CN104240262A

CN104240262A - Camera external parameter calibration device and calibration method for photogrammetry

Info

Publication number: CN104240262A
Application number: CN201410549442.1A
Authority: CN
Inventors: 杨威; 贺善金; 周进; 罗剑; 王卫文
Original assignee: Institute of Optics and Electronics of CAS
Current assignee: Institute of Optics and Electronics of CAS
Priority date: 2014-10-16
Filing date: 2014-10-16
Publication date: 2014-12-24
Anticipated expiration: 2034-10-16
Also published as: CN104240262B

Abstract

The invention provides a camera external parameter calibration device and a calibration method for photogrammetry. The calibration device is composed of four parts: a target rod, a centering rod, a leveling mechanism and a measurement reference point. The calibration method is as follows: First, adjust the camera to point to the target to be measured, bury four reference points in the direction of the camera, and measure their high-precision coordinates in the reference coordinate system. According to the design size of the calibration device, when the calibration device is When the center pole is adjusted vertically and the leveling mechanism is placed horizontally, the coordinates of the marker points in the reference coordinate system can be deduced. Secondly, by taking the image of the marker on the calibration device with the camera, using the ellipse fitting algorithm to extract the coordinates of the marker point, combining its coordinates in the reference coordinate system and the calibration results of the internal parameters of the camera, the external distance between the camera and the reference coordinate system can be calculated. parameters to complete the calibration. Compared with the prior art, the scheme is suitable for the occasion of wide measurement range and multi-camera stereo calibration, and has the characteristics of easy operation and high calibration accuracy.

Description

Camera extrinsic parameter calibration device and calibration method for photogrammetry

技术领域technical field

本发明涉及用于摄影测量的相机的标定的技术领域，具体涉及一种用于摄影测量的相机外参数标定装置及标定方法。The invention relates to the technical field of camera calibration for photogrammetry, in particular to a camera external parameter calibration device and calibration method for photogrammetry.

背景技术Background technique

摄影测量被广泛应用于三维模型重建、物体表面尺寸测量、目标位置和姿态测量、空间对接、医学诊断以及运动恢复等领域。为了获取目标三维信息，摄影测量一般需要两台或以上的相机进行交会测量从而形成立体视觉测量系统，因此，标定多个相机在统一基准坐标系的位置和姿态就成为测量系统测量精度的一个关键影响因素。本发明中相机的外参数即相机相对于基准坐标系的旋转矩阵和平移向量。传统的相机参数标定比较典型的有zhang提出了基于共面标定参照物方法，该方法允许共面参照物在视场内自由移动，通过获取多幅高质量的标定图像，进行相机的内参数标定，固定拍摄某一幅，可以标定相机相对于此时固定的标定参照物坐标系的外参数，该方法标定过程简单，对靶标的要求低，但该方法不能实现多个平面坐标系和基准坐标系的统一，只适用于测量范围较小的相机标定场合；此外，还有一种使用辅助像机进行全视场法标定，要求辅助像机同时采集到标定参考系控制点和基准系控制点的图像，这需要辅助像机有较大的视场范围，从而其成像分辨率会比较低，影响标定的精度；上述标定方法中的辅助像机可以用激光跟踪仪(Laser Tracker)代替，激光跟踪仪能够高精度测量空间点，对于“全视场”的范围很大的情况，以激光跟踪仪代替辅助像机进行全视场法标定有利于提高标定精度，但激光跟踪仪成本较高，且标定流程较为繁琐。Photogrammetry is widely used in 3D model reconstruction, object surface size measurement, target position and attitude measurement, space docking, medical diagnosis and sports recovery and other fields. In order to obtain the three-dimensional information of the target, photogrammetry generally requires two or more cameras to perform intersection measurement to form a stereo vision measurement system. Therefore, calibrating the position and attitude of multiple cameras in the unified reference coordinate system becomes a key to the measurement accuracy of the measurement system. influencing factors. The external parameters of the camera in the present invention are the rotation matrix and translation vector of the camera relative to the reference coordinate system. Traditional camera parameter calibration is more typical. Youzhang proposed a method based on coplanar calibration reference objects. This method allows the coplanar reference objects to move freely in the field of view. By acquiring multiple high-quality calibration images, the internal parameters of the camera are calibrated. , fixedly shooting a certain frame, you can calibrate the external parameters of the camera relative to the fixed calibration reference coordinate system at this time, the calibration process of this method is simple, and the requirements for the target are low, but this method cannot realize multiple plane coordinate systems and reference coordinates The unification of the system is only applicable to camera calibration occasions with a small measurement range; in addition, there is a full field of view calibration using the auxiliary camera, which requires the auxiliary camera to simultaneously collect the control points of the calibration reference system and the reference system. image, which requires the auxiliary camera to have a larger field of view, so that its imaging resolution will be relatively low, which will affect the accuracy of calibration; the auxiliary camera in the above calibration method can be replaced by a laser tracker (Laser Tracker). The instrument can measure space points with high precision. For the case of a large "full field of view", using the laser tracker instead of the auxiliary camera for full field of view calibration is beneficial to improve the calibration accuracy, but the cost of the laser tracker is high, and The calibration process is more cumbersome.

从上述分析可知，立体视觉测量系统中的相机外参数标定既要满足精度要求，也尽量使得标定靶标使用简便，成本低廉，适用范围广，可重复多次使用。从这个角度出发，如何将上述两种典型方案中，取其精华弃其糟粕，设计一套立体视觉系统中的外参数标定方法和装置，成为了一个有待解决的关键问题。From the above analysis, it can be seen that the camera external parameter calibration in the stereo vision measurement system should not only meet the accuracy requirements, but also try to make the calibration target easy to use, low in cost, wide in application range, and can be used repeatedly. From this point of view, how to take the essence and discard the dross of the above two typical solutions, and design a set of external parameter calibration methods and devices in the stereo vision system has become a key problem to be solved.

发明内容Contents of the invention

本发明的主要目的在于克服现有技术的不足，提供一套外参数标定装置和方法，该装置测量范围广，便于加工和使用，测量精度高，为大范围全视场中多相机立体标定提供很好的解决方案。The main purpose of the present invention is to overcome the deficiencies of the prior art and provide a set of external parameter calibration device and method. The device has a wide measurement range, is easy to process and use, and has high measurement accuracy. Great solution.

本发明采用的技术方案为：一种用于摄影测量的相机外参数标定装置，整个相机外参数标定装置由靶标杆、对中杆、调平机构和测量基准点四个部分组成。靶标杆在标定杆机构上方，靶标杆上面安装有10个一列的圆形标志点，标志点圆心在靶标平面成直线排列。机构的下方是对中杆，用于对准测量基准点，保证标定架设的位置精度，且标志点连线与对中杆中轴线在同一直线上，且每个标志点圆心到对中杆底部的距离已知，即相对标定杆下方基准点的位置已精确获得，若使得对中杆垂直于水平面，则通过预先标定的基准点坐标(基准坐标系的Y轴垂直于水平面)，即可以获得每个圆形标志点的中心在基准坐标系下的坐标。为了使得对中杆垂直于水平面，那么要求与对中杆垂直的调平机构所在平面保证水平，因此，该装置在对中杆后面有两根支撑杆，支撑杆底部靠近地面位置有调平螺钉，用于调节使靶标杆垂直于水平面；调平时，首先将倾斜角传感器固定在载物台上，然后通过旋转调平螺钉，使传感器读数达到最接近0值即可。此外，当对中杆下端与基准点位连接后，且调平机构调整水平，整个标定装置可以绕基准点竖直方向进行360°旋转，使得靶标杆可以被多个相机观测，从而可以实现多台相机同时标定。The technical solution adopted in the present invention is: a camera external parameter calibration device for photogrammetry, the entire camera external parameter calibration device is composed of four parts: a target rod, a centering rod, a leveling mechanism and a measurement reference point. The target rod is above the calibration rod mechanism, and 10 circular marking points in a row are installed on the target rod, and the centers of the marking points are arranged in a straight line on the target plane. Below the mechanism is the centering rod, which is used to align the measurement reference point to ensure the position accuracy of the calibration and erection, and the line connecting the marking points is on the same line as the centering axis of the centering rod, and the center of each marking point reaches the bottom of the centering rod The distance is known, that is, the position relative to the reference point below the calibration rod has been accurately obtained. If the centering rod is perpendicular to the horizontal plane, then through the pre-calibrated reference point coordinates (the Y axis of the reference coordinate system is perpendicular to the horizontal plane), you can get The coordinates of the center of each circular marker point in the datum coordinate system. In order to make the centering rod perpendicular to the horizontal plane, the plane of the leveling mechanism perpendicular to the centering rod is required to be horizontal. Therefore, the device has two support rods behind the centering rod, and there are leveling screws at the bottom of the support rod near the ground. , used to adjust the target rod to be perpendicular to the horizontal plane; when leveling, first fix the tilt angle sensor on the stage, and then rotate the leveling screw to make the sensor reading reach the closest value to 0. In addition, when the lower end of the centering pole is connected to the reference point, and the leveling mechanism is adjusted horizontally, the entire calibration device can rotate 360° around the vertical direction of the reference point, so that the target pole can be observed by multiple cameras, so that multiple Cameras are calibrated simultaneously.

基于上述装置，本发明提供一种相机外参数标定方法，相机外参数标定的方法流程如下：Based on the above-mentioned device, the present invention provides a camera extrinsic parameter calibration method, and the process flow of the camera extrinsic parameter calibration method is as follows:

步骤1)、对外参数标定的相机现进行内参数标定，内参数包括：相机的光心坐标、等效焦距和畸变系数；Step 1), the camera calibrated with external parameters is now calibrated with internal parameters, and the internal parameters include: optical center coordinates, equivalent focal length and distortion coefficient of the camera;

步骤2)、在标定杆安放位置预埋有四个测量基准点，每个测量基准点的在基准坐标系下的坐标事前已测量得到；Step 2), four measurement reference points are pre-embedded in the position where the calibration rod is placed, and the coordinates of each measurement reference point in the reference coordinate system have been measured in advance;

步骤3)、首先将靶标下方的对中杆放置在点位1上，然后调整标定杆支架底部的两个调平机构使整个靶标杆垂直于水平面，如图5所示。在靶标杆底部的安装平板上有倾斜量传感器，可根据其读数判断当前位置是否已调平；Step 3), first place the centering rod below the target on point 1, and then adjust the two leveling mechanisms at the bottom of the calibration rod bracket so that the entire target rod is perpendicular to the horizontal plane, as shown in Figure 5. There is a tilt sensor on the mounting plate at the bottom of the target pole, and it can be judged whether the current position has been leveled according to its reading;

步骤4)、然后使用相机拍摄当前的靶标杆图像并记录。接着将靶标杆移动到点位2，重复上述对准和调平的过程，然后拍摄在点位2处的靶标杆图像。直到四个点位的图像拍摄完毕；Step 4), then use the camera to shoot the current target rod image and record it. Then move the target rod to point 2, repeat the alignment and leveling process above, and then take an image of the target rod at point 2. Until the images of the four points are taken;

步骤5)、根据预先标定四个基准点在基准坐标系下的坐标，可以标定装置调节水平后，其平面板上的十个标志点在基准坐标系下的坐标；Step 5), according to pre-marking the coordinates of four reference points under the reference coordinate system, the coordinates of the ten mark points on the plane plate under the reference coordinate system after the adjustment of the level of the device can be calibrated;

步骤6)、通过外参数标定装置采集四幅圆形标志点图像，如图6所示，利用椭圆拟合的方法提取标志点中心坐标，通过拼接，组合成四十个标志点成像数据；Step 6), collect four circular marker point images through the external parameter calibration device, as shown in Figure 6, use the method of ellipse fitting to extract the central coordinates of the marker points, and combine them into forty marker point imaging data by splicing;

步骤7)、输入标志点在基准坐标系下的坐标和成像提取的像素坐标，以及相机内参数，计算相机外参数，即相机相对于基准坐标系的平移向量(光心位置)和相机坐标系到基准坐标系的旋转矩阵。Step 7), input the coordinates of the marker point in the reference coordinate system and the pixel coordinates extracted by imaging, and the camera internal parameters, and calculate the camera external parameters, that is, the translation vector (optical center position) of the camera relative to the reference coordinate system and the camera coordinate system Rotation matrix to the base coordinate system.

进一步的，对于多个相机，标定装置可以基准点为中心进行旋转，使标志点平面对着需要标定的相机，重复步骤5)至步骤7)，可以完成所有相机的标定。Further, for multiple cameras, the calibration device can be rotated around the reference point, so that the plane of the marker points faces the camera to be calibrated, and steps 5) to 7) are repeated to complete the calibration of all cameras.

与现有技术相比，本发明有益效果如下：Compared with the prior art, the beneficial effects of the present invention are as follows:

1)、该发明通过测量基准坐标系下所有标定相机的基准点坐标，就可实现多台相机立体标定，且测量范围广；1), the invention can realize multi-camera stereo calibration by measuring the reference point coordinates of all calibration cameras under the reference coordinate system, and the measurement range is wide;

2)、通过四十个标志点建立标定参照物的三维坐标已知点和图像点的对应关系，采用非线性方法来计算相机外参数，可以得到较高的测量精度；2) Establish the corresponding relationship between the known three-dimensional coordinates of the calibration reference object and the image points through forty marker points, and use a nonlinear method to calculate the external parameters of the camera, which can obtain higher measurement accuracy;

3)、该标定装置加工成本低，使用方便简单，可重复多次使用。3). The calibration device has low processing cost, is convenient and simple to use, and can be used repeatedly.

附图说明Description of drawings

图1为相机外参数标定装置的组成结构图；FIG. 1 is a structural diagram of a calibration device for extrinsic camera parameters;

图2为相机外参数标定方法流程；Fig. 2 is the flow chart of the camera extrinsic parameter calibration method;

图3为相机内参数标定图像；Figure 3 is a calibration image of the internal parameters of the camera;

图4为相机内参数标定图像标志点提取示意图；Fig. 4 is a schematic diagram of extracting marker points from the camera internal parameter calibration image;

图5为相机外参数标定时采集的图像，(a)为标定装置安放在基准点位1时采集的标定图像，(b)为标定装置安放在基准点位2时采集的标定图像，(c)为标定装置安放在基准点位3时采集的标定图像，(d)为标定装置安放在基准点位4时采集的标定图像；Figure 5 shows the images collected when the external parameters of the camera are calibrated, (a) is the calibration image collected when the calibration device is placed at the reference point 1, (b) is the calibration image collected when the calibration device is placed at the reference point 2, (c ) is the calibration image collected when the calibration device is placed at the reference point 3, and (d) is the calibration image collected when the calibration device is placed at the reference point 4;

图6为相机外参数标定图像标志点提取示意图。Fig. 6 is a schematic diagram of extracting marker points from a camera extrinsic parameter calibration image.

具体实施方式Detailed ways

下面结合附图以及具体实施例进一步说明本发明。The present invention will be further described below in conjunction with the accompanying drawings and specific embodiments.

步骤1)、对每台相机进行内参数标定，即将内参数标定板放置在相机前方2米位置，如图3所示，变化标定板的方位和姿态，采集20幅标定板图像，提取每幅图像的标志点坐标，如图4所示，进行内参数标定，并保存标定结果；Step 1), perform internal parameter calibration for each camera, that is, place the internal parameter calibration board at a position 2 meters in front of the camera, as shown in Figure 3, change the orientation and attitude of the calibration board, collect 20 calibration board images, and extract each The marker point coordinates of the image, as shown in Figure 4, carry out internal parameter calibration, and save the calibration result;

步骤2)、根据相机的视场范围，在标定杆安放位置预埋有四个测量基准点，每个测量基准点的在基准坐标系下的坐标事前已测量得到，第i个基准点坐标记为：Step 2), according to the field of view of the camera, there are four measurement reference points embedded in the position of the calibration rod, and the coordinates of each measurement reference point in the reference coordinate system have been measured in advance, and the i-th reference point coordinate mark for:

${P P}_{i i}^{G G} = = {(({X x}_{i i}^{G G},, {Y Y}_{i i}^{G G},, {Z Z}_{i i}^{G G}))}^{T T},, {{i i = = 1,2,3,4 1,2,3,4}}$

其中，i为基准点序号，为第i个基准点在基准坐标系下三维坐标，为第i个基准点在基准坐标系下的三维坐标X分量，为第i个基准点在基准坐标系下的三维坐标Y分量，为第i个基准点在基准坐标系下的三维坐标Z分量。Among them, i is the serial number of the datum point, is the three-dimensional coordinates of the i-th datum point in the datum coordinate system, is the three-dimensional coordinate X component of the i-th datum point in the datum coordinate system, is the three-dimensional coordinate Y component of the i-th datum point in the datum coordinate system, is the three-dimensional coordinate Z component of the i-th datum point in the datum coordinate system.

步骤3)、首先将靶标下方的对中杆放置在点位1上，如图5图像(a)中所示，然后调整标定杆支架底部的两个调平机构使三角支撑平面水平，整个靶标杆垂直于水平面，在靶标杆底部的安装平板上有倾斜量传感器，可根据其读数判断当前位置是否已调平；Step 3), first place the centering rod below the target on point 1, as shown in Figure 5 (a), then adjust the two leveling mechanisms at the bottom of the calibration rod bracket to make the triangular support plane horizontal, and the entire target The benchmark pole is perpendicular to the horizontal plane, and there is a tilt sensor on the installation plate at the bottom of the target pole, which can judge whether the current position has been leveled according to its reading;

步骤4)、然后使用相机拍摄当前的靶标杆图像并记录。接着将靶标杆移动到点位2，重复上述对准和调平的过程，然后拍摄在点位2处的靶标杆图像，直到四个点位的图像拍摄完毕；Step 4), then use the camera to shoot the current target rod image and record it. Then move the target rod to point 2, repeat the above-mentioned alignment and leveling process, and then shoot the image of the target rod at point 2 until the images of the four points are taken;

步骤5)、当标定装置调平机构调节水平，对中杆调垂直后，根据预先标定四个基准点在基准坐标系下的坐标和标定装置上参考标志点设计位置和尺寸，可以计算靶标杆上的十个标志点在基准坐标系下的坐标，标志点从下到上，第i个基准点位上第j个标志点三维坐标记为：Step 5), when the leveling mechanism of the calibration device is adjusted horizontally and the centering rod is vertically adjusted, the target rod can be calculated according to the coordinates of the four reference points pre-calibrated in the reference coordinate system and the design position and size of the reference mark point on the calibration device The coordinates of the ten marker points above in the reference coordinate system, the marker points are from bottom to top, and the three-dimensional coordinates of the jth marker point on the ith reference point are marked as:

${P P}_{ij ij}^{G G} = = {(({X x}_{ij ij}^{G G},, {Y Y}_{ij ij}^{G G},, {Z Z}_{ij ij}^{G G}))}^{T T},, {{i i = = 1,2,3,4 1,2,3,4;; j j = = 0,1 0,1,, . . . . . .,, 99}}$

其中，i为基准点序号，j为标志点序号，为第i个基准点位上第j个标志点在基准坐标系下三维坐标，为该三维坐标X分量，为该三维坐标Y分量，为该三维坐标Z分量。已知每个标志点到基准点位固定端的垂直距离，记为L_j，则：Among them, i is the reference point serial number, j is the marker point serial number, is the three-dimensional coordinates of the j-th marker point on the i-th datum point in the datum coordinate system, is the three-dimensional coordinate X component, is the Y component of the three-dimensional coordinates, is the Z component of the three-dimensional coordinates. The vertical distance from each marker point to the fixed end of the reference point is known, denoted as L _j , then:

${P P}_{ij ij}^{G G} = = {P P}_{i i}^{G G} + + [\begin{matrix} 00 & 11 & 00 \end{matrix}] {L L}_{j j},, {{i i = = 1,2,3,4 1,2,3,4;; j j = = 0,1 0,1,, . . . . . .,, 99}}$

其中，i为基准点序号，j为标志点序号，为i个基准点位上第j个标志点在基准坐标系下三维坐标，为i个基准点在基准坐标系下三维坐标，L_j为第j个标志点到基准点位固定端的垂直距离。Among them, i is the reference point serial number, j is the marker point serial number, is the three-dimensional coordinates of the jth marker point on the i reference point in the reference coordinate system, is the three-dimensional coordinates of the i reference point in the reference coordinate system, and L _j is the vertical distance from the jth marker point to the fixed end of the reference point.

步骤6)、通过外参数标定装置采集四幅圆形标志点图像，如图6所示，利用椭圆拟合的方法提取标志点中心坐标，通过四幅图像提取点坐标，组合成四十个标志点成像数据；Step 6), collect four circular marker point images through the external parameter calibration device, as shown in Figure 6, use the ellipse fitting method to extract the center coordinates of the marker points, extract the point coordinates through the four images, and combine them into forty marker point images data;

步骤7)、根据中心透视投影成像摄影测量原理，输入标志点在基准坐标系下的坐标和成像提取的像素坐标，具有以下关系：Step 7), according to the principle of central perspective projection imaging photogrammetry, the coordinates of the input marker points in the reference coordinate system and the pixel coordinates extracted by imaging have the following relationship:

$k k \cdot &Center Dot; [\begin{matrix} {X x}_{ij ij} \\ {Y Y}_{ij ij} \\ 11 \end{matrix}] = = [\begin{matrix} {F f}_{x x} & 00 & {C C}_{x x} & 00 \\ 00 & {F f}_{y the y} & {C C}_{y the y} & 00 \\ 00 & 00 & 11 & 00 \end{matrix}] [\begin{matrix} {R R}_{g g 22 x x} & {T T}_{g g 22 x x} \\ 00^{T T} & 11 \end{matrix}] [\begin{matrix} {X x}_{ij ij}^{G G} \\ {Y Y}_{ij ij}^{G G} \\ {Z Z}_{ij ij}^{G G} \\ 11 \end{matrix}]$

其中，(X_ij,Y_ij),{i＝1,2,3,4；j＝0,1,…,9}为第i个基准点位对应的第j个标志点提取的像素坐标，k为标志点在相机坐标系下三维坐标的Z分量，(C_x,C_y)为图像主点，是光轴与像面交点的图像坐标，(F_x,F_y)为横纵向等效焦距，是实际光学焦距与像元的横、纵向尺寸之比，R_g2x为基准坐标系到相机坐标系的旋转矩阵，T_g2x为基准坐标系到相机坐标系的平移向量。主点和等效焦距是相机的内参数，描述相机本身的特性；而旋转矩阵和平移向量描述的是基准坐标系与相机坐标系间的相对位置关系和姿态关系，通过该旋转矩阵和平移向量，可以反求出相机坐标系到基准坐标系的旋转矩阵和平移向量，即相机的外参数。R_g2x和T_g2x定义如下：Among them, (X _ij ,Y _ij ), {i=1,2,3,4; j=0,1,...,9} is the pixel coordinate extracted from the jth marker point corresponding to the ith reference point, k is the Z component of the three-dimensional coordinates of the marker point in the camera coordinate system, (C _x , C _y ) is the principal point of the image, and is the image coordinate of the intersection point of the optical axis and the image plane, (F _x , F _y ) is the horizontal and vertical equivalent The focal length is the ratio of the actual optical focal length to the horizontal and vertical dimensions of the pixel, R _g2x is the rotation matrix from the reference coordinate system to the camera coordinate system, and T _g2x is the translation vector from the reference coordinate system to the camera coordinate system. The principal point and equivalent focal length are the internal parameters of the camera, which describe the characteristics of the camera itself; while the rotation matrix and translation vector describe the relative position and attitude relationship between the reference coordinate system and the camera coordinate system, through the rotation matrix and translation vector , the rotation matrix and translation vector from the camera coordinate system to the reference coordinate system can be obtained inversely, that is, the external parameters of the camera. R _g2x and T _g2x are defined as follows:

${R R}_{g g 22 x x} = = [\begin{matrix} {r r}_{00} & {r r}_{11} & {r r}_{22} \\ {r r}_{33} & {r r}_{44} & {r r}_{55} \\ {r r}_{66} & {r r}_{77} & {r r}_{88} \end{matrix}]$

T_g2x＝(T_x,T_y,T_z)^T T _g2x ＝(T _x ,T _y ,T _z ) ^T

步骤8)、定义一个投影矩阵M：Step 8), define a projection matrix M:

$M m = = [\begin{matrix} {F f}_{x x} & 00 & {C C}_{x x} & 00 \\ 00 & {F f}_{y the y} & {C C}_{y the y} & 00 \\ 00 & 00 & 11 & 00 \end{matrix}] [\begin{matrix} {R R}_{g g 22 x x} & {T T}_{g g 22 x x} \\ 00^{T T} & 11 \end{matrix}]$

M的展开式：The expansion of M:

$M m = = [\begin{matrix} {m m}_{00} & {m m}_{11} & {m m}_{22} & {m m}_{33} \\ {m m}_{44} & {m m}_{55} & {m m}_{66} & {m m}_{77} \\ {m m}_{88} & {m m}_{99} & {m m}_{1010} & {m m}_{1111} \end{matrix}] = = [\begin{matrix} {F f}_{x x} {r r}_{00} + + {C C}_{x x} {r r}_{66} & {F f}_{x x} {r r}_{11} + + {C C}_{x x} {r r}_{77} & {F f}_{x x} {r r}_{22} + + {C C}_{x x} {r r}_{88} & {F f}_{x x} {T T}_{x x} + + {C C}_{x x} {T T}_{z z} \\ {F f}_{y the y} {r r}_{33} + + {C C}_{y the y} {r r}_{66} & {F f}_{y the y} {r r}_{44} + + {C C}_{y the y} {r r}_{77} & {F f}_{y the y} {r r}_{55} + + {C C}_{y the y} {r r}_{88} & {F f}_{y the y} {T T}_{y the y} + + {C C}_{y the y} {T T}_{z z} \\ {r r}_{66} & {r r}_{77} & {r r}_{88} & {T T}_{z z} \end{matrix}]$

则中心透视投影成像关系可以用投影矩阵描述为：Then the central perspective projection imaging relationship can be described by the projection matrix as:

$k k [\begin{matrix} {X x}_{ij ij} \\ {Y Y}_{ij ij} \\ 11 \end{matrix}] = = M m [\begin{matrix} {X x}_{ij ij}^{G G} \\ {Y Y}_{ij ij}^{G G} \\ {Z Z}_{ij ij}^{G G} \\ 11 \end{matrix}]$

将上式展开成纯量形式并消去k，就得到描述中心透视投影成像中的物点、像点、光心三点共线关系的共线方程：Expanding the above formula into a scalar form and eliminating k, the collinear equation describing the collinear relationship of the object point, image point, and optical center in central perspective projection imaging is obtained:

$\{\begin{matrix} \frac{{X x}_{ij ij} - - {C C}_{x x}}{{F f}_{x x}} = = \frac{{r r}_{00} {X x}_{ij ij}^{G G} + + {r r}_{11} {Y Y}_{ij ij}^{G G} + + {r r}_{22} {Z Z}_{ij ij}^{G G} + + {T T}_{x x}}{{r r}_{66} {X x}_{ij ij}^{G G} + + {r r}_{77} {Y Y}_{ij ij}^{G G} + + {r r}_{88} {Z Z}_{ij ij}^{G G} + + {T T}_{z z}} \\ \frac{{Y Y}_{ij ij} - - {C C}_{y the y}}{{F f}_{y the y}} = = \frac{{r r}_{33} {X x}_{ij ij}^{G G} + + {r r}_{44} {Y Y}_{ij ij}^{G G} + + {r r}_{55} {Z Z}_{ij ij}^{G G} + + {T T}_{y the y}}{{r r}_{66} {X x}_{ij ij}^{G G} + + {r r}_{77} {Y Y}_{ij ij}^{G G} + + {r r}_{88} {Z Z}_{ij ij}^{G G} + + {T T}_{z z}} \end{matrix}$

当内参数已知，则通过移项将上式转化为关于T_x、T_y、T_z和r₀～r₉的齐次线性方程组：When the internal parameters are known, the above formula can be transformed into a homogeneous linear equation system about T _x , _Ty , T _z and r ₀ ~ r ₉ through transposition:

$\{\begin{matrix} {r r}_{00} {X x}_{ij ij}^{G G} + + {r r}_{11} {Y Y}_{ij ij}^{G G} + + {r r}_{22} {Z Z}_{ij ij}^{G G} + + {T T}_{x x} - - \frac{{X x}_{ij ij} - - {C C}_{x x}}{{F f}_{x x}} (({r r}_{66} {X x}_{ij ij}^{G G} + + {r r}_{77} {Y Y}_{ij ij}^{G G} + + {r r}_{88} {Z Z}_{ij ij}^{G G} + + {T T}_{z z})) = = 00 \\ {r r}_{33} {X x}_{ij ij}^{G G} + + {r r}_{44} {Y Y}_{ij ij}^{G G} + + {r r}_{55} {Z Z}_{ij ij}^{G G} + + {T T}_{y the y} - - \frac{{Y Y}_{ij ij} - - {C C}_{y the y}}{{F f}_{y the y}} (({r r}_{66} {X x}_{ij ij}^{G G} + + {r r}_{77} {Y Y}_{ij ij}^{G G} + + {r r}_{88} {Z Z}_{ij ij}^{G G} + + {T T}_{z z})) = = 00 \end{matrix}$

由于T_z＞0，可令t_i＝r_i/T_z，i＝0，1，…，8，t₉＝T_x/T_z，t₁₀＝T_y/T_z，上式可以转化为关于t₀～t₁₀的线性方程组：Since T _z >0, t _i =r _i /T _z , i=0, 1,...,8, t ₉ =T _x /T _z , t ₁₀ =T _y /T _z , the above formula can be transformed into About the linear equation system of t ₀ ~ t ₁₀ :

$\{\begin{matrix} {X x}_{ij ij}^{G G} {t t}_{00} + + {Y Y}_{ij ij}^{G G} {t t}_{11} + + {Z Z}_{ij ij}^{G G} {t t}_{22} + + {t t}_{99} - - \frac{{X x}_{ij ij} - - {C C}_{x x}}{{F f}_{x x}} (({X x}_{ij ij}^{G G} {t t}_{66} + + {Y Y}_{ij ij}^{G G} {t t}_{77} + + {Z Z}_{ij ij}^{G G} {t t}_{88})) = = \frac{{X x}_{ij ij} - - {C C}_{x x}}{{F f}_{x x}} \\ {X x}_{ij ij}^{G G} {t t}_{33} + + {Y Y}_{ij ij}^{G G} {t t}_{44} + + {Z Z}_{ij ij}^{G G} {t t}_{55} + + {t t}_{1010} - - \frac{{Y Y}_{ij ij} - - {C C}_{y the y}}{{F f}_{y the y}} (({X x}_{ij ij}^{G G} {t t}_{66} + + {Y Y}_{ij ij}^{G G} {t t}_{77} + + {Z Z}_{ij ij}^{G G} {t t}_{88})) = = \frac{{Y Y}_{ij ij} - - {C C}_{y the y}}{{F f}_{y the y}} \end{matrix}$

其中未知数11个，而从每个标志点可以列出两个方程，当标志点在基准坐标系下的三维坐标{i＝1,2,3,4；j＝0,1,…,9}和标志点提取坐标(X_ij,Y_ij),{i＝1,2,3,4；j＝0,1,…,9}已知，通过40个标志点对应的方程组，计算得到t₀～t₁₀。再根据r₆ ²+r₇ ²+r₈ ²＝1，有 $t_{6}^{2} + t_{7}^{2} + t_{8}^{2} = \frac{1}{T_{z}^{2}},$ 则：Among them, there are 11 unknowns, and two equations can be listed from each marker point, when the three-dimensional coordinates of the marker point in the reference coordinate system {i=1,2,3,4; j=0,1,...,9} and marker point extraction coordinates (X _ij ,Y _ij ), {i=1,2,3,4; j=0,1 ,…,9} are known, through the equations corresponding to 40 marker points, t ₀ ～t ₁₀ can be calculated. Then according to r ₆ ² +r ₇ ² +r ₈ ² =1, we have $t_{6}^{2} + t_{7}^{2} + t_{8}^{2} = \frac{1}{T_{z}^{2}},$ but:

${T T}_{z z} = = \frac{11}{\sqrt{{t t}_{66}^{22} + + {t t}_{77}^{22} + + {t t}_{88}^{22}}}$

进而得到旋转矩阵和平移向量的另外两个分量r_i＝t_iT_z,(i＝0,1,…,8)和T_x＝t₉T_z,T_y＝t₁₀T_z，从而计算出基准坐标系到相机坐标系的旋转矩阵R_g2x和平移向量T_g2x，进而推出相机坐标系到基准坐标系的旋转矩阵为和平移向量完成该相机的外参数标定。Then get the other two components r _i =t _i T _z ,(i=0,1,…,8) and T _x =t ₉ T _z ,T _y =t ₁₀ T _z of the rotation matrix and translation vector, so as to calculate The rotation matrix R _g2x and the translation vector T _g2x from the reference coordinate system to the camera coordinate system are obtained, and then the rotation matrix from the camera coordinate system to the reference coordinate system is deduced as and translation vector The extrinsic parameter calibration of the camera is completed.

进一步的，若同时标定多台相机，当靶标杆处于某一基准点位，对中杆下端与基准点位连接后，且调平机构调整水平时，可以使标定装置绕基准点竖直方向旋转，使得靶标标志点能够被下一台相机观测到，并拍摄靶标图像，从而完成多台相机标定。Further, if multiple cameras are calibrated at the same time, when the target rod is at a certain reference point, the lower end of the centering rod is connected to the reference point, and when the leveling mechanism is adjusted horizontally, the calibration device can be rotated vertically around the reference point , so that the target mark point can be observed by the next camera, and the target image is taken, thereby completing the calibration of multiple cameras.

Claims

1. A camera external parameter calibration device for photogrammetry, characterized in that it is composed of four parts: a target rod, a centering rod, a leveling mechanism and a measurement reference point; the target rod is above the calibration rod mechanism, and the target rod is a cuboid , there are 10 circular marking points in a row installed on the target, and the center of the marking points is arranged in a straight line on the target plane; below the target rod is a centering rod, which is used to align the measurement reference point to ensure the position accuracy of the calibration erection, and the marking points The connecting line is on the same straight line as the axis of the centering rod, and the distance from the center of each mark point to the bottom of the centering rod is known; if the position coordinates of the reference point below the calibration rod are known, when the centering rod is perpendicular to the horizontal plane, then Through the pre-calibrated reference point coordinates, the coordinates of the center of each circular mark point in the reference coordinate system can be obtained, wherein the Y-axis of the reference coordinate system is perpendicular to the horizontal plane. The leveling mechanism is as follows: behind the centering rod there is Two support rods, the centering rod is perpendicular to the plane formed by the two support rods, there is a leveling screw at the bottom of the support rod close to the ground, which is used to adjust the level, fixed on the stage by the tilt angle sensor, and then adjusted by rotation Flat screw to make the sensor reading reach the closest value to 0; in addition, when the lower end of the centering rod is connected to the reference point, and the leveling mechanism is adjusted horizontally, the entire calibration device can rotate 360° around the reference point in the vertical direction. The target pole can be observed by multiple cameras, so that multiple cameras can be calibrated simultaneously.

2. A camera external parameter calibration method for photogrammetry, utilizing the calibration device described in claim 1, characterized in that the external parameter calibration method process is as follows:

Step 1), 4 measurement datum points are pre-buried in the placement position of the calibration rod, and their three-dimensional coordinates under the datum coordinate system have been measured in advance;

Step 2), first place the centering rod below the target on point 1, then adjust the leveling mechanism at the bottom of the calibration rod bracket so that the entire target rod is perpendicular to the horizontal plane, as shown in Figure 5; the mounting plate at the bottom of the target rod There is an inclination sensor on it, which can judge whether the current position has been leveled according to its reading;

Step 3), then use the camera to take the current target pole image and record it; then move the target pole to point 2, repeat the above-mentioned alignment and leveling process, and then shoot the target pole image at point 2; until 4 After the images of the points are captured, the calibration of the external parameters of the camera is completed;

Step 4), if multiple cameras are calibrated at the same time, when the target rod is at a certain reference point, the calibration device can be rotated vertically around the reference point, so that the target mark point can be observed by the next camera, and the target can be photographed images, thereby simplifying the calibration process of multiple cameras and completing the calibration of multiple cameras;

Step 5), according to pre-marking the coordinates of four reference points under the reference coordinate system, the coordinates of the ten mark points on the plane plate under the reference coordinate system after the adjustment of the level of the device can be calibrated;

Step 6), collect four circular marker point images through the external parameter calibration device, use the method of ellipse fitting to extract the central coordinates of the marker points, and combine them into forty marker point imaging data by splicing;

Step 7), input the coordinates of the marker point in the reference coordinate system and the pixel coordinates extracted by imaging, as well as the internal parameters of the camera, and calculate the external parameters of the camera, that is, the optical center position of the camera in the reference coordinate system and the rotation from the camera coordinate system to the reference coordinate system matrix.

3. according to the said camera extrinsic parameter calibration method of claim 2, it is characterized in that, for a plurality of cameras, the calibration device can rotate around the reference point, so that the marker point plane is facing the camera that needs to be calibrated, repeating step 5)-step 7), can complete the calibration of all cameras.