CN113870364A - Self-adaptive binocular camera calibration method - Google Patents

Self-adaptive binocular camera calibration method Download PDF

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CN113870364A
CN113870364A CN202111159656.4A CN202111159656A CN113870364A CN 113870364 A CN113870364 A CN 113870364A CN 202111159656 A CN202111159656 A CN 202111159656A CN 113870364 A CN113870364 A CN 113870364A
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CN113870364B (en
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张晋东
冯天琦
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Chongqing Research Institute Of Jilin University
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Abstract

The invention discloses a self-adaptive binocular camera calibration method, which respectively performs monocular calibration on a left camera and a right camera and performs stereo calibration on the binocular camera, and the obtained result matrixes are respectively as follows: inner reference matrices, cameramatrix r, cameramatrix l, of the left and right cameras; distortion matrices distCoeffeL, distCoeffeR of the left and right cameras; and finally storing a calibration result by a rotation matrix R and a translation matrix T between the two lenses of the binocular camera. Compared with the existing camera calibration tool, the camera calibration tool has the advantages that a calibration user can freely select the number of the pictures used for calibration and the sizes of the pictures, and the independent calibration results of the left camera and the right camera and the calibration results of the binocular camera can be stored when the calibration results are output.

Description

Self-adaptive binocular camera calibration method
Technical Field
The invention relates to the technical field of image processing, in particular to a self-adaptive binocular camera calibration method.
Background
In the application of image measurement and computer vision, in order to confirm the corresponding relationship between the three-dimensional point coordinates and the image coordinates in the space, and facilitate the stereo imaging performed by the binocular camera and the matching of the image points of the left camera and the right camera, the camera needs to be calibrated, that is, parameters required for converting the pixel coordinates and the actual coordinates are calculated. Generally, the binocular calibration of the camera requires that the left camera and the right camera are respectively calibrated in a monocular mode, and then the data obtained by calculating calibration parameters are used for calibrating the binocular camera. However, the existing camera calibration tool cannot select the number of the used images and the size of the images to be calibrated, and can not define the storage mode of the calibration result by user.
Disclosure of Invention
Aiming at the defects of the prior art, the invention aims to provide a self-adaptive binocular camera calibration method.
In order to achieve the purpose, the invention adopts the following technical scheme:
a self-adaptive binocular camera calibration method comprises the following specific processes:
s1, determining the number of corner points of the calibration board in the transverse and longitudinal directions and the distance between the corner points on the calibration board; determining a storage path of the pictures taken by the left camera and the right camera; determining the number of pictures used by the left camera and the right camera for calibration, and defining the size of the pictures used for calibrating the pictures and a storage path of a calibration result; shooting a set number of checkerboard pictures at different angles by using a binocular camera respectively, and requiring the checkerboard serving as a calibration board in the pictures to be a complete checkerboard; respectively storing the checkerboard pictures obtained by the left camera and the right camera;
s2, corner point search:
uniformly adjusting the checkerboard pictures to a set resolution ratio, and converting the checkerboard pictures into a gray scale image; searching and determining the positions of the angular points in the checkerboard picture by using a Harris algorithm; the obtained corner position is refined by using a sub-pixel precision method, and then the image coordinate of the corner is obtained;
s3, performing monocular calibration on the left camera and the right camera respectively:
solving a projection matrix M of which the angular points are converted from a world coordinate system to a pixel coordinate system by utilizing pixel coordinates of images of the calibration plate shot by the left camera and the right camera and the world coordinates of the calibration plate; setting a pixel coordinate system of a camera as a coordinate system Mp (x, y) taking the upper left corner of the image as an origin, and setting a world coordinate system as a coordinate system Mw (x, y, z) taking the corner point coordinate of the upper left corner of the calibration plate as the origin; thus, the process of converting from the world coordinate system to the pixel coordinate system is represented as:
Mp＝MMw
converting the image from a world coordinate system to a pixel coordinate system, wherein the three processes of converting the world coordinate system to a camera coordinate system Mc, converting the camera coordinate system to an image coordinate system Mxy and converting the image coordinate system to a pixel coordinate system Mp are included;
(1) conversion from world to camera coordinate system:
setting a rotation matrix as R and a translation matrix as T;
Figure BDA0003289592850000031
Figure BDA0003289592850000032
projection matrix M for converting image from world coordinate system to camera coordinate system1Consisting of R and T, i.e.
Figure BDA0003289592850000033
That is, the process of converting the image from the world coordinate system to the camera coordinate system is Mc＝M1Mw，McRepresenting images in the camera coordinate system, MwRepresenting an image in a world coordinate system;
(2) conversion from camera coordinate system to image coordinate system:
regarding the camera coordinate system as the same plane as the image coordinate system, and setting the coordinate under the image coordinate system as Mxy(x, y), then can be expressed as:
Figure BDA0003289592850000034
xc, Yc and Zc are image coordinates of angular points in a camera coordinate system;
then the matrix multiplication can be expressed as:
Figure BDA0003289592850000035
assuming that the matrix used for the transformation is M2, the process of converting from the camera coordinate system to the image coordinate system is represented as:
Mxy＝M2Mc
(3) from image coordinate system to pixel coordinate system:
since the origin of the image coordinate system is at the center point of the image, the pixel coordinate system sets the upper left corner of the image as the origin, and takes the right and the down as the positive directions of the x and the y axes; let cx and cy be coordinates of an original point of an image coordinate system under a pixel coordinate system, fx and fy be pixel numbers represented by x and y axes per millimeter respectively, and (u, v) be coordinates of an angular point under the pixel coordinate system, and convert the image coordinate system into the pixel coordinate system according to the following formula:
Figure BDA0003289592850000041
i.e. can be expressed as Mt＝M3Mxy；
Therefore, the projection matrix M of the image from the world coordinate system to the pixel coordinate system is M3M2M1Wherein the unknown quantities include a rotation matrix R, a translation matrix T, and fx, fy, cx, cy, and a focal length f; the unknown quantity can be solved through camera calibration;
(4) distortion of camera
The camera distortion model is as follows:
Figure BDA0003289592850000042
the Taylor expansion between the real coordinates and the ideal coordinates of the camera; x is the number ofdistortedAnd ydistortedThe coordinates of the pixel points in the image, x and y are the coordinates under the ideal condition, r2＝x2+y2；
Therefore, camera calibration is to solve unknowns R, T, fx, fy, cx, cy and radial distortion k by using the pixel coordinates of the corner points and the world coordinates of the corner points obtained by using a corner point search function to obtain an internal reference matrix, an external reference matrix and a distortion matrix of the camera;
s4, calculation of world coordinates of corner points:
according to Zhang YOU calibration method, setting the first angular point at the upper left corner of the checkerboard as the origin of coordinates, the side of the checkerboard as the positive direction of x axis and y axis, the vertical checkerboard as the z axis, and making the checkerboard arranged on the plane where z is 0, and taking 1mm as a coordinate unit, then the coordinate of each angular point is expressed as:
(xn1,yn2,zn3)＝(n1×N,n2×N,n3×N)
wherein N is the distance between two corner points;
s5, calibrating a binocular camera:
let the left camera and the right camera external parameter matrixes obtained according to monocular calibration be R respectivelyr，TrAnd Rl，Tl(ii) a Then, the relationship matrix between the left camera and the right camera can be expressed as:
Figure BDA0003289592850000051
s6, data storage:
and after the monocular and binocular calibration of the camera is completed, the acquired calibration results are respectively stored.
Further, in step S2, the resolution set is 640 × 400.
Further, in step S6, after the calibration is completed, the result to be saved includes: an internal reference matrix of the left camera and the right camera, a distortion matrix of the left camera and the right camera, a rotation matrix and a translation matrix between the left camera and the right camera; therefore, the calibration results of the monocular camera are respectively stored in the text files under the file paths of the checkerboard pictures shot by the left camera and the right camera, and the calibration results of the binocular camera are stored under the image file folder.
The invention has the beneficial effects that: compared with the existing camera calibration tool, the camera calibration tool has the advantages that a calibration user can freely select the number of the pictures used for calibration and the sizes of the pictures, and the independent calibration results of the left camera and the right camera and the calibration results of the binocular camera can be stored when the calibration results are output.
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FIG. 1 is a schematic flow chart of a method according to an embodiment of the present invention.
Detailed Description
The present invention will be further described with reference to the accompanying drawings, and it should be noted that the present embodiment is based on the technical solution, and the detailed implementation and the specific operation process are provided, but the protection scope of the present invention is not limited to the present embodiment.
The embodiment provides a self-adaptive binocular camera calibration method, which is divided into two processes: and respectively carrying out monocular calibration on the left camera and the right camera and carrying out three-dimensional calibration on the binocular camera. Firstly, determining result matrixes required to be obtained in the whole calibration process as follows: the internal reference matrices, cameramatrix r, cameramatrix l, of the left and right cameras; distortion matrices distCoeffeL, distCoeffeR for the left and right cameras, and rotation and translation matrices R, T between the left and right cameras. The reference matrix is stored by using a 3 × 3 matrix, and the distortion matrix is stored by using a 5 × 1 vector. The rotation matrix R between the left and right cameras is a 3 × 3 matrix and the translation matrix T is a 3 × 1 vector. In order to calibrate the binocular camera, two queue containers are also needed to store the corner point coordinates of checkerboard pictures taken by the left camera and the right camera respectively. The specific process is shown in fig. 1.
1. Front preparation for camera calibration
The camera to be calibrated in this embodiment may be a binocular camera such as an IR camera. And determining the number of the angle points of the calibration plate in the transverse and longitudinal directions and the grid distance between the angle points of the calibration plate (manual measurement is needed) for defining in the initial global variable. In addition, in the method of the embodiment, the variables which need to be defined in advance for calibration also include storage paths of pictures taken by the left camera and the right camera.
Determining the number of pictures used by the left camera and the right camera for calibration, and defining the size of the pictures used for calibrating the pictures and a storage path of a calibration result. There is no limitation on the picture size and type in this embodiment.
Specifically, in this embodiment, the calibrated image is a binocular camera, a checkerboard with an angular point number of 16 × 11 and an angular point distance of 15mm is used as the calibration board, six checkerboard pictures are respectively taken at different angles by using the binocular camera before calibration, and the checkerboard in the pictures used as the calibration board is required to be a complete checkerboard. And then, respectively storing the obtained checkerboard pictures according to the left camera and the right camera, and using the obtained pictures for calibration.
2. Corner point search
The checkerboard pictures shot by the binocular camera are uniformly adjusted to the resolution of 640 multiplied by 400 and converted into a gray scale picture. And (5) searching and determining the position of the corner point in each checkerboard picture by using a Harris algorithm.
In this embodiment, the Harris algorithm is used to position the corner, and the sub-pixel precision method is used to refine the obtained position of the corner, so as to obtain the image coordinates of the corner. Further, the present embodiment uses two-dimensional arrays to store the image coordinates of the corner points of the checkerboard pictures obtained by the left camera and the right camera, respectively. Specifically, angular point search is sequentially performed on each checkerboard picture according to the storage sequence of each checkerboard picture.
3. Monocular calibration
The calibration of the monocular camera is a process of utilizing the pixel coordinates of the image of the calibration plate shot by the camera and the world coordinates of the calibration plate, and solving a projection matrix M of which the angular point is converted from the world coordinate system to the pixel coordinate system. Let the pixel coordinate system of the camera be the coordinate system Mp (x, y) with the top left corner of the image as the origin, and the world coordinate system be the coordinate system Mw (x, y, z) with the corner point coordinates of the top left corner of the calibration plate as the origin. Therefore, the process of converting from the world coordinate system to the pixel coordinate system can be considered as:
Mp＝MMw
the image is converted from a world coordinate system to a pixel coordinate system, and the method comprises three steps of converting the world coordinate system Mw to a camera coordinate system Mc, converting the camera coordinate system Mxy to an image coordinate system Mxy, and converting the image coordinate system Mp to the pixel coordinate system Mp.
(1) Conversion from world to camera coordinate systems
Coordinate transformation between two different coordinate systems can be regarded as transformation consisting of rotation and translation, and a rotation matrix of a single camera is set as R, and a translation matrix is set as T;
Figure BDA0003289592850000081
Figure BDA0003289592850000082
projection matrix M for converting images from world coordinate system to camera coordinate system1Consists of R and T;
Figure BDA0003289592850000083
that is, the process of converting the image from the world coordinate system to the camera coordinate system is Mc＝M1Mw，McRepresenting images in the camera coordinate system, MwRepresenting an image in a world coordinate system.
(2) Conversion from camera coordinate system to image coordinate system
The camera coordinate system is considered to be on the same plane as the image coordinate system, and therefore, the conversion of the camera coordinate system and the image coordinate system can be considered as a similar triangular transformation with respect to the camera focal length f. Let the coordinate under the image coordinate system be Mxy(x, y), then can be expressed as:
Figure BDA0003289592850000091
xc, Yc and Zc are image coordinates of the corner points in a camera coordinate system.
Then the matrix multiplication can be expressed as:
Figure BDA0003289592850000092
let M be the transformation matrix used to convert the camera coordinate system to the image coordinate system2The process of converting from the camera coordinate system to the image coordinate system can be expressed as:
Mxy＝M2Mc
(3) from image coordinate system to pixel coordinate system
Since the origin of the image coordinate system is at the center point of the image, for the sake of calculation convenience, the pixel coordinate system sets the upper left corner of the image as the origin, with the right and down as the x and y-axis forward directions. Let cx and cy be coordinates of an original point of an image coordinate system under a pixel coordinate system, fx and fy be pixel numbers represented by x and y axes per millimeter respectively, and (u, v) be coordinates of an angular point under the pixel coordinate system, and convert the image coordinate system into the pixel coordinate system according to the following formula:
Figure BDA0003289592850000093
i.e. can be expressed as Mp＝M3Mxy
Combining the above formulas, the projection matrix M of the image from the world coordinate system to the pixel coordinate system is M3M2M1Where the unknowns include a rotation matrix R, a translation matrix T, and fx, fy, cx, cy, and a focal length f. The above unknown quantities can be solved by camera calibration.
(4) Distortion of camera
The distortion model of the camera is as follows:
Figure BDA0003289592850000101
wherein x isdistortedAnd ydistortedThe coordinates of the pixel points in the image, x and y are the coordinates under the ideal condition, r2＝x2+y2In the Zhangzhen scaling method adopted in this embodiment, only the radial distortion of the camera is considered, that is, the distortion model of the camera is considered as
Figure BDA0003289592850000102
I.e. the taylor expansion between the real and ideal coordinates of the camera.
Therefore, the camera calibration is to solve the unknowns R, T, fx, fy, cx, cy and the radial distortion k for the pixel coordinates of the corner point and the world coordinates of the corner point obtained by using the corner point search function.
The present embodiment uses the gnomon scaling method, that is, the world coordinate system is used as the plane where the scaling board is located, where Z is 0.
Hence world coordinate MwI.e. can be represented by (x, y, z,1) as (x, y, 1). Let MA＝M3M2Namely, it is
Figure BDA0003289592850000103
There are a total of 8 unknowns. Wherein M isAThe method is composed of 4 unknowns, alpha and beta are focal length parameters of a camera, and u0 and v0 are offset parameters of a focus relative to an origin point at the upper left corner.
According to Zhangyingyou scaling method, the plane z of the scaling plate under the world coordinate system is made to be 0, so that
Figure BDA0003289592850000111
Wherein r is1＝[a11 a21 a31]T，r2＝[a12 a22 a32]TThen M isAM1That is, at least three homography matrices are needed to solve the solved matrix. In order to ensure the error range of the result, the present embodiment calibrates the left camera and the right camera respectively by using six pictures, and solves the internal reference matrix, the distortion matrix, and the external reference matrix of the left camera and the right camera respectively.
4. Calculation of corner world coordinates
According to Zhangzhengyou calibration method, for the convenience of calculation, the first corner point at the upper left corner of the checkerboard is set as the origin of coordinates, the side of the checkerboard is taken as the positive direction of the x axis and the y axis, the vertical checkerboard is taken as the z axis, the checkerboard is arranged on the plane where z is 0, and the coordinate of each corner point can be expressed as follows by taking 1mm as a coordinate unit:
(xn1,yn2,zn3)＝(n1×N,n2×N,n3×N)
wherein N is the distance between two corner points.
Therefore, the world coordinates of the corner points on the calibration board can be obtained, and the present embodiment uses six 16 × 11 pictures for calibration, so a two-dimensional dynamic array container is used to store the world coordinates of the checkerboard obtained by calculation.
5. Binocular camera calibration
The binocular camera is a camera structure simulating human eye imaging, and binocular stereo calibration is a parallax relation between a left camera and a right camera which calculate and obtain the binocular camera, namely a rotation matrix R between the left camera and the right cameralrAnd translation matrix TlrAnd may utilize a rotation matrix RlrAnd translation matrix TlrAnd correcting the binocular vision image, and drawing the two pictures shot by the left camera and the right camera to the same horizontal plane through rotation and translation transformation.
Firstly, let the left camera and right camera external parameter matrixes obtained according to monocular calibration be R respectivelyr，TrAnd Rl，Tl. Then, a relationship matrix R between the left camera and the right cameralrAnd TlrCan be expressed as:
Figure BDA0003289592850000121
therefore, the external reference matrix R between the binocular cameras can be solved by using the pixel coordinates and the world coordinates of the corner pointslrAnd Tlr。
6. Data preservation
And after the monocular and binocular calibration of the camera is completed, the acquired calibration results are respectively stored. After calibration is completed, the results to be saved include: an internal reference matrix for the left and right cameras, a distortion matrix for the left and right cameras, a rotation matrix between the left and right cameras, and a translation matrix. Therefore, in the embodiment, the calibration results of the monocular camera are respectively stored in the text files in the file paths where the checkerboard pictures shot by the left camera and the right camera are located, and the calibration results of the binocular camera are stored in the image file folder. For convenience of use and reference, the embodiment simultaneously stores result data of a rotation matrix and a translation matrix of the monocular camera obtained by calibration calculation relative to each calibration sample image, and simultaneously stores an essential matrix, a basic matrix and a back projection matrix obtained after binocular calibration into a calibration result file.
Various corresponding changes and modifications can be made by those skilled in the art based on the above technical solutions and concepts, and all such changes and modifications should be included in the protection scope of the present invention.

Claims (3)

1. A self-adaptive binocular camera calibration method is characterized by comprising the following specific processes:
s1, determining the number of corner points of the calibration board in the transverse and longitudinal directions and the distance between the corner points on the calibration board; determining a storage path of the pictures taken by the left camera and the right camera; determining the number of pictures used by the left camera and the right camera for calibration, and defining the size of the pictures used for calibrating the pictures and a storage path of a calibration result; shooting a set number of checkerboard pictures at different angles by using a binocular camera respectively, and requiring the checkerboard serving as a calibration board in the pictures to be a complete checkerboard; respectively storing the checkerboard pictures obtained by the left camera and the right camera;
s2, corner point search:
uniformly adjusting the checkerboard pictures to a set resolution ratio, and converting the checkerboard pictures into a gray scale image; searching and determining the positions of the angular points in the checkerboard picture by using a Harris algorithm; the obtained corner position is refined by using a sub-pixel precision method, and then the image coordinate of the corner is obtained;
s3, performing monocular calibration on the left camera and the right camera respectively:
solving a projection matrix M of which the angular points are converted from a world coordinate system to a pixel coordinate system by utilizing pixel coordinates of images of the calibration plate shot by the left camera and the right camera and the world coordinates of the calibration plate; setting a pixel coordinate system of a camera as a coordinate system Mp (x, y) taking the upper left corner of the image as an origin, and setting a world coordinate system as a coordinate system Mw (x, y, z) taking the corner point coordinate of the upper left corner of the calibration plate as the origin; thus, the process of converting from the world coordinate system to the pixel coordinate system is represented as:
Mp＝MMw
converting the image from a world coordinate system to a pixel coordinate system, wherein the three processes of converting the world coordinate system to a camera coordinate system Mc, converting the camera coordinate system to an image coordinate system Mxy and converting the image coordinate system to a pixel coordinate system Mp are included;
(1) conversion from world to camera coordinate system:
setting a rotation matrix as R and a translation matrix as T;
Figure FDA0003289592840000021
Figure FDA0003289592840000022
projection matrix M for converting image from world coordinate system to camera coordinate system1Consisting of R and T, i.e.
Figure FDA0003289592840000023
That is, the process of converting the image from the world coordinate system to the camera coordinate system is Mc＝M1Mw，McRepresenting images in the camera coordinate system, MwRepresenting an image in a world coordinate system;
(2) conversion from camera coordinate system to image coordinate system:
regarding the camera coordinate system as the same plane as the image coordinate system, and setting the coordinate under the image coordinate system as Mxy(x, y), then can be expressed as:
Figure FDA0003289592840000024
xc, Yc and Zc are image coordinates of angular points in a camera coordinate system;
then the matrix multiplication can be expressed as:
Figure FDA0003289592840000025
assuming that the matrix used for the transformation is M2, the process of converting from the camera coordinate system to the image coordinate system is represented as:
Mxy＝M2Mc
(3) from image coordinate system to pixel coordinate system:
since the origin of the image coordinate system is at the center point of the image, the pixel coordinate system sets the upper left corner of the image as the origin, and takes the right and the down as the positive directions of the x and the y axes; let cx and cy be coordinates of an original point of an image coordinate system under a pixel coordinate system, fx and fy be pixel numbers represented by x and y axes per millimeter respectively, and (u, v) be coordinates of an angular point under the pixel coordinate system, and convert the image coordinate system into the pixel coordinate system according to the following formula:
Figure FDA0003289592840000031
i.e. can be expressed as Mt＝M3Mxy；
Therefore, the projection matrix M of the image from the world coordinate system to the pixel coordinate system is M3M2M1Wherein the unknown quantities include a rotation matrix R, a translation matrix T, and fx, fy, cx, cy, and a focal length f; by cameraThe unknown quantity can be solved by calibration;
(4) distortion of camera
The camera distortion model is as follows:
Figure FDA0003289592840000032
the Taylor expansion between the real coordinates and the ideal coordinates of the camera; x is the number ofdistortedAnd ydistortedThe coordinates of the pixel points in the image, x and y are the coordinates under the ideal condition, r2＝x2+y2；
Therefore, camera calibration is to solve unknowns R, T, fx, fy, cx, cy and radial distortion k by using the pixel coordinates of the corner points and the world coordinates of the corner points obtained by using a corner point search function to obtain an internal reference matrix, an external reference matrix and a distortion matrix of the camera;
s4, calculation of world coordinates of corner points:
according to Zhang YOU calibration method, setting the first angular point at the upper left corner of the checkerboard as the origin of coordinates, the side of the checkerboard as the positive direction of x axis and y axis, the vertical checkerboard as the z axis, and making the checkerboard arranged on the plane where z is 0, and taking 1mm as a coordinate unit, then the coordinate of each angular point is expressed as:
(xn1,yn2,zn3)＝(n1×N,n2×N,n3×N)
wherein N is the distance between two corner points;
s5, calibrating a binocular camera:
let the left camera and the right camera external parameter matrixes obtained according to monocular calibration be R respectivelyr，TrAnd Rl，Tl(ii) a Then, the relationship matrix between the left camera and the right camera can be expressed as:
Figure FDA0003289592840000041
s6, data storage:
and after the monocular and binocular calibration of the camera is completed, the acquired calibration results are respectively stored.
2. The method according to claim 1, wherein in step S2, the set resolution is 640 x 400.
3. The method according to claim 1, wherein in step S6, after completing calibration, the result to be saved includes: an internal reference matrix of the left camera and the right camera, a distortion matrix of the left camera and the right camera, a rotation matrix and a translation matrix between the left camera and the right camera; therefore, the calibration results of the monocular camera are respectively stored in the text files under the file paths of the checkerboard pictures shot by the left camera and the right camera, and the calibration results of the binocular camera are stored under the image file folder.
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