CN108198219B - Error compensation method for camera calibration parameters for photogrammetry - Google Patents
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Abstract
The invention discloses an error compensation method for camera calibration parameters for photogrammetry, which comprises the following steps: s1, measuring and calculating the offset of the plane target feature point relative to the reference plane in the z-axis direction; s2, calibrating the initial value of the lower camera parameter without error compensation; s3, obtaining the offset of the z-axis direction of the plane target feature point relative to the reference plane to cause the offset of the pixel coordinate of the corresponding feature point on the image corresponding to the plane target according to the initial value; s4, correcting the pixel coordinates on the image corresponding to the feature points on the plane target through an offset correction process; and S5, calibrating the camera parameters again by using the corrected image coordinates. Compared with the prior art, the technical scheme of the invention has the advantages that the high-precision target is high in processing cost, and the accuracy of the calibration result can be improved by the uneven plane target through the pixel coordinate error compensation method deduced by the scheme without increasing the cost.
Description
Technical Field
The invention relates to the technical field of photogrammetry, in particular to an error compensation method for camera calibration parameters used for photogrammetry. The method can be particularly applied to compensating the camera calibration parameter error caused by the flatness error of the plane target application.
Background
Photogrammetry techniques are widely used in artificial intelligence, vision measurement and robotics. Camera calibration is a key step of photogrammetry, and the accuracy of a calibration result directly influences the accuracy of a measurement result. The plane target is simple to process, stable in calibration algorithm and wide in application. In order to further improve the precision of the calibration result, the method for improving the precision of the calibration result is to consider the errors existing in each link in the calibration process and perform error compensation. The processing precision of the plane calibration target is particularly important to influence the calibration result. Therefore, the method for improving the target machining precision or performing additional target machining error compensation is a method for improving the precision of the calibration result from two-angle analysis.
At present, the improvement of the calibration precision of the plane target is mainly carried out from the aspects of improving the manufacturing precision of the calibration target and improving the extraction precision of the characteristic points of the target. For example, in patent application No. CN201310140445.5 filed by wu macrojie et al, a method for compensating calibration errors of a multi-dimensional feature camera is proposed, which mainly compensates the center errors of an optical target by calculating the deviations of the x axis and the y axis of feature points. This solution does not compensate for z-axis deviations.
In addition, a visual measurement camera parameter optimization method is proposed in patent application No. CN201210035098.5 filed by zhou fu et al. The method carries out distortion correction on the image coordinates of the feature points and calculates a projection ray equation connecting a projection center and the undistorted image feature points; and comparing the three-dimensional coordinates of the feature points in the camera coordinate system with the intersection points of the projection rays and the corresponding target planes, and performing optimized search on the camera parameters by taking the distance between the three-dimensional coordinates and the intersection points as a target function. This solution does not compensate for errors caused by unevenness of the planar target.
Further, a method for compensating image parameters is proposed in patent No. CN201510408436.9, which was proposed by zhao, thrifty, and thrifty. The method only aims at a planar checkerboard calibration target, calculates the root mean square error between the three-dimensional distance between adjacent characteristic points of a calibration image and a standard distance by taking the minimum distance between grid points as the standard distance, then reversely projects the image characteristic points of each test image to a target plane to form intersection points, and calculates the root mean square error between the intersection points and the distances between the intersection points and all spatial characteristic points. This solution only finds the root mean square error and therefore the error compensation is not accurate.
Alternatively, a method for on-line robot error compensation of a camera system is proposed in a patent application No. CN201610608257.4 by zhan fosamian et al. The method uses a two-dimensional dip angle measuring instrument to measure the angular postures of the two directions at the tail end of the robot, combines an angular data with higher precision calculated by the robot to realize the measurement of the three-dimensional posture at the tail end of the robot, performs data fusion and comparison with the posture data measured by a photographic system to obtain a compensation value, and controls the industrial robot to compensate errors. In the scheme, the attitude data is directly calibrated and compared with the solution of the robot, and the error caused by the unevenness of the plane target is difficult to compensate essentially.
Therefore, a method for effectively compensating the offset of the uneven target in the Z-axis direction is still lacked in the prior art, and improvement is urgently needed.
Disclosure of Invention
In view of the above problems in the prior art, an object of the present invention is to provide an error compensation method for camera calibration parameters for photogrammetry, which can further improve the accuracy of camera calibration results.
In order to achieve the above object, an embodiment of the present invention provides an error compensation method for camera calibration parameters used in photogrammetry, including:
s1, measuring and calculating the offset of the plane target feature point relative to the reference plane in the z-axis direction;
s2, calibrating the initial value of the lower camera parameter without error compensation;
s3, obtaining the offset of the z-axis direction of the plane target feature point relative to the reference plane to cause the offset of the pixel coordinate of the corresponding feature point on the image corresponding to the plane target according to the initial value;
s4, correcting the pixel coordinates on the image corresponding to the feature points on the plane target through an offset correction process;
and S5, calibrating the camera parameters again by using the corrected image coordinates.
Preferably, step S1 includes: firstly setting the z-axis coordinate of any one of the feature points on the planar target as 0, secondly measuring the z-axis coordinate of other feature points on the planar target relative to any one of the feature points, wherein the feature point coordinate measured in the measuring process is (x)n,yn,zn) Obtaining the reference plane equation ax + by + z + c as 0 by using a least square method, wherein the offset amount delta z isn＝zn+(axn+byn+c)。
Preferably, the offset correction process in step S4 includes: obtaining a homography matrix according to the initial value and the offset
The pixel coordinate in the image corresponding to the characteristic point is (u)n，vn) The corrected pixel coordinate is (u'n，v′n) Wherein the pixel coordinate compensation formula is u'n＝un-h3ΔznAnd v'n＝vn-h7Δzn。
Preferably, after the step S5, the steps S4 and S5 are repeatedly performed n times, where n is an integer greater than 0.
Compared with the prior art, the technical scheme of the invention has the advantages that the high-precision target is high in processing cost, and the accuracy of the calibration result can be improved by the uneven plane target through the pixel coordinate error compensation method deduced by the scheme without increasing the cost. When the offset of the uneven target in the z-axis direction is solved, the least square method is used, so that the offset result is more reliable, and the calculation precision of the image coordinate compensation process is improved. The optimization process of the scheme needs iteration, the accuracy of the calibration result is further improved, the times of the iteration process can be set by self according to the measurement accuracy requirement, and the algorithm has high practicability.
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FIG. 1 is a basic flow chart of the method for error compensation of camera calibration parameters for photogrammetry according to the present invention;
FIG. 2 is a flowchart illustrating an algorithm of an embodiment of a method for error compensation of camera calibration parameters for photogrammetry in accordance with the present invention;
FIG. 3 is a mathematical model of the image point and space point representation of the method for error compensation of camera calibration parameters for photogrammetry of the present invention;
FIG. 4 is a diagram illustrating an initial parameter calibration process of the method for error compensation of camera calibration parameters for photogrammetry according to the present invention.
Detailed Description
In order to make the technical solutions of the present invention better understood, the present invention will be described in detail below with reference to the accompanying drawings and specific embodiments.
These and other characteristics of the invention will become apparent from the following description of a preferred form of embodiment, given as a non-limiting example, with reference to the accompanying drawings.
It should also be understood that, although the invention has been described with reference to some specific examples, a person of skill in the art shall certainly be able to achieve many other equivalent forms of the invention, having the characteristics as set forth in the claims and hence all coming within the field of protection defined thereby.
Specific embodiments of the present invention are described hereinafter with reference to the accompanying drawings; however, it is to be understood that the disclosed embodiments are merely exemplary of the invention, which can be embodied in various forms. Well-known and/or repeated functions and constructions are not described in detail to avoid obscuring the invention in unnecessary or unnecessary detail based on the user's historical actions. Therefore, specific structural and functional details disclosed herein are not to be interpreted as limiting, but merely as a basis for the claims and as a representative basis for teaching one skilled in the art to variously employ the present invention in virtually any appropriately detailed structure.
The specification may use the phrases "in one embodiment," "in another embodiment," "in yet another embodiment," or "in other embodiments," which may each refer to one or more of the same or different embodiments in accordance with the invention.
The invention mainly aims to optimize calibration parameters by compensating the deviation of pixel points on a corresponding image caused by the unevenness of a plane target through an iteration method, firstly calibrating the initial value of camera parameters, then measuring the offset of the plane target in the z-axis direction of characteristic points, solving the offset of the plane target in the z-axis direction relative to a reference plane by using a least square method, then deducing an offset calculation formula of pixel coordinates of the corresponding characteristic points on the image according to a camera parameter mathematical model, calibrating the camera parameters again after correcting the offset of the pixel coordinates of the characteristic points, obtaining a new calibration result as the initial value, and repeating the steps, wherein the result after n times of iteration is used as the final calibration result. Fig. 1 is a basic flowchart of the present invention, and as shown in the figure, the present invention provides an error compensation method for camera calibration parameters of photogrammetry, which includes:
s1, measuring and calculating the offset of the plane target feature point relative to the reference plane in the z-axis direction;
s2, calibrating the initial value of the lower camera parameter without error compensation;
s3, obtaining the offset of the z-axis direction of the plane target feature point relative to the reference plane to cause the offset of the pixel coordinate of the corresponding feature point on the image corresponding to the plane target according to the initial value;
s4, correcting the pixel coordinates on the image corresponding to the feature points on the plane target through an offset correction process;
and S5, calibrating the camera parameters again by using the corrected image coordinates.
In an embodiment of the present invention, the initial values of the camera parameters include: the camera internal parameters and the rotation matrix, the translation vector and the scale factor of the plane target relative to the two camera coordinate systems respectively under different postures. Solving the initial parameters by a Zhangyingyou calibration method.
The offset solving method of the plane target characteristic point in the z-axis direction relative to the reference plane comprises the following steps: firstly, assuming any point on a plane target as a coordinate round point, measuring the coordinate value of a z axis at other points, and according to the measured characteristic point coordinate on the target, obtaining the coordinate (x)n,yn,zn) Solving the reference plane equation Ax + By + z + C as 0 By the least square method, wherein the offset amount is delta zn＝zn+(Axn+Byn+C)。
The solution formula of the offset of the pixel coordinate of the corresponding characteristic point on the image deduced by the scheme is as follows: firstly, an initial value of a calibration result is solved according to a Zhang-Yong calibration method, and a homography matrix is solved according to the initial value
The pixel coordinate in the image corresponding to the feature point is (u)n，vn)，The corrected pixel coordinate is (u'n，v′n) Wherein u'n＝un-h3ΔznV 'to'n＝vn-h7Δzn。
And (3) taking the pixel coordinate value after the error compensation is solved as an initial known parameter, combining the plane coordinate of the feature point on the target, and solving the camera parameter after the compensation in a Zhangyingyou calibration formula.
And taking the camera parameters after secondary compensation as initial values, calculating a new homography matrix, solving the pixel coordinates after offset compensation of the pixel coordinates of the corresponding characteristic points on the image according to an offset solving formula of the pixel coordinates of the corresponding characteristic points on the image and the new homography matrix values, and re-calibrating the camera parameters for repeating n times.
The obtained camera parameters after n-times optimization are taken as final correction camera parameters and are generally repeated for more than 4 times.
Compared with other methods, the method has the advantages that the high-precision target is high in processing cost, and the accuracy of the calibration result can be improved by the uneven plane target through the pixel coordinate error compensation method derived by the method without increasing the cost. When the offset of the uneven target in the z-axis direction is solved, the least square method is used, so that the offset result is more reliable, and the calculation precision of the image coordinate compensation process is improved. The optimization process of the scheme needs iteration, the accuracy of the calibration result is further improved, the times of the iteration process can be set by self according to the measurement accuracy requirement, and the algorithm has high practicability.
Referring to fig. 2, a flow chart of an error compensation algorithm is shown, and each step is implemented as follows.
Step, assuming a certain characteristic point on the target as a coordinate origin, measuring the coordinate values of other points in the z-axis direction, wherein the x-axis coordinate and the y-axis coordinate of the characteristic point are known. Obtaining the coordinate of the measured characteristic point as (x)n,yn,zn) The three-dimensional coordinates of the nth feature point are represented, and N feature points are total.
Step By setting the equation of the reference plane as Ax + By + z + C as 0, wherein A, B, C is an unknown quantity, and the solution process of the least square method is as follows:
let epsilon be Ax + By + z + C
So that the residual error is minimal:
∑ε2＝∑(Ax+By+z+C)2 1.1
1.4 according to formulae 1.2-1.4:
substituting formula 1.5 into the above formulae 1.2-1.4 can result in:
N∑xz-∑x∑z＝-A(∑x2-∑x∑x)-B(N∑xy-∑x∑y) 1.6
z′1＝N∑xz-∑x∑z 1.7
a1＝∑x2-∑x∑x 1.8
b1＝N∑xy-∑x∑y 1.9
N∑yz-∑y∑z＝-A(∑xy-∑x∑y)-B(N∑y2-∑y∑y) 1.10
z′2＝N∑yz-∑y∑z 1.11
a2＝∑xy-∑x∑y 1.12
b2＝N∑y2-∑y∑y 1.13
-z′1＝Aa1+Bb1 1.14
-z′2＝Aa2+Bb2 1.15
thirdly, calculating the offset delta z of the plane target characteristic point in the z-axis direction according to the solved reference plane Ax + By + z + C as 0nComprises the following steps:
Δzn＝zn+(Axn+Byn+C)。 1.19
and fourthly, writing a calibration program in the OpenCV through the planar checkerboard calibration target or the circular mark point planar target according to the Zhang Zhengyou calibration principle. The initial parameter calibration process is shown in fig. 2, a plurality of images of a plane target are shot by a binocular camera at the same time, and initial parameters of the camera are solved from the coordinate relation of the positions of the images and the positions of the characteristic points on the calibration target. The mathematical model reflecting the relationship between the pixel coordinates of the image and the coordinates of the feature points on the target in the Zhang-Yongyou scheme is as follows:
according to the Zhangling friend plane target camera parameter model, the relation between the coordinates (u, v) of the pixel points on the image and the coordinates (x, y, z) of the corresponding space points is as follows:
where s is a scale factor, H is a homography matrix, H ═ a [ R | T ] where R is a rotation matrix, T is a translation vector, and a is an in-camera parameter. Assuming that the points on the target are in one plane, the above formula can be translated into:
and fifthly, setting the number of times of optimization iteration to be N (N >0), wherein N represents the process repetition number of the optimization iteration and is used for the optimization program to finally judge whether the optimization output result is finished. And (3) automatically adding 1 to the iteration number flag N every time the iteration number flag N is performed, judging the size relationship between the iteration flag N and the iteration flag N after each iteration is completed, and outputting the camera parameters after the iteration optimization as a final result when N is greater than or equal to the iteration number N set by the initial user.
And sixthly, deducing the corrected pixel coordinates according to the camera parameter mathematical model, wherein the specific deduction process is as follows:
as shown in fig. 3, the relationship between the representative pixel coordinate and the target coordinate system is represented, the assumed target in the zhangyou model is a planar target, but the coordinate value of the actual target in the z-axis direction is not zero due to the unevenness of the planar target, and the offset of the target in the z-axis direction relative to the reference plane is calculated in the above steps. In fig. 4, it is assumed that the planar target is a three-dimensional coordinate, the target is projected on the image plane through the camera lens, and a certain mathematical relationship exists between a point on the target and a point on the corresponding image according to the imaging model. R, T represent the rotation matrix and translation vector between the target coordinate system and the image plane coordinate system, respectively. The projection point of the characteristic point A on the target on the image plane is A'.
For an uneven plane target, the coordinates (x, y, z) of the characteristic point correspond to the coordinates (u) of the pixel point on the image with errore，ve) The corresponding relationship between the two can be expressed as:
the homography matrix and the scale factor are initial values calibrated by the uneven target through a Zhang Zhengyou calibration method. From the above formulae 1.21 and 1.22 it is possible to obtain:
u＝h1x+h2y 1.23
v＝h5x+h6y 1.24
ue＝h1x+h2y+h3z 1.25
ve＝h5x+h6y+h7z 1.26
wherein z is Δ znLet the pixel coordinate in the image corresponding to the n-th feature point be (u)n，vn) The corrected pixel coordinate is (u'n，v′n) From 1.23 to 1.26, the following formulae are known:
u′n＝un-h3Δzn 1.27
v′n＝vn-h7Δzn 1.28
substituting formulae 1.19 to 1.27 and 1.28 yields:
u′n＝un-h3(zn+(Axn+Byn+C)) 1.29
v′n＝vn-h7(zn+(Axn+Byn+C)) 1.30
seventh step of calculating corrected pixel coordinates (u'n，v′n) And coordinates (x, y) of a point on the corresponding planar target as known conditions are substituted into the equation:
and solving internal and external parameters of the camera according to a Zhangyingyou plane target calibration method, wherein s is a scale factor, A is an internal reference, R is a rotation matrix, and T is a translation vector.
And in the eighth step, after each optimization solution is completed, the iteration flag bit n is automatically added by one, and n represents that the iteration optimization is performed for n times.
The ninth step is to judge the relation between the iteration flag bit N and the set optimized iteration number N, if N<And N, taking the camera parameter obtained in the eighth step after the nth compensation as an initial value to return to the sixth step, and repeating the calculation from the sixth step to the eighth step again. The camera parameters obtained by error compensation are substituted into the corrected pixel coordinates (u 'as initial values'n，v′n) And coordinates (x, y) of a point on the corresponding plane target are put into the formula, and new camera parameters are solved. Then making a judgment. The accuracy of this step repetition n sub-optimal results will increase. And taking the result of N sub-optimization as the final correction camera parameter until N is larger than or equal to N. Namely, the compensation of the camera calibration parameter error caused by the plane target flatness error is completed.
Various operations or functions are described herein that may be implemented as or defined as software code or instructions. Such content may be directly executable ("object" or "executable" form) source code or differential code ("delta" or "patch" code). Software implementations of embodiments described herein may be provided via an article of manufacture having code or instructions stored therein or via a method of operating a communication interface to transmit data via the communication interface. A machine or computer-readable storage medium may cause a machine to perform the functions or operations described, and includes any mechanism for storing information in a form accessible by a machine (e.g., a computing device, an electronic system, etc.), such as recordable/non-recordable media (e.g., Read Only Memory (ROM), Random Access Memory (RAM), magnetic disk storage media, optical storage media, flash memory devices, etc.). A communication interface includes any mechanism that interfaces to any of a hardwired, wireless, optical, etc. medium to communicate with another device, such as a memory bus interface, a processor bus interface, an internet connection, a disk controller, etc. The communication interface may be configured by providing configuration parameters and/or transmitting signals to prepare the communication interface to provide data signals describing the software content. The communication interface may be accessed via one or more commands or signals sent to the communication interface.
The above description is only for the preferred embodiment of the present invention, and is not intended to limit the scope of the present invention. Any modification, equivalent replacement, and improvement made within the spirit and principle of the present invention should be included in the protection scope of the present invention.
Claims (2)
1. The error compensation method of the camera calibration parameters for photogrammetry comprises the following steps:
s1, measuring and calculating the z-axis direction of the plane target feature pointAn offset to the reference plane; the method comprises the following steps: firstly setting the coordinate of any one characteristic point on a plane target in the z-axis direction as 0, secondly measuring the coordinate value of other characteristic points on the plane target in the z-axis direction relative to any one characteristic point, wherein the coordinate of other characteristic points measured in the measuring process is
The equation of the reference plane is obtained by the least square method
Offset of z-axis direction of planar target feature point from reference plane
；
S2, calibrating the initial value of the lower camera parameter without error compensation;
s3, obtaining the offset of the z-axis direction of the plane target feature point relative to the reference plane to cause the offset of the pixel coordinate of the corresponding feature point on the image corresponding to the plane target according to the initial value;
s4, correcting the pixel coordinates of the planar target feature point on the image through an offset correction process; the method comprises the following steps: obtaining a homography matrix according to the initial value and the offset of the pixel coordinate of the corresponding characteristic point on the image corresponding to the plane target
The pixel coordinate in the image corresponding to the planar target feature point is
The corrected pixel coordinate is
Wherein the pixel coordinate compensation formula is
And
；
and S5, calibrating the camera parameters again by using the corrected image coordinates.
2. The method for error compensation of calibration parameters of camera for photogrammetry as claimed in claim 1, wherein after step S5, steps S4 and S5 are repeated m times, wherein m is an integer greater than 0.
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