CN119006609A - Camera calibration method - Google Patents
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- G06T7/80—Analysis of captured images to determine intrinsic or extrinsic camera parameters, i.e. camera calibration
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Abstract
The invention relates to the technical field of photogrammetry, and discloses a camera calibration method, which takes checkerboard image data of different angles shot by a camera to be calibrated as input, and outputting accurate distortion parameters participating in a corresponding camera model in the camera through the steps of sampling point extraction, inner parameter and outer parameter solving, distortion parameter estimation and anti-distortion iteration. And the iterative optimization process is introduced, the distortion correction is carried out on the sampling points, the camera parameters are re-estimated, the influence of the distortion on the parameter estimation can be effectively reduced, and the calibration precision is improved. By continuing the iteration, the re-projection error can be gradually reduced until the requirement is met or the maximum number of iterations is reached. And by utilizing anti-distortion iteration, the internal and external parameters and distortion parameters of the camera are optimized alternately, so that the possibility that the parameter optimization is trapped into a local minimum value is effectively reduced, and the robustness and the universality of calibration are improved.
Description
Technical Field
The invention relates to the technical field of photogrammetry, in particular to a camera calibration method.
Background
The camera self-calibration method mainly utilizes the constraint of camera motion or the constraint in a scene to estimate camera parameters. For example, using parallel lines or orthogonal information in the scene, camera parameters are estimated by computing vanishing points. The self-calibration method has strong flexibility and can calibrate the camera on line. But because it is an absolute conic or curved based method, its algorithm robustness is poor.
The conventional camera calibration method needs to use calibration objects with known sizes, such as a checkerboard or a round calibration plate, and obtain internal and external parameters of a camera model by using a certain algorithm through establishing correspondence between points with known coordinates on the calibration objects and image points of the calibration objects. The three-dimensional calibration object and the planar calibration object can be classified according to different calibration objects. The three-dimensional calibration object can be calibrated by a single image, the calibration precision is higher, but the processing and maintenance of the high-precision three-dimensional calibration object are more difficult. The planar calibration object is simpler to manufacture than the three-dimensional calibration object, the precision is easy to ensure, but two or more images are needed to be adopted in the calibration. In the conventional calibration method, since the external parameters obtained by linear solution are not accurate enough, the external parameters are usually optimized together in nonlinear optimization. This, while being able to solve in-place in one step, would make the optimization problem non-convex, i.e., there are multiple local minima for the optimization function, resulting in the optimization being likely to fall into a local minimum. Under the weak distortion condition, the external parameters obtained by linear solution are used as initial values in nonlinear optimization, so that the optimization is prevented from being trapped into local minimum, but the method is not applicable under the strong distortion condition.
Zhang Zhengyou calibration method: zhang Zhengyou calibration is a method that is intermediate between the conventional calibration method and the self-calibration method. The method uses a printed checkerboard calibration plate, and solves the internal and external parameters of the camera by shooting calibration plate images with different angles and utilizing angular point information in the images. Patent CN113920201a proposes a calibration method based on polar geometric constraints. However, the calibration method needs to establish an indoor three-dimensional calibration field, measure the artificial mark points in the field, and is inconvenient to deploy and operate.
Disclosure of Invention
In order to solve the problems, the invention provides a camera calibration method, which inherits the usability characteristic of Zhang Zhengyou calibration method, can automatically calibrate by shooting checkerboard image, has convenient operation, uses checkerboard calibration plate to calibrate the camera, accurately determines the internal parameters, external parameters and distortion parameters of the camera through the steps of angular point detection, homography matrix estimation, minimized re-projection error, distortion correction, anti-distortion iteration and the like, and specifically comprises the following steps:
S1, shooting Zhang Qipan more images by using a camera to be calibrated;
S2, extracting sampling points through angular point detection, wherein the angular points correspond to the cross points of the checkerboard;
S3, reading sampling points, and estimating camera parameters by utilizing a homography matrix, wherein the camera parameters comprise: camera internal parameters and camera external parameters;
S4, constructing a minimized re-projection error, and estimating to obtain a camera distortion parameter;
s5, outputting camera parameters if the re-projection error obtained in the S4 is small, otherwise, entering the S6;
S6, carrying out distortion correction on the sampling points, and circulating S3-S5.
Further, in S2, specifically: using corner detection, extracting corner points from the original checkered image in S1 acquired by the user as sampling points, and saving the extracted sampling points as a specified file for subsequent processing.
Further, in the step S3, the estimation of the camera internal parameters and the camera external parameters by using the homography matrix specifically includes:
The homography matrix H is defined as:
H＝sK(r1,r2,t)
Wherein, it is 3*3 matrix, s is scaling factor, K is camera internal reference matrix, r 1,r2 is first and second columns of external reference rotation matrix, t is displacement vector of external reference; m=hp is substituted into different sampling points for solving, the sampling points are recorded as m (u, v), u and v are coordinates of normalized points, an object point P (X, Y, 0) is set as the position of a checkerboard sampling point under a world coordinate system, after a homography matrix is solved, the homography matrix is substituted into the constraint of a rotation matrix, and the participation camera external parameters in the camera are respectively solved.
Further, the minimizing the re-projection error by the construction in S4 is specifically:
Wherein alpha and beta are distortion parameters in the extended unified camera model, initial values alpha=0 and beta=1 are set, parameter ranges alpha epsilon [0,1] are limited, beta is more than or equal to 0, m ij is the point of the j-th row of the sampled i-th row, For the camera model, R j,tj is the distance of pixel offset, P ij is the position of the pixel on the original checkerboard, n is the number of rows of the checkerboard corner points, and k is the number of columns of the checkerboard corner points.
Further, the distortion correction of the sampling point in S6 specifically includes:
and (3) carrying out anti-distortion iteration on the sampling points through the camera distortion parameters obtained through estimation in the step (S4), solving the camera internal parameters and the camera external parameters again, updating the camera distortion parameters obtained through estimation, and prompting the precision of parameter calibration.
Further, the anti-distortion iteration is specifically: and carrying out anti-distortion on the original sampling point by using the updated estimated camera distortion parameters, so that the re-projection error between the original sampling point and the re-projected object point is minimized.
Further, the anti-distortion iteration specifically includes the following steps:
s61, performing anti-distortion iteration according to the camera distortion parameters obtained in the S4, substituting the camera internal parameters as fixed values, solving the minimum re-projection errors of the camera external parameters, and updating the camera distortion parameters;
s62, substituting the camera external parameters obtained in the previous step and the updated camera distortion parameters as fixed values, solving the camera internal parameters to minimize the re-projection errors, and updating the camera distortion parameters;
S63, substituting the camera internal parameters obtained in the previous step and the updated camera distortion parameters as fixed values, solving the camera external parameters to minimize the re-projection errors again, and updating the camera distortion parameters;
S64, circulating S62-S63 until the re-projection error between the original sampling point and the re-projected object point is minimized.
Further, the checkerboard image shot in the step S1 is a checkerboard calibration plate, and comprises a checkerboard with known size and position.
Further, the camera internal parameters in S3 include: including focal length, principal point coordinates, camera external parameters include: the rotation matrix and translation vector.
The beneficial effects of the invention are as follows:
1. The accuracy is high: by using the checkerboard calibration plate and the corner detection algorithm, the characteristic points for parameter estimation can be accurately extracted. The method for minimizing the re-projection error can accurately estimate the internal parameters, the external parameters and the distortion parameters of the camera, thereby improving the accuracy of camera calibration.
2. The robustness is strong: the method can adapt to checkerboard images with different angles and positions, and therefore has stronger robustness. Even under some complex scenes, such as illumination change, noise interference and the like, the method can obtain more accurate estimation results of camera parameters. Parameters to be estimated in nonlinear optimization are effectively reduced, the problem is changed into a convex optimization problem, and the calibration robustness is improved.
3. Iterative optimization: and the iterative optimization process is introduced, the distortion correction is carried out on the sampling points, the camera parameters are re-estimated, the influence of the distortion on the parameter estimation can be effectively reduced, and the calibration precision is improved. The internal parameters and the external parameters of the camera are respectively and alternately iterated gradually, the camera is made to be optimal by successive approximation, the distortion parameters of the camera are continuously updated, and the re-projection error can be gradually reduced by continuous iteration until the requirements are met or the maximum iteration times are reached. And by utilizing anti-distortion iteration, the internal and external parameters and distortion parameters of the camera are optimized alternately, so that the possibility that the parameter optimization is trapped into a local minimum value is effectively reduced, and the robustness and the universality of calibration are improved.
4. The application range is wide: the method is not only suitable for common cameras, but also suitable for special types of cameras such as wide-angle cameras, fisheye cameras and the like. The method can provide accurate camera parameters for various computer vision tasks, such as three-dimensional reconstruction, target positioning, augmented reality and the like.
5. Easy realization: the method is based on a mature image processing algorithm and a mathematical optimization method, and is easy to realize and program. The implementation can be simplified by using an open-sourced computer vision library. The basic framework of the method can be easily extended to other types of calibration plates or feature point extraction algorithms. The algorithm can be optimized and improved according to specific requirements so as to adapt to different application scenes and camera types.
Drawings
FIG. 1 is a schematic flow chart of a camera calibration method;
FIG. 2 is a checkerboard picture of different angles taken with a camera to be calibrated in an embodiment;
FIG. 3 is a checkerboard picture of sampling points extracted by corner detection in an embodiment;
FIG. 4 is a schematic diagram of an anti-distortion iteration process in an embodiment;
Fig. 5 is a schematic diagram of a distorted image correction result in the embodiment.
Detailed Description
The preferred embodiments of the present invention will be described in detail below with reference to fig. 1-5 so that the advantages and features of the present invention can be more readily understood by those skilled in the art, thereby making clear and defining the scope of the present invention.
A camera calibration method specifically comprises the following steps:
S1, shooting Zhang Qipan more images by using a camera to be calibrated;
S2, extracting sampling points through angular point detection, wherein the angular points correspond to the cross points of the checkerboard;
S3, reading sampling points, and carrying out parameter estimation by utilizing a homography matrix, wherein the parameters comprise: camera internal parameters and camera external parameters;
S4, constructing a minimized re-projection error, and estimating to obtain a camera distortion parameter;
s5, outputting camera parameters if the re-projection error obtained in the S4 is small, otherwise, entering the S6;
S6, carrying out distortion correction on the sampling points, and circulating S3-S5.
Specifically, first, a camera to be calibrated is used to capture Zhang Qipan more frames of images from different angles and positions. The checkerboard calibration plate typically contains a checkerboard of known size and location for subsequent feature point extraction and camera parameter estimation.
Then, corner points are extracted from the checkerboard image as sampling points by a corner point detection algorithm (such as Harris corner point detection, FAST and the like). These corner points correspond to the intersections of the checkerboard and are used for subsequent parameter estimation.
And then, parameter estimation is carried out by utilizing a homography matrix, and a bidirectional projection process of the camera model with distortion and a jacobian matrix of model parameters for projection point coordinates are defined. Homography matrix: a mapping from one plane to another is described. In camera calibration, it describes the mapping of a checkerboard plane (world coordinate system) to an image plane (pixel coordinate system). Camera internal parameters: including focal length, principal point coordinates, etc., for describing internal properties of the camera. Camera external parameters: including rotation matrices and translation vectors, for describing the relative position and pose between the camera coordinate system and the world coordinate system. The homography matrix H can be solved by substituting different sampling points and corresponding object points (points on the checkerboard). The internal parameters and external parameters of the camera can be solved by utilizing the decomposition of the homography matrix.
Then, the minimum re-projection error is constructed, and the accuracy of camera calibration can be effectively compared under different data sets through the root mean square error of the re-projection error of scale normalization. Reprojection error: refers to the error between a point in three-dimensional space projected onto a two-dimensional image plane by camera parameters and then actually detected. Distortion parameters: for describing image distortion due to lens distortion (e.g., radial distortion, tangential distortion, etc.). The distortion parameters are solved by constructing an objective function that minimizes the reprojection error and using an optimization algorithm.
Then, checking the re-projection error, and if the re-projection error obtained in the last step is small (smaller than a preset threshold), considering that the estimation of the camera parameters is accurate, and outputting the camera parameters. Otherwise, the distortion correction is performed.
Distortion correction: and performing anti-distortion processing on the original sampling points by using the distortion parameters obtained by estimation, and eliminating or reducing the influence of distortion on parameter estimation. And solving the internal parameters and the external parameters of the corrected sampling points and estimating distortion parameters, and iterating circularly until the re-projection error meets the requirement or reaches the maximum iteration times.
The method specifically comprises the following steps:
s61, performing anti-distortion iteration according to the camera distortion parameters obtained in the S4, substituting the camera internal parameters as fixed values, solving the minimum re-projection errors of the camera external parameters, and updating the camera distortion parameters;
s62, substituting the camera external parameters obtained in the previous step and the updated camera distortion parameters as fixed values, solving the camera internal parameters to minimize the re-projection errors, and updating the camera distortion parameters;
S63, substituting the camera internal parameters obtained in the previous step and the updated camera distortion parameters as fixed values, solving the camera external parameters to minimize the re-projection errors again, and updating the camera distortion parameters;
S64, circulating S62-S63 until the re-projection error between the original sampling point and the re-projected object point is minimized.
The traditional method is to solve the camera external parameters and the camera internal parameters simultaneously at one time, so that the parameter optimization falls into the dead office of the local minimum value, for example, assuming that the camera external parameters are represented as A and B, the camera internal parameters are represented as C and D, solving the ABCD once by the traditional method, and ending the iteration when one value of the ABCD is optimal.
The specific process of the anti-distortion iteration is to utilize the estimated distortion parameters to carry out anti-distortion processing on the original sampling points, so that the re-projection error between the original sampling points and the re-projected object points is minimized. The process can be realized by an iterative optimization algorithm, and the distortion parameters are updated and the re-projection errors are recalculated for each iteration until the errors meet the requirements or the maximum iteration times are reached. And by utilizing anti-distortion iteration, the internal and external parameters and distortion parameters of the camera are optimized alternately, so that the possibility that the parameter optimization is trapped into a local minimum value is effectively reduced, and the robustness and the universality of calibration are improved.
By the method, internal parameters, external parameters and distortion parameters of the camera can be accurately estimated, and accurate camera parameters are provided for subsequent tasks such as three-dimensional reconstruction and target positioning.
Examples:
first, as shown in fig. 2, a user uses a camera to be calibrated to take several checkerboard pictures of different angles. Picture requirements: the resolution is consistent with the distortion of the subsequent application, no obvious shadow or reflection exists, and the shooting is carried out at different angles.
Next, sampling points are extracted by corner detection, and the number of rows and columns of each graph sampling point is specified by the user, as shown in fig. 3, which is 5*5. The module will save the extracted sample points as a specified file.
Then, reading the sampling points, and carrying out parameter estimation:
(1) Solution of internal and external parameters
In this step, a homography matrix is used for constructing a linear equation set to solve internal and external parameters.
The sampling points are recorded as m (u, v), the column number of each sampling graph checkerboard corner is k, the line number of each sampling graph checkerboard corner is n, and the total number of the sampling points is n x k. The object point P (X, Y, 0) is set as the position of the checkered sampling point in the world coordinate system, which corresponds to the sampling point on each sampling map one by one.
The homography matrix H is defined as:
H＝sK(r1,r2,t) (1)
It is 3*3 matrix, s is scaling factor, K is camera internal reference matrix, r 1,r2 is first and second columns of external reference rotation matrix, t is displacement vector of external reference, and it has 8 degrees of freedom due to scale invariance under homogeneous coordinates. Each sampling graph corresponds to a homography matrix, and m=hp is substituted into different sampling points to solve.
After solving the homography matrix, substituting the constraint of the rotation matrix into the constraint of the rotation matrix in the formula (1) to respectively solve the internal participation and the external participation.
(2) Distortion parameter estimation
In this step, the task of minimizing the re-projection error is constructed:
The method adopts the Levenberg-Marquardt method to solve, alpha and beta are distortion parameters in the extended unified camera model, initial values of alpha=0 and beta=1 are set, parameter ranges of alpha epsilon [0,1], beta is larger than or equal to 0, m ij is the point of the j-th row of the sampling, For the camera model, R j,tj is the distance of pixel offset, P ij is the position of the pixel on the original checkerboard, n is the number of rows of the checkerboard corner points, and k is the number of columns of the checkerboard corner points.
The correction of the internal reference principal point u 0,v0 is added while the distortion parameters are estimated, so that the calibration accuracy can be effectively improved. The parameters required to be estimated are alpha, beta and u 0,v0, so that the calibration accuracy is further ensured.
Then, the re-projection error is checked, and if the obtained re-projection error is small (smaller than a preset threshold), the camera parameter estimation is considered to be accurate, and the camera parameter is output. Otherwise, the distortion correction is performed.
Considering that when the image has strong radial distortion, the camera inner parameter and the camera outer parameter solved above have larger errors, which further affects the estimation accuracy of distortion parameters. The invention designs the anti-distortion iteration, and carries out the steps of solving the internal parameters and the external parameters and estimating the distortion parameters after carrying out the anti-distortion on the distortion parameters estimated by the sampling point in the last step, thereby improving the parameter calibration precision.
As shown in fig. 4, the red dot array is an original sampling point, the green dot array is a target point after re-projection, and the blue dot array is a result after the original sampling point is de-distorted by using the estimated distortion parameter. The aim of minimizing the re-projection error is to make the red and green points coincide as much as possible, and through the estimated distortion parameters of the blue point array and the continuous alternate iteration of the internal parameters of the camera and the external parameters of the camera, the re-projection error is rapidly reduced along with the progress of the anti-distortion iteration step, the straight line degree of the anti-distortion result is better and better, and the anti-distortion iteration has remarkable improvement on the calibration precision. As shown in fig. 5, the distortion image correction result is shown.
The results are shown in the following table:
| Tool for cutting tools | loss | Distortion parameter |
| Opencv::calibrateCamera | 1.614104 | 5 |
| Opencv::Fisheye::calibrate | 0.258343 | 4 |
| Proposed | 0.253071 | 2 |
The number of anti-distortion iterations of the present invention in the example is 3.
Wherein, loss evaluation index: normalized Root Mean Square Error (RMSE) of reprojection error, loss physical meaning: average pixel error per sample point on unit checkerboard area, loss unit: one ten thousandth pixel/(sampling point) checkerboard.
By the method, internal parameters, external parameters and distortion parameters of the camera can be accurately estimated, and accurate camera parameters are provided for subsequent tasks such as three-dimensional reconstruction and target positioning.
Any embodiment of the invention can be used as an independent technical scheme or can be combined with other embodiments. All patents and publications mentioned in the specification are indicative of those of ordinary skill in the art to which this invention pertains and which may be applied. All patents and publications cited herein are hereby incorporated by reference to the same extent as if each individual publication were specifically and individually indicated to be incorporated by reference. The invention may be practiced without any element or elements, limitation or limitations, which are not expressly described herein. The terms and expressions which have been employed herein are used as terms of description and not of limitation, and there is no intention in the use of such terms and expressions of excluding any equivalents of the features shown and described, but it is recognized that various modifications are possible within the scope of the invention and of the claims. It is to be understood that the embodiments described herein are illustrative of the embodiments and features disclosed herein and that modifications and variations may be resorted to by those skilled in the art without departing from the spirit of this invention as those aspects are considered to fall within the scope of this invention as defined by the independent claims and the appended claims.
Claims (9)
1. The camera calibration method is characterized by comprising the following steps of:
S1, shooting Zhang Qipan more images by using a camera to be calibrated;
S2, extracting sampling points through angular point detection, wherein the angular points correspond to the cross points of the checkerboard;
S3, reading sampling points, and estimating camera parameters by utilizing a homography matrix, wherein the camera parameters comprise: camera internal parameters and camera external parameters;
S4, constructing a minimized re-projection error, and estimating to obtain a camera distortion parameter;
s5, outputting camera parameters if the re-projection error obtained in the S4 is small, otherwise, entering the S6;
S6, carrying out distortion correction on the sampling points, and circulating S3-S5.
2. The camera calibration method according to claim 1, wherein in S2, specifically: using corner detection, extracting corner points from the original checkered image in S1 acquired by the user as sampling points, and saving the extracted sampling points as a specified file for subsequent processing.
3. The method for calibrating a camera according to claim 1, wherein the estimating of the camera internal parameter and the camera external parameter by using the homography matrix in S3 specifically comprises:
The homography matrix H is defined as:
H＝sK(r1,r2,t)
Wherein, it is 3*3 matrix, s is scaling factor, K is camera internal reference matrix, r 1,r2 is first and second columns of external reference rotation matrix, t is displacement vector of external reference; m=hp is substituted into different sampling points for solving, the sampling points are recorded as m (u, v), u and v are coordinates of normalized points, an object point P (X, Y, 0) is set as the position of a checkerboard sampling point under a world coordinate system, after a homography matrix is solved, the homography matrix is substituted into the constraint of a rotation matrix, and the participation camera external parameters in the camera are respectively solved.
4. The camera calibration method according to claim 1, wherein the minimizing the re-projection error by the construction in S4 is specifically:
Wherein alpha and beta are distortion parameters in the extended unified camera model, initial values alpha=0 and beta=1 are set, parameter ranges alpha epsilon [0,1] are limited, beta is more than or equal to 0, m ij is the point of the j-th row of the sampled i-th row, For the camera model, R j,tj is the distance of pixel offset, P ij is the position of the pixel on the original checkerboard, n is the number of rows of the checkerboard corner points, and k is the number of columns of the checkerboard corner points.
5. The camera calibration method according to claim 1, wherein the distortion correction of the sampling points in S6 is specifically:
And (3) carrying out anti-distortion iteration on the sampling points through the camera distortion parameters obtained through estimation in the step (S4), solving the camera internal parameters and the camera external parameters again, updating the camera distortion parameters obtained through estimation, and improving the precision of parameter calibration.
6. The camera calibration method according to claim 5, wherein the anti-distortion iteration is specifically: and carrying out anti-distortion on the original sampling point by using the updated estimated camera distortion parameters, so that the re-projection error between the original sampling point and the re-projected object point is minimized.
7. The camera calibration method according to claim 6, wherein the anti-distortion iteration specifically comprises the steps of:
s61, performing anti-distortion iteration according to the camera distortion parameters obtained in the S4, substituting the camera internal parameters as fixed values, solving the minimum re-projection errors of the camera external parameters, and updating the camera distortion parameters;
s62, substituting the camera external parameters obtained in the previous step and the updated camera distortion parameters as fixed values, solving the camera internal parameters to minimize the re-projection errors, and updating the camera distortion parameters;
S63, substituting the camera internal parameters obtained in the previous step and the updated camera distortion parameters as fixed values, solving the camera external parameters to minimize the re-projection errors again, and updating the camera distortion parameters;
S64, circulating S62-S63 until the re-projection error between the original sampling point and the re-projected object point is minimized.
8. The camera calibration method according to claim 1, wherein the checkerboard image captured in S1 is a checkerboard calibration plate comprising a checkerboard of known size and location.
9. The method for calibrating a camera according to claim 1, wherein the camera parameters in S3 include: including focal length, principal point coordinates, camera external parameters include: the rotation matrix and translation vector.
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| CN119295358A (en) * | 2024-12-12 | 2025-01-10 | 苏州镁伽科技有限公司 | Image distortion correction method, device, electronic device and storage medium |
| CN119379814A (en) * | 2024-12-25 | 2025-01-28 | 上海米仁科技有限公司 | Infrared irradiation point position recognition method, system and computer program |
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| Publication number | Priority date | Publication date | Assignee | Title |
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| CN119295358A (en) * | 2024-12-12 | 2025-01-10 | 苏州镁伽科技有限公司 | Image distortion correction method, device, electronic device and storage medium |
| CN119379814A (en) * | 2024-12-25 | 2025-01-28 | 上海米仁科技有限公司 | Infrared irradiation point position recognition method, system and computer program |
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