as balls numbered 1-3. First, place the origin O_w of the world coordinate system at the center ofball 1, and determine the vector from the center of ball 2 and ball 3 to the center ofball 1

Defined as the direction of the X_w axis, from which the Z_w axis can be determined,$\stackrel{\&OverBar;}{o_w{Z}_w}=\stackrel{\&OverBar;}{o_2{\mathrm{<figure-callout\; label="o"\; filenames="HDA00002868767600021.png,HDA00002868767600031.png"\; state="\{\{state\}\}">o</figure-callout>}}_1}\&times;\stackrel{\&OverBar;}{o_3{\mathrm{<figure-callout\; label="o"\; filenames="HDA00002868767600021.png,HDA00002868767600031.png"\; state="\{\{state\}\}">o</figure-callout>}}_1},$ Finalize the Y_w axis:$\stackrel{\&OverBar;}{o_w{Y}_w}=\stackrel{\&OverBar;}{o_w{Z}_w}\&times;\stackrel{\&OverBar;}{o_2{\mathrm{<figure-callout\; label="o"\; filenames="HDA00002868767600021.png,HDA00002868767600031.png"\; state="\{\{state\}\}">o</figure-callout>}}_1}.$ After determining the direction of the coordinate axis vector, unitize each direction vector to complete the establishment of the world coordinate system.

4.3、当摄像机处于位置1时，由步骤2确立世界坐标系，则摄像机坐标系和世界坐标系之间的关系确定[R_w-1,T_w-1]，当摄像机移动到第i个位置后，同理可确定第i个位置摄像机坐标系和世界坐标系之间的关系[R_w-i,T_w-i]。选取摄像机在第一个位置时的坐标系为参考坐标系，将所有位置时测量数据统一到参考坐标系下实现数据拼接。第i个摄像机坐标系与第1个位置摄像机坐标系的关系可推出：4.3. When the camera is atposition 1, the world coordinate system is established by step 2, then the relationship between the camera coordinate system and the world coordinate system is determined [R_w-1 , T_w-1 ]. When the camera moves to the i-th position Finally, similarly, the relationship [R_wi , T_wi ] between the i-th position camera coordinate system and the world coordinate system can be determined. Select the coordinate system of the camera at the first position as the reference coordinate system, and unify the measurement data at all positions into the reference coordinate system to realize data splicing. The relationship between the i-th camera coordinate system and the first position camera coordinate system can be deduced as follows:

${\mathrm{<span><span>R</span>R</span>}}_{\mathrm{<span><span>1</span>1</span>}<span><span>-</span>-</span>\mathrm{<span><span>i</span>i</span>}}<span><span>=</span>=</span>{\mathrm{<span><span>R</span>R</span>}}_{\mathrm{<span><span>w</span>w</span>}<span><span>-</span>-</span>\mathrm{<span><span>i</span>i</span>}}{\mathrm{<span><span>R</span>R</span>}}_{\mathrm{<span><span>w</span>w</span>}<span><span>-</span>-</span>\mathrm{<span><span>1</span>1</span>}}^{<span><span>-</span>-</span>\mathrm{<span><span>1</span>1</span>}}$

$T_{1-i}=T_{w-i}-R_{w-i}{R}_{w-1}^{-1}{T}_{w-1}$  (7)$T_{1-i}=T_{w-i}-R_{w-i}{R}_{w-1}^{-1}{T}_{w-1}$ (7)

本发明为实现单目测量系统下的深度信息获取提供了一种可行途径，实施快速方便，成本低廉。在实现摄像机标定的同时完成了空间点测量，可以通过增加球体部分圆球数量和保持测尖不动旋转球靶标多幅拍摄的方式优化测量精度。本发明同时为多目系统和单目测量系统移动标定和数据拼接提供了一种可行途径，多目系统标定原理和单目移动标定原理类似，可以通过第四阶段的步骤完成坐标系统一和数据拼接。The invention provides a feasible way for realizing the acquisition of depth information under the monocular measurement system, and the implementation is fast and convenient, and the cost is low. The spatial point measurement is completed while the camera is calibrated, and the measurement accuracy can be optimized by increasing the number of spheres in the sphere part and keeping the measuring tip stationary and rotating the ball target for multiple shots. The present invention provides a feasible way for multi-objective system and monocular measurement system mobile calibration and data splicing at the same time. The principle of multi-objective system calibration is similar to that of monocular mobile calibration. Coordinatesystem 1 and data can be completed through the steps of the fourth stage. stitching.

Claims (10)

1. a portable ball target that is used for single camera vision system Fast Calibration and measurement, is characterized in that: mainly be comprised of spheroid, contiguous block (5) and probe; Described contiguous block (5) is used for supporting each spheroid and linking probe, and described probe is comprised of extension bar (2) and gauge head (1), and described spheroid is comprised of non-coplanar ball more than three, and described spheroid is connected with contiguous block by screw rod (4).

2. portable ball target according to claim 1, it is characterized in that: described contiguous block (5) is spheroid form.

3. single camera vision system based on portable ball target claimed in claim 1, it is characterized in that: described single camera vision system comprises portable ball target and video camera, described shooting function is seen complete ball target spherical part.

4. measuring method based on single camera vision system claimed in claim 3, it is characterized in that: (1) takes a width ball target image by single camera vision system, based on absolute conic imaging geometry calibrating camera inner parameter K, described intrinsic parameters of the camera K comprises video camera photocentre (u according to video camera perspective imaging model and spheroid projection model₀, v₀), focal distance f and inclination factor s; (2) utilize intrinsic parameters of the camera and the ball perspective imaging geometric model demarcated to determine the three-dimensional coordinate of each centre of sphere under camera coordinate system; (3) ask in the ball target each ball centre of sphere to the distance of gauge head; (4) determine the position of gauge head according to the position relationship of ball target ball and gauge head, i.e. the three-dimensional coordinate of tested point.

5. measuring method as claimed in claim 4, it is characterized in that: the concrete grammar of step (1) comprises the following steps:

(5.1) adopt image processing method to extract with edge detection operator the elliptic contour that each ball becomes in video camera, then adopt the curvilinear equation C of the corresponding elliptic contour of least square fitting_i, wherein, i is the number of ball;

(5.2) according to spheroid perspective projection imaging model, camera coordinate system O_cX_cY_cZ_cSpherical coordinate system O with i ball_siX_siY_siZ_siBetween homography matrix be: H_i=KR_iDiag{1,1, Λ_i, wherein, Λ_i=Z_i0/ r_i, Z_i0Be that the centre of sphere of i ball is to the distance between the video camera photocentre, r_iBe the radius of i ball, R_iBe rotation matrix, the quadratic curve equation C of ball imaging ellipse in video camera_iRepresentation is in dual space:

$C_i^{*}=H_i{C}_{\mathrm{ui}}^{*}{H}_i^T=K{R}_i\mathrm{diag}(\mathrm{1,1}-{\mathrm{\&Lambda;}}_i^2)R_i^T{K}^T={\mathrm{KK}}^T-o_i{o}_i^T,$Formula (5.1)

Wherein,

The centre of sphere imager coordinate of i ball, r_3iBe corresponding rotation matrix R_iThe 3rd row, R_iBe rotation matrix, K is the matrix that intrinsic parameters of the camera forms.

6. measuring method as claimed in claim 5 is characterized in that: in described step (5.2), when finding the solution intrinsic parameters of the camera K, introduce absolute conic, the image of this absolute conic under homography matrix is w=(KK^T)^-1, be expressed as in dual space: w^*=KK^THomography matrix between the imaging elliptic curve equation of every two balls in the ball target is

A, B=1,2,3 and A ≠ B, wherein,Imaging elliptic curve equation C for ball A_ARepresentation in dual space, C_BBe the oval wireless equation of the imaging of ball B; Theoretical according to view geometry, the homography matrix of every a pair of imaging ellipse includes one and passes the right proper vector of corresponding ellipse, is called the polar curve of homography matrix, is expressed as l_AB, wherein, A, B=1,2,3 and A ≠ B, each proper vector characteristic of correspondence value is called limit, is expressed as v_AB, A, B=1,2,3 and A ≠ B.l_AB, v_ABAnd w satisfies following formula (6.1):

[l_AB]×wv_AB=0 (6.1)

Obtain w according to svd, and then according to formula w^*=KK^TOrthogonal Decomposition namely gets intrinsic parameters of the camera K.

7. measuring method as claimed in claim 5, it is characterized in that: the concrete grammar of step (2) is: the formula (5.1) in step (5.2) is out of shape obtains:

${\mathrm{\&beta;}}_i{K}^{-1}{C}_i^{*}{K}^{-T}=R_i\mathrm{diag}(\mathrm{1,1},-{\mathrm{\&Lambda;}}_i^2)R_i^T,$Wherein, β_iIt is the imaging scale factor of i ball;

The expression formula on the equation left side is obtained the form consistent with equation the right by svd, thereby, rotation matrix R obtained_iAnd Λ_i, obtain the three-dimensional coordinate of each centre of sphere.

8. measuring method as claimed in claim 4 is characterized in that: the position coordinates of described tested point (x, y, z) is according to following calculating:

(x_i-x)²+ (y_i-y)²+ (z_i-z)²=(d_i)², formula (8.1)

Wherein, i is the number of ball, (x_i, y_i, z_i) be i ball sphere centre coordinate, d_iBe the distance between ball and gauge head, i ball namely gets i formula (8.1), unites the position coordinates (x, y, z) that namely gets tested point.

9. measuring method as claimed in claim 8, it is characterized in that: before measurement, at first the ball target is carried out from demarcating, obtain the distance between ball and gauge head, from the method for demarcating be: make gauge head be fixed on a bit motionless, the ball target rotates a plurality of angle shot m width images around gauge head, utilize the constant constraint of concentric circles radius to unite all centre ofs sphere and set up the error minimize function, obtain the tested point locus by minimizing total distance error, namely obtain at last the centre of sphere of each ball and the distance between tested point.

10. one kind is moved based on single camera vision system claimed in claim 3 and demarcates and the method for data splicing, and it is characterized in that: at first place the ball target in place (10.1), and the assurance video camera can be seen ball target spherical part; (10.2) set up world coordinate system O_wX_wY_wZ_w, choose in order three balls of ball target, wherein, the initial point O of world coordinate system_wBe the centre of sphere of first ball, the X of world coordinate system_wAxle is that the centre of sphere of second ball is to the vector of the centre of sphere of first ball

The Z of world coordinate system_wAxle is:The Y of world coordinate system_wAxle is

(10.3) namely get relation [R between camera coordinate system and world coordinate system by step (10.2)_w-1, T_w-1], when video camera moved to other non-primary importances, video camera was [R at the coordinate system of this position and the pass between world system_w-i, T_w-i], setting the coordinate of video camera when primary importance is reference frame, the data unification of measuring during with other all positions realizes the splicing of data under the reference frame.

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