CN110060305B - High-precision simplified linear array camera calibration method - Google Patents

High-precision simplified linear array camera calibration method Download PDF

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CN110060305B
CN110060305B CN201910294845.9A CN201910294845A CN110060305B CN 110060305 B CN110060305 B CN 110060305B CN 201910294845 A CN201910294845 A CN 201910294845A CN 110060305 B CN110060305 B CN 110060305B
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梁灵飞
鲍秋旭
董永生
杨春蕾
刘中华
普杰信
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Henan University of Science and Technology
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Abstract

A high-precision simplified linear array camera calibration method is disclosed, in which the internal relation r in the rotary matrix of the linear array camera imaging model is derived 1 T r 1 ＝r 2 T r 2 1 and r 1 T r 2 0, and A ‑T A ‑1 Forming a symmetric matrix, forming an overrun equation
Figure DDA0002026145360000011
More than 2H matrixes can be obtained by selecting coordinates (X, Y) of a target point to coordinates (u) of an imaging point in more than 2 calibration plates with different angles or different distances, an equation is established, and a parameter B is solved 11 ，B 12 ，B 22 And then obtaining the internal and external parameters of the linear array camera. The method has simple system and less unknown parameter calculation, and has important significance and practical value for the application of the linear array camera calibration.

Description

一种高精度简化式线阵相机标定方法A high-precision simplified line scan camera calibration method

技术领域technical field

本发明属于相机标定领域，具体说的是一种高精度简化式线阵相机标定方法。The invention belongs to the field of camera calibration, in particular to a high-precision simplified line array camera calibration method.

背景技术Background technique

摄像机的标定是确定空间摄像机标定是非常关键的环节，其标定结果的精度及算法的稳定性将直接影响摄像机工作产生结果的准确性。因此，提高摄像机标定精度是摄像机标定的重点。The calibration of the camera is a very critical link to determine the calibration of the space camera. The accuracy of the calibration results and the stability of the algorithm will directly affect the accuracy of the results produced by the camera work. Therefore, improving the camera calibration accuracy is the focus of camera calibration.

由于线阵相机每次成像只能成像一行，线阵成像模型不同于传统的面阵相机成像模型，导致适用于面阵相机的内外参数计算方法不适用于线阵相机。现有的线阵相机内外参数约束方程较复杂，因此，根据线阵相机的成像模型建立简单有效的约束方程，具有现实的研究价值和实际应用价值。Because the line scan camera can only image one line at a time, the line scan imaging model is different from the traditional area scan camera imaging model, so the calculation method of internal and external parameters suitable for the area scan camera is not suitable for the line scan camera. Existing line scan camera internal and external parameter constraint equations are relatively complex. Therefore, establishing a simple and effective constraint equation based on the imaging model of the line scan camera has practical research value and practical application value.

发明专利《单线阵相机内外参数标定方法》所用求取3个单应性矩阵H时，需要知道标定板中特征点的在世界坐标系中的空间坐标，目前常用的标定板为平面标定板，空间坐标中的(X,Y)容易确定，但在Z方向的坐标需要运用精密定位设备才能得到；或运用立体标定物，但此类标定制作复杂，也不容易达到精度要求。When the three homography matrices H are obtained in the invention patent "Single-Line Array Camera Internal and External Parameters Calibration Method", it is necessary to know the spatial coordinates of the feature points in the calibration plate in the world coordinate system. At present, the commonly used calibration plate is a plane calibration plate. The (X, Y) in the space coordinates are easy to determine, but the coordinates in the Z direction need to be obtained by using precision positioning equipment; or using a three-dimensional calibration object, but such calibration is complicated to make and it is not easy to meet the accuracy requirements.

本发明通过理论推导，摒弃对特征点Z方向的精度要求，运用平面标定板可达到同样的高精度标定效果，对标定物的需求低，标定过程方便。如何摒弃特征点Z方向的精度要求，不影响标定后的高精度，是目前所要解决的技术问题。Through theoretical derivation, the invention abandons the precision requirement for the Z direction of the feature point, and can achieve the same high-precision calibration effect by using a plane calibration plate, has low demand for calibration objects, and facilitates the calibration process. How to abandon the accuracy requirements of the feature point Z direction, without affecting the high accuracy after calibration, is a technical problem to be solved at present.

发明内容SUMMARY OF THE INVENTION

为解决上述技术问题，本发明提供一种高精度简化式线阵相机标定方法，对原有的标定方法进行简化，在不影响标定精度的同时，只利用容易确定的空间坐标完成线阵相机标定。In order to solve the above technical problems, the present invention provides a high-precision simplified line scan camera calibration method, which simplifies the original calibration method, and only uses easily determined spatial coordinates to complete the line scan camera calibration without affecting the calibration accuracy. .

为实现上述技术目的，所采用的技术方案是：一种高精度简化式线阵相机标定方法，包括以下步骤：In order to achieve the above technical purpose, the adopted technical solution is: a high-precision simplified line scan camera calibration method, comprising the following steps:

步骤1、根据面阵相机成像模型，推导出线阵相机成像模型，得到单应性矩阵H模型Step 1. According to the imaging model of the area scan camera, deduce the imaging model of the line scan camera, and obtain the homography matrix H model

Figure BDA0002026145340000021
Figure BDA0002026145340000021

步骤2、根据线阵相机成像模型，推导出线阵相机的内参数矩阵A和外参数矩阵[r1r2 t]；Step 2. According to the imaging model of the line scan camera, derive the internal parameter matrix A and the external parameter matrix [r 1 r 2 t] of the line scan camera;

步骤3、根据外参数矩阵中旋转参数矩阵r1 Tr1＝r2 Tr2＝1和r1 Tr1＝0，推导出内参数A中参数与单应性矩阵H中参数的联系

Figure BDA0002026145340000024
Step 3. According to the rotation parameter matrix r 1 T r 1 =r 2 T r 2 =1 and r 1 T r 1 =0 in the external parameter matrix, deduce the relationship between the parameters in the internal parameter A and the parameters in the homography matrix H
Figure BDA0002026145340000024

步骤4、计算A-TA-1的矩阵，并设B11、B12、B22替换A-TA-1矩阵中的参数，代入

Figure BDA0002026145340000025
得到
Figure BDA0002026145340000026
步骤5、选取2副以上不同角度或不同距离标定板目标点坐标(X,Y)到成像点坐标(u)，计算得到2个以上的H矩阵，代入
Figure BDA0002026145340000027
式，运用最小二乘法得到B11、B12、B22的值；Step 4. Calculate the matrix of A- T A -1 , and set B 11 , B 12 , and B 22 to replace the parameters in the A- T A -1 matrix, and substitute them into
Figure BDA0002026145340000025
get
Figure BDA0002026145340000026
Step 5. Select more than 2 pairs of different angles or different distances from the target point coordinates (X, Y) of the calibration plate to the imaging point coordinates (u), calculate and obtain more than 2 H matrices, and substitute them into
Figure BDA0002026145340000027
formula, use the least squares method to obtain the values of B 11 , B 12 , and B 22 ;

步骤6、根据B11、B12、B22计算内参数矩阵A，再根据内参数矩阵A，任取一个步骤五得到的H矩阵，计算外参数矩阵[r1 r2 t]。Step 6: Calculate the internal parameter matrix A according to B 11 , B 12 , and B 22 , and then according to the internal parameter matrix A, take any H matrix obtained in step 5, and calculate the external parameter matrix [r 1 r 2 t].

本发明所述的步骤1中单应性矩阵H模型的构成方法为：The composition method of the homography matrix H model in step 1 of the present invention is:

步骤1.1、面阵相机成像模型

Figure BDA0002026145340000028
Step 1.1, area scan camera imaging model
Figure BDA0002026145340000028

s为任意的实数；s is any real number;

步骤1.2、线阵相机的每次成像一行，根据面阵相机成像模型，可得到Step 1.2. The line scan camera images one line at a time. According to the imaging model of the area scan camera, we can get

Figure BDA0002026145340000029
Figure BDA0002026145340000029

步骤1.3、对步骤1.2中的成像模型再逆推，可得Step 1.3. Reverse the imaging model in step 1.2 to get

Figure BDA0002026145340000031
Figure BDA0002026145340000031

步骤1.4、假设z＝0，因此Step 1.4. Assume z=0, so

Figure BDA0002026145340000032
Figure BDA0002026145340000032

本发明所述的步骤2中内参数矩阵A和外参数矩阵[r1r2t]推导方法为：The derivation method of the internal parameter matrix A and the external parameter matrix [r 1 r 2 t] in step 2 of the present invention is:

步骤2.1、面阵相机的包括内外参数的成像模型Step 2.1. Imaging model of area scan camera including internal and external parameters

Figure BDA0002026145340000033
Figure BDA0002026145340000033

m＝[u v 1]T，M＝[x y z 1]T m=[uv 1] T , M=[xyz 1] T

步骤2.2、由于线阵相机的每次成像只能成像一行，因此根据面阵相机成像模型，假设z＝0，可得到Step 2.2. Since each imaging of the line scan camera can only image one line, according to the imaging model of the area scan camera, assuming z=0, we can get

Figure BDA0002026145340000034
Figure BDA0002026145340000034

步骤2.3、假设z＝0，因此Step 2.3. Assume z=0, so

Figure BDA0002026145340000035
Figure BDA0002026145340000035

本发明所述的步骤3中

Figure BDA0002026145340000036
推导方法为：In step 3 of the present invention
Figure BDA0002026145340000036
The derivation method is:

步骤3.1、由于[h1 h2 h4]＝sA[r 1r2 t]，可得Step 3.1. Since [h 1 h 2 h 4 ]=sA[r 1 r 2 t], we can get

h1＝sAr1或r1＝λA-1h1 h 1 =sAr 1 or r 1 =λA −1 h 1

h2＝sAr2或r2＝λA-1h2 h 2 =sAr 2 or r 2 =λA −1 h 2

h4＝sAt或t＝λA-1h4 h 4 =sAt or t=λA -1 h 4

Figure BDA0002026145340000041
Figure BDA0002026145340000041

步骤3.2、由于r1 Tr1＝r2 Tr2＝1和r1 Tr2＝0，将r1，r2代入，可得Step 3.2. Since r 1 T r 1 =r 2 T r 2 =1 and r 1 T r 2 =0, substituting r 1 and r 2 into

Figure BDA0002026145340000042
Figure BDA0002026145340000042

本发明所述的步骤4中

Figure BDA0002026145340000043
推导方法为：In step 4 of the present invention
Figure BDA0002026145340000043
The derivation method is:

步骤4.1、计算A-TA-1 Step 4.1. Calculate A -T A -1

Figure BDA0002026145340000044
Figure BDA0002026145340000044

步骤4.2、设定B11、B12、B22三参数替换A-TA-1矩阵中的参数；Step 4.2, set the three parameters of B 11 , B 12 and B 22 to replace the parameters in the A- T A -1 matrix;

Figure BDA0002026145340000045
Figure BDA0002026145340000045

步骤4.3、将B代入

Figure BDA0002026145340000046
得Step 4.3. Substitute B into
Figure BDA0002026145340000046
have to

Figure BDA0002026145340000047
Figure BDA0002026145340000047

本发明所述的步骤6中的内参数矩阵A以及外参数矩阵[r1r2t]的计算方法如下：The calculation methods of the internal parameter matrix A and the external parameter matrix [r 1 r 2 t] in step 6 of the present invention are as follows:

步骤6.1设

Figure BDA0002026145340000048
由
Figure BDA0002026145340000049
得Step 6.1 set
Figure BDA0002026145340000048
Depend on
Figure BDA0002026145340000049
have to

Figure BDA0002026145340000051
Figure BDA0002026145340000051

cu＝-B12/B11 c u = -B 12 /B 11

Figure BDA0002026145340000052
Figure BDA0002026145340000052

步骤6.2、将fu，cu代入A，得内参数矩阵A；Step 6.2. Substitute f u and c u into A to obtain the internal parameter matrix A;

步骤6.3、任取步骤5得到的H矩阵，将A、H代入λ＝1/s＝1/||A-1h1||＝1/||A-1h2||，可得λ，进一步代入r1＝λA-1h1，r2＝λA-1h2，t＝λA-1h4，可得外参数矩阵[r1 r2 t]。Step 6.3. Take the H matrix obtained in step 5 arbitrarily, and substitute A and H into λ=1/s=1/||A -1 h 1 ||=1/||A -1 h 2 ||, to obtain λ , and further substitute r 1 =λA -1 h 1 , r 2 =λA -1 h 2 , t=λA -1 h 4 , the external parameter matrix [r 1 r 2 t] can be obtained.

本发明的有益效果是：采用本发明推出的线阵相机成像模型旋转矩阵中的内在联系r1 Tr1＝r2 Tr2＝1和r1 Tr2＝0，以及A-TA-1形成的对称矩阵，形成超限方程

Figure BDA0002026145340000053
只要选取2副以上不同角度或不同距离标定板中目标点坐标(X,Y)到成像点坐标(u)，就可得到2个以上的H矩阵，建立方程，求取参数B11，B12，B22，进而得到线阵相机的内外参数。本方法系统简单，未知参数求取少，对于线阵相机标定的应用具有重要意义和实用价值。The beneficial effects of the present invention are: adopting the intrinsic relationship r 1 T r 1 =r 2 T r 2 =1 and r 1 T r 2 =0 in the rotation matrix of the imaging model of the line scan camera deduced by the present invention, and A - T A A symmetric matrix formed by -1 forms a transfinite equation
Figure BDA0002026145340000053
As long as two or more pairs of different angles or different distances are selected from the target point coordinates (X, Y) in the calibration plate to the imaging point coordinates (u), more than two H matrices can be obtained, the equations can be established, and the parameters B 11 and B 12 can be obtained. , B 22 , and then obtain the internal and external parameters of the line scan camera. The method is simple in system, less unknown parameters are obtained, and has important significance and practical value for the application of line scan camera calibration.

附图说明Description of drawings

图1是本发明方法流程示意图。Fig. 1 is the schematic flow chart of the method of the present invention.

具体实施方式Detailed ways

为了更好地理解本发明的技术方案，下面结合附图对本发明的实施方式进行详细的说明。In order to better understand the technical solutions of the present invention, the embodiments of the present invention are described in detail below with reference to the accompanying drawings.

如图1所示，本发明根据外参数矩阵中旋转参数矩阵r1 Tr1＝r2 Tr2＝1和r1 Tr2＝0，推导出内参数中参数与单应性矩阵中参数的联系，建立约束方程，利用标定板目标点坐标(X,Y)到成像点坐标(u)，求出多个目标点到成像点单应性矩阵，代入约束方程，进而计算出线阵相机的内外参数。As shown in Fig. 1, the present invention derives the parameters in the internal parameters and the homography matrix according to the rotation parameter matrix r 1 T r 1 =r 2 T r 2 =1 and r 1 T r 2 =0 in the external parameter matrix. The relationship between the parameters, establish the constraint equation, use the target point coordinates (X, Y) of the calibration board to the imaging point coordinates (u), obtain the homography matrix from multiple target points to the imaging point, substitute the constraint equation, and then calculate the line array camera internal and external parameters.

本发明的具体实施如下：The specific implementation of the present invention is as follows:

一种高精度简化式线阵相机标定方法，包括以下步骤：A high-precision simplified line scan camera calibration method, comprising the following steps:

步骤1、根据面阵相机成像模型，推导出线阵相机成像模型，得到单应性矩阵H模型

Figure BDA0002026145340000061
Step 1. According to the imaging model of the area scan camera, deduce the imaging model of the line scan camera, and obtain the homography matrix H model
Figure BDA0002026145340000061

步骤1.1、面阵相机成像模型

Figure BDA0002026145340000062
Step 1.1, area scan camera imaging model
Figure BDA0002026145340000062

s为任意的实数。s is an arbitrary real number.

步骤1.2、线阵相机的每次成像一行，根据面阵相机成像模型，可得到Step 1.2. The line scan camera images one line at a time. According to the imaging model of the area scan camera, we can get

Figure BDA0002026145340000063
Figure BDA0002026145340000063

步骤1.3、对步骤1.2中的成像模型再逆推，可得Step 1.3. Reverse the imaging model in step 1.2 to get

Figure BDA0002026145340000064
Figure BDA0002026145340000064

步骤1.4、假设z＝0，因此Step 1.4. Assume z=0, so

Figure BDA0002026145340000065
Figure BDA0002026145340000065

步骤2、根据线阵相机成像模型，推导出线阵相机的内参数矩阵A和外参数矩阵[r1r2t]；Step 2. According to the imaging model of the line scan camera, derive the internal parameter matrix A and the external parameter matrix [r 1 r 2 t] of the line scan camera;

步骤2.1、面阵相机的包括内外参数的成像模型Step 2.1. Imaging model of area scan camera including internal and external parameters

Figure BDA0002026145340000066
Figure BDA0002026145340000066

m＝[u v 1]T，M＝[x y z 1]T m=[uv 1] T , M=[xyz 1] T

步骤2.2、由于线阵相机的每次成像只能成像一行，因此根据面阵相机成像模型，假设z＝0，可得到Step 2.2. Since each imaging of the line scan camera can only image one line, according to the imaging model of the area scan camera, assuming z=0, we can get

Figure BDA0002026145340000071
Figure BDA0002026145340000071

步骤2.3、假设z＝0，因此Step 2.3. Assume z=0, so

Figure BDA0002026145340000072
Figure BDA0002026145340000072

步骤3、根据外参数矩阵中旋转参数矩阵r1 Tr1＝r2 Tr2＝1和r1 Tr20推导出内参数A中参数与单应性矩阵H中参数的联系

Figure BDA0002026145340000075
Step 3. According to the rotation parameter matrix r 1 T r 1 =r 2 T r 2 =1 and r 1 T r 2 0 in the external parameter matrix, deduce the relationship between the parameters in the internal parameter A and the parameters in the homography matrix H
Figure BDA0002026145340000075

步骤3.1、由于[h1 h2 h4]＝sA[r1 r2 t]，可得Step 3.1. Since [h 1 h 2 h 4 ]=sA[r 1 r 2 t], we can get

h1＝sAr1或r1＝λA-1h1 h 1 =sAr 1 or r 1 =λA −1 h 1

h2＝sAr2或r2＝λA-1h2 h 2 =sAr 2 or r 2 =λA −1 h 2

h4＝sAt或t＝λA-1h4 h 4 =sAt or t=λA -1 h 4

Figure BDA0002026145340000076
Figure BDA0002026145340000076

步骤3.2、由于r1 Tr1＝r2 Tr2＝1和r1 Tr2＝0，将r1，r2代入，可得Step 3.2. Since r 1 T r 1 =r 2 T r 2 =1 and r 1 T r 2 =0, substituting r 1 and r 2 into

Figure BDA0002026145340000077
Figure BDA0002026145340000077

步骤4、计算A-TA-1的矩阵，并设B11，B12，B22替换A-TA-1矩阵中的参数，代入

Figure BDA0002026145340000078
得到Step 4. Calculate the matrix of A- T A -1 , and set B 11 , B 12 , B 22 to replace the parameters in the A- T A -1 matrix, and substitute them into
Figure BDA0002026145340000078
get

Figure BDA0002026145340000079
Figure BDA0002026145340000079

步骤4.1、计算A-TA-1 Step 4.1. Calculate A -T A -1

Figure BDA0002026145340000081
Figure BDA0002026145340000081

步骤4.2、设定B11、B12、B22三参数替换A-TA-1矩阵中的参数；Step 4.2, set the three parameters of B 11 , B 12 and B 22 to replace the parameters in the A- T A -1 matrix;

Figure BDA0002026145340000082
Figure BDA0002026145340000082

步骤4.3、将B代入

Figure BDA0002026145340000083
得Step 4.3. Substitute B into
Figure BDA0002026145340000083
have to

Figure BDA0002026145340000084
Figure BDA0002026145340000084

步骤5、选取2副以上不同角度或不同距离标定板目标点坐标(X,Y)到成像点坐标(u)，计算得到2个以上的H矩阵，代入

Figure BDA0002026145340000085
式，运用最小二乘法得到B11、B12、B22的值。Step 5. Select more than 2 pairs of different angles or different distances from the target point coordinates (X, Y) of the calibration plate to the imaging point coordinates (u), calculate and obtain more than 2 H matrices, and substitute them into
Figure BDA0002026145340000085
Formula, use the least squares method to obtain the values of B 11 , B 12 , and B 22 .

步骤6根据B11，B12，B22计算内参数矩阵A，再内参数矩阵A，任取一得到的H矩阵，计算外参数矩阵[r1 r2 t]；Step 6: Calculate the internal parameter matrix A according to B 11 , B 12 , and B 22 , then the internal parameter matrix A, take any one of the obtained H matrices, and calculate the external parameter matrix [r 1 r 2 t];

步骤6.1设

Figure BDA0002026145340000086
得Step 6.1 set
Figure BDA0002026145340000086
have to

Figure BDA0002026145340000087
Figure BDA0002026145340000087

cu＝-B12/B11 c u = -B 12 /B 11

Figure BDA0002026145340000088
Figure BDA0002026145340000088

步骤6.2、将fu、cu代入A，得内参数矩阵A；Step 6.2. Substitute f u and c u into A to obtain the internal parameter matrix A;

步骤6.3、任取步骤5得到的H矩阵，将A、H代入λ＝1/s＝1/||A-1h1||＝1/||A-1h2||，可得λ，进一步代入r1＝λA-1h1，r2＝λA-1h2，t＝λA-1h4，可得外参数矩阵[r1 r2 t]。Step 6.3. Take the H matrix obtained in step 5 arbitrarily, and substitute A and H into λ=1/s=1/||A -1 h 1 ||=1/||A -1 h 2 ||, to obtain λ , and further substitute r 1 =λA -1 h 1 , r 2 =λA -1 h 2 , t=λA -1 h 4 , the external parameter matrix [r 1 r 2 t] can be obtained.

尽管实施例对本发明进行了详细说明，本领域的普通技术人员应当理解，对本发明的技术方案进行修改或者等同替换，都不脱离本发明技术方案的精神和范围，其均应涵盖在本发明的权利要求范围当中。Although the embodiments describe the present invention in detail, those of ordinary skill in the art should understand that any modification or equivalent replacement of the technical solutions of the present invention will not depart from the spirit and scope of the technical solutions of the present invention, and should be included within the scope of the present invention. within the scope of the claims.

Claims (6)

1.一种高精度简化式线阵相机标定方法，其特征在于，包括以下步骤：1. a high-precision simplified linear array camera calibration method, is characterized in that, comprises the following steps: 步骤1、根据面阵相机成像模型，推导出线阵相机成像模型，得到单应性矩阵H模型Step 1. According to the imaging model of the area scan camera, deduce the imaging model of the line scan camera, and obtain the homography matrix H model
Figure FDA0002026145330000011
Figure FDA0002026145330000011
 步骤2、根据线阵相机成像模型，推导出线阵相机的内参数矩阵A和外参数矩阵[r1 r2t]；Step 2. According to the imaging model of the line scan camera, derive the internal parameter matrix A and the external parameter matrix [r 1 r 2 t] of the line scan camera; 步骤3、根据外参数矩阵中旋转参数矩阵r1 Tr1＝r2 Tr2＝1和r1 Tr2＝0，推导出内参数A中参数与单应性矩阵H中参数的联系
Figure FDA0002026145330000012
Step 3. According to the rotation parameter matrix r 1 T r 1 =r 2 T r 2 =1 and r 1 T r 2 =0 in the external parameter matrix, deduce the relationship between the parameters in the internal parameter A and the parameters in the homography matrix H
Figure FDA0002026145330000012
 步骤4、计算A-TA-1的矩阵，并设B11、B12、B22替换A-TA-1矩阵中的参数，代入
Figure FDA0002026145330000013
得到
Figure FDA0002026145330000014
Step 4. Calculate the matrix of A- T A -1 , and set B 11 , B 12 , and B 22 to replace the parameters in the A- T A -1 matrix, and substitute them into
Figure FDA0002026145330000013
get
Figure FDA0002026145330000014
 步骤5、选取2副以上不同角度或不同距离标定板目标点坐标(X,Y)到成像点坐标(u)，计算得到2个以上的H矩阵，代入
Figure FDA0002026145330000015
式，运用最小二乘法得到B11、B12、B22的值；Step 5. Select more than 2 pairs of different angles or different distances from the target point coordinates (X, Y) of the calibration plate to the imaging point coordinates (u), calculate and obtain more than 2 H matrices, and substitute them into
Figure FDA0002026145330000015
formula, use the least squares method to obtain the values of B 11 , B 12 , and B 22 ; 步骤6、根据B11、B12、B22计算内参数矩阵A，再根据内参数矩阵A，任取一个步骤五得到的H矩阵，计算外参数矩阵[r1 r2 t]。Step 6: Calculate the internal parameter matrix A according to B 11 , B 12 , and B 22 , and then according to the internal parameter matrix A, take any H matrix obtained in step 5, and calculate the external parameter matrix [r 1 r 2 t]. 2.如权利要求1所述的一种高精度简化式线阵相机标定方法，其特征在于：所述的步骤1中单应性矩阵H模型的构成方法为：2. a kind of high-precision simplified line scan camera calibration method as claimed in claim 1, is characterized in that: in described step 1, the formation method of homography matrix H model is: 步骤1.1、面阵相机成像模型
Figure FDA0002026145330000016
Step 1.1, area scan camera imaging model
Figure FDA0002026145330000016
 s为任意的实数；s is any real number; 步骤1.2、线阵相机的每次成像一行，根据面阵相机成像模型，可得到Step 1.2. The line scan camera images one line at a time. According to the imaging model of the area scan camera, we can get
Figure FDA0002026145330000021
Figure FDA0002026145330000021
 步骤1.3、对步骤1.2中的成像模型再逆推，可得Step 1.3. Reverse the imaging model in step 1.2 to get
Figure FDA0002026145330000022
M＝[x y z 1]T
Figure FDA0002026145330000022
M=[xyz 1] T 步骤1.4、假设z＝0，因此Step 1.4. Assume z=0, so
Figure FDA0002026145330000023
Figure FDA0002026145330000023
 3.如权利要求1所述的一种高精度简化式线阵相机标定方法，其特征在于：所述的步骤2中内参数矩阵A和外参数矩阵[r1 r2 t]推导方法为：3. A kind of high-precision simplified line scan camera calibration method as claimed in claim 1, is characterized in that: in described step 2, the derivation method of internal parameter matrix A and external parameter matrix [r 1 r 2 t] is: 步骤2.1、面阵相机的包括内外参数的成像模型Step 2.1. Imaging model of area scan camera including internal and external parameters
Figure FDA0002026145330000024
Figure FDA0002026145330000024
 m＝[u v 1]T，M＝[x y z 1]T m=[uv 1] T , M=[xyz 1] T 步骤2.2、由于线阵相机的每次成像只能成像一行，因此根据面阵相机成像模型，假设z＝0，可得到Step 2.2. Since each imaging of the line scan camera can only image one line, according to the imaging model of the area scan camera, assuming z=0, we can get
Figure FDA0002026145330000025
Figure FDA0002026145330000025
 步骤2.3、假设z＝0，因此Step 2.3. Assume z=0, so
Figure FDA0002026145330000031
Figure FDA0002026145330000031
 4.如权利要求1所述的一种高精度简化式线阵相机标定方法，其特征在于：所述的步骤3中
Figure FDA0002026145330000032
推导方法为：4. A high-precision simplified line scan camera calibration method as claimed in claim 1, characterized in that: in the step 3
Figure FDA0002026145330000032
The derivation method is: 步骤3.1、由于[h1 h2 h4]＝sA[r1 r2 t]，可得Step 3.1. Since [h 1 h 2 h 4 ]=sA[r 1 r 2 t], we can get h1＝sAr1或r1＝λA-1h1 h 1 =sAr 1 or r 1 =λA −1 h 1 h2＝sAr2或r2＝λA-1h2 h 2 =sAr 2 or r 2 =λA −1 h 2 h4＝sAt或t＝λA-1h4 h 4 =sAt or t=λA -1 h 4
Figure FDA0002026145330000033
Figure FDA0002026145330000033
 步骤3.2、由于r1 Tr1＝r2 Tr2＝1和r1 Tr2＝0，将r1，r2代入，可得Step 3.2. Since r 1 T r 1 =r 2 T r 2 =1 and r 1 T r 2 =0, substituting r 1 and r 2 into
Figure FDA0002026145330000034
Figure FDA0002026145330000034
 5.如权利要求1所述的一种高精度简化式线阵相机标定方法，其特征在于：所述的步骤4中
Figure FDA0002026145330000035
推导方法为：5. A high-precision simplified line scan camera calibration method as claimed in claim 1, characterized in that: in the step 4
Figure FDA0002026145330000035
The derivation method is: 步骤4.1、计算A-TA-1 Step 4.1. Calculate A -T A -1
Figure FDA0002026145330000036
Figure FDA0002026145330000036
 步骤4.2、设定B11、B12、B22三参数替换A-TA-1矩阵中的参数；Step 4.2, set the three parameters of B 11 , B 12 and B 22 to replace the parameters in the A- T A -1 matrix;
Figure FDA0002026145330000037
Figure FDA0002026145330000037
 步骤4.3、将B代入
Figure FDA0002026145330000041
得Step 4.3. Substitute B into
Figure FDA0002026145330000041
have to
Figure FDA0002026145330000042
Figure FDA0002026145330000042
 6.如权利要求1所述的一种高精度简化式线阵相机标定方法，其特征在于：所述的步骤6中的内参数矩阵A以及外参数矩阵[r1 r2 t]的计算方法如下：6. A high-precision simplified line scan camera calibration method according to claim 1, characterized in that: the calculation method of the internal parameter matrix A and the external parameter matrix [r 1 r 2 t] in the step 6 as follows: 步骤6.1设
Figure FDA0002026145330000043
由
Figure FDA0002026145330000044
得Step 6.1 set
Figure FDA0002026145330000043
Depend on
Figure FDA0002026145330000044
have to
Figure FDA0002026145330000045
Figure FDA0002026145330000045
 cu＝-B12/B11 c u = -B 12 /B 11
Figure FDA0002026145330000046
Figure FDA0002026145330000046
 步骤6.2、将fu，cu代入A，得内参数矩阵A；Step 6.2. Substitute f u and c u into A to obtain the internal parameter matrix A; 步骤6.3、任取步骤5得到的H矩阵，将A、H代入λ＝1/s＝1/||A-1h1||＝1/||A-1h2||，可得λ，进一步代入r1＝λA-1h1，r2＝λA-1h2，t＝λA-1h4，可得外参数矩阵[r1 r2 t]。Step 6.3. Take the H matrix obtained in step 5, and substitute A and H into λ=1/s=1/||A -1 h 1 ||=1/||A -1 h 2 ||, to obtain λ , and further substitute r 1 =λA -1 h 1 , r 2 =λA -1 h 2 , t=λA -1 h 4 , the external parameter matrix [r 1 r 2 t] can be obtained.
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