CN108198219A - 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 present invention relates to photogrammetric technology fields, and in particular to a kind of mistake for photogrammetric camera calibration parameter
Poor compensation method.Camera calibration parameter error is mended caused by being applied particularly to the flatness error applied to plane target drone
It repays.
Background technology
Photogrammetric technology is widely used in artificial intelligence, vision measurement and robot technology.Camera calibration is photogrammetric
One step of key, the precision of calibration result directly influences the accuracy of measurement result.Plane target drone is because of the simple calibration of its processing
Algorithmic stability is widely used.To further improve the precision of calibration result, error existing for links in calibration process is considered
And it is a kind of method for improving calibration result precision to carry out error compensation.Wherein the machining accuracy of plane reference target ties calibration
The influence of fruit is particularly important.Therefore it is from two angles to improve target machining accuracy or carry out additional target mismachining tolerance compensation
The method that degree analysis improves calibration result precision.
Plane target drone stated accuracy is improved at present mainly to carry from the raising calibration target accuracy of manufacture with target characteristic point is improved
Two aspects of precision is taken to carry out.For example, the patent for being CN201310140445.5 in Wu Hongjie et al. number of patent application submitted
Middle proposition is a kind of to multidimensional characteristic camera calibration error compensating method, mainly by calculating characteristic point x-axis and y-axis deviation compensation
Light target errors of centration.This scheme can not make compensation for z-axis deviation.
In addition, propose that one kind regards in the patent that the number of patent application submitted in Zhou Fuqiang et al. is CN201210035098.5
Feel and measure camera parameter optimization method.This method carries out distortion correction to the image coordinate of characteristic point, calculates connection projection centre
With the projection ray equation of orthoscopic image characteristic point；By three-dimensional coordinate and projection ray of the characteristic point under camera coordinate system
Compared with the intersection point of corresponding target plane, camera parameters are optimized with search using the two distance as object function.The party
Case can not be compensated for error caused by the irregularity degree of plane target drone.
Further more, propose a kind of benefit of image parameter in the patent of the Patent No. CN201510408436.9 proposed in Zhao Jian
Compensation method.This method demarcates target just for plane gridiron pattern, and this method is by regarding the minimum spacing between lattice point as mark
Quasi- distance, calculates the root-mean-square error of the three-dimensional distance and gauged distance between the adjacent feature point of uncalibrated image, then by every width
The image characteristic point of test image is counter to project target planar shaped commercial base, calculates the distance between itself and all space characteristics points
Root-mean-square error.The program can only be obtained root-mean-square error, therefore error compensation and inaccurate.
Or it is proposed in the patent that the number of patent application proposed in Zhang Fumin et al. is CN201610608257.4 a kind of
The online error compensating method of robot of camera chain.The two-dimentional dipmeter robot measurement end both direction of this method
Angular pose can realize robot end's 3 d pose with reference to a higher angle-data of the precision that robot itself resolves
Measure, and the attitude data measured with camera chain carry out data fusion, compare after be compensated value, industrial robot is controlled to make
Error is compensated.Attitude data is directly calibrated in the program and robot itself solution is compared compensation, it is substantially also difficult
Error compensates caused by the irregularity degree to plane target drone.
It can thus be seen that still lack in the prior art a kind of offset in out-of-flatness target Z-direction into
The method of row effective compensation, it would be highly desirable to improve.
Invention content
In view of the above problem of the existing technology, the purpose of the present invention is to provide one kind can further improve camera
The error compensating method for photogrammetric camera calibration parameter of the precision of calibration result.
To achieve these goals, a kind of mistake for photogrammetric camera calibration parameter provided in an embodiment of the present invention
Poor compensation method, including：
S1, the offset of the relative datum plane in z-axis direction for measuring and calculating the plane target drone characteristic point；
S2, the initial value for not adding camera parameter under error compensation is calibrated；
S3, according to the initial value, obtain the offset of the relative datum plane in the z-axis direction of the plane target drone characteristic point
Amount causes the offset of character pair point pixel coordinate in the plane target drone correspondence image；
S4, pass through the pixel coordinate in the characteristic point correspondence image described in offset correction course corrections on plane target drone；
S5, camera parameter calibration is re-started with the image coordinate after the correction.
Preferably, step S1, including：The z-axis side of any one of characteristic point on the plane target drone is set first
It is 0 to coordinate, next measures the z-axis side of the relatively any one of characteristic point of other described characteristic points on the plane target drone
To coordinate value, the feature point coordinates that above-mentioned measurement process is measured is (xn,yn,zn), show that the benchmark is put down with least square method
Face equation ax+by+z+c=0, the offset Δ zn=zn+(axn+byn+c)。
Preferably, the offset correction processes in step S4, including：According to the initial value and the offset,
Obtain homography matrixPixel coordinate in the corresponding image of the characteristic point is (un,
vn), the pixel coordinate after correction is (u 'n, v 'n), wherein the pixel coordinate compensation formula is u 'n=un-h3ΔznWith v 'n=
vn-h7Δzn。
Preferably, step S5 and then repeating S4 and S5 step n times, the n is the integer more than 0.
Technical solution of the present invention compared with prior art the advantages of be, high-precision target processing charges is high, injustice leveling
The pixel coordinate error compensating method that face target is derived by this programme can improve calibration in the case where not improving cost
As a result precision.This programme has used least square method so that offset in the offset for asking out-of-flatness target z-axis direction
Result it is relatively reliable, improve the computational accuracy of image coordinate compensation process.This programme optimization process needs iteration, is conducive to
The precision of calibration result is further improved, and iterative process number can require sets itself according to measurement accuracy, algorithm can be real
With property height.
Description of the drawings
Fig. 1 is the basic flow chart of the error compensating method for photogrammetric camera calibration parameter of the present invention；
Fig. 2 is the calculation of one embodiment of the error compensating method for photogrammetric camera calibration parameter of the present invention
Method flow chart；
Fig. 3 is the picture point and spatial point of the error compensating method for photogrammetric camera calibration parameter of the present invention
The mathematical model of presentation；
Fig. 4 is that the initial parameter of the error compensating method for photogrammetric camera calibration parameter of the present invention is calibrated
Journey.
Specific embodiment
For those skilled in the art is made to be better understood from technical scheme of the present invention, below in conjunction with the accompanying drawings and specific embodiment party
Formula elaborates to the present invention.
It is of the invention by the description of the preferred form of the embodiment with reference to the accompanying drawings to being given as non-limiting examples
These and other characteristic will become apparent.
It is also understood that although invention has been described with reference to some specific examples, people in the art
Member realize with can determine the present invention many other equivalents, they have feature as claimed in claim and therefore all
In the protection domain limited whereby.
Specific embodiments of the present invention are described hereinafter with reference to attached drawing；It will be appreciated, however, that the embodiment invented is only
Various ways implementation can be used in the example of the present invention.Function and structure that is known and/or repeating is not described in detail with basis
True intention is distinguished in the operation of the history of user, and unnecessary or extra details is avoided so that the present invention is smudgy.Cause
This, the specific structural and functional details invented herein are not intended to restriction, but as just the base of claim
Plinth and representative basis are used to that those skilled in the art to be instructed diversely to use this hair with substantially any appropriate detailed construction
It is bright.
This specification can be used phrase " in one embodiment ", " in another embodiment ", " in another embodiment
In " or " in other embodiments ", it can be referred to one or more of identical or different embodiment according to the present invention.
Present invention is primarily intended to compensate plane target drone out-of-flatness by the method for iteration to cause pixel in correspondence image
Deviation optimize calibrating parameters, it is necessary first to calibrate the initial value of camera parameter, then measure plane target drone characteristic point z
The offset of axis direction the offset of the relative datum plane in plane target drone characteristic point z-axis direction is obtained with least square method, so
Go out the offset calculation formula of the character pair point pixel coordinate on image according to camera parameter Derivation of Mathematical Model afterwards, correct
Camera parameter calibration is re-started after the offset of characteristic point pixel coordinate, it is heavy multiple as initial value to obtain new calibration result
Above-mentioned steps, the result after n times iteration is as final calibration result.Fig. 1 is shown as the basic flow chart of the present invention, as schemed institute
Show, a kind of error compensating method for photogrammetric camera calibration parameter proposed by the present invention, including：
S1, the offset of the relative datum plane in z-axis direction for measuring and calculating the plane target drone characteristic point；
S2, the initial value for not adding camera parameter under error compensation is calibrated；
S3, according to the initial value, obtain the offset of the relative datum plane in the z-axis direction of the plane target drone characteristic point
Amount causes the offset of character pair point pixel coordinate in the plane target drone correspondence image；
S4, pass through the pixel coordinate in the characteristic point correspondence image described in offset correction course corrections on plane target drone；
S5, camera parameter calibration is re-started with the image coordinate after the correction.
In embodiments of the present invention, camera parameter initial value includes：The plane under camera intrinsic parameter and different postures
Target is respectively with respect to the spin matrix of two camera coordinate systems, translation vector and scale factor.It is asked with Zhang Zhengyou scaling methods
Solve initial parameter.
The offset method for solving of the relative datum plane in plane target drone characteristic point z-axis direction is：Assume initially that flat target
It puts at arbitrary point as coordinate dot, measures the z-axis coordinate value at other points, the spy measured according on the target
Sign point coordinates is (xn,yn,zn) with least square method the datum plane equation Ax+By+z+C=0, the offset Δ is obtained
zn=zn+(Axn+Byn+C)。
The offset solution formula of the character pair point pixel coordinate is on the image that this programme is derived：Basis first
Zhang Zhengyou scaling methods solve the initial value of calibration result, and homography matrix is solved according to initial value
Pixel coordinate in the corresponding image of characteristic point is (un, vn), after correction
Pixel coordinate is (u 'n, v 'n), wherein the u 'n=un-h3Δzn, the v 'n=vn-h7Δzn。
Using the above-mentioned pixel coordinate value solved after carrying out error compensation as characteristic point on initial known parameters combination target
Plane coordinates, the camera parameter after compensation is solved in Zhang Zhengyou calibration formulas.
Using the camera parameter after secondary compensation as initial value, new homography matrix is calculated, according to institute on above-mentioned image
The offset solution formula for stating character pair point pixel coordinate solves the correspondence on image with reference to new homography matrix value
Pixel coordinate after the offset compensation of characteristic point pixel coordinate re-scales camera parameter and repeats n times.
Obtained camera parameter after n times are optimized is typically repeated 4 times or more as correction of a final proof camera parameter.
This programme is that high-precision target processing charges is high, and out-of-flatness plane target drone leads to compared to the advantages of other methods
The essence of calibration result can be improved in the case where not improving cost by crossing the pixel coordinate error compensating method that this programme is derived
Degree.This programme has used least square method so that the result of offset is more in the offset for asking out-of-flatness target z-axis direction
Add the computational accuracy for reliably, improving image coordinate compensation process.This programme optimization process needs iteration, is conducive to further carry
The precision of high calibration result, and iterative process number can require sets itself according to measurement accuracy, algorithm can practicability height.
Additionally referring to Fig. 2, it is as follows often to walk concrete methods of realizing for Error Compensation Algorithm flow chart.
Step assumes that a certain characteristic point is coordinate origin on target, measures the z-axis direction coordinate value of other points, characteristic point
X-axis and y-axis coordinate are known.The feature point coordinates measured is (xn,yn,zn), represent the three-dimensional of n-th of characteristic point
Coordinate shares N number of characteristic point.
Step set its datum plane equation as Ax+By+z+C=0, wherein A, B, C be unknown quantity, least square method solution procedure
It is as follows：
If ε=Ax+By+z+C
So that residual error is minimum：
∑ε2=∑ (Ax+By+z+C)2 1.1
1.4 from 1.2-1.4 formulas：
1.5 formulas, which are brought into upper 1.2-1.4 formulas, to be obtained：
N ∑ xz- ∑ x ∑s z=-A (∑ x2-∑x∑x)-B(N∑xy-∑x∑y) 1.6
z′1=N ∑ xz- ∑ x ∑s z 1.7
a1=∑ x2-∑x∑x 1.8
b1=N ∑ xy- ∑ x ∑s y 1.9
N ∑ yz- ∑ y ∑s z=-A (∑ xy- ∑ x ∑ y)-B (N ∑s y2-∑y∑y) 1.10
z′2=N ∑ yz- ∑ y ∑s z 1.11
a2=∑ xy- ∑ x ∑s y 1.12
b2=N ∑s y2-∑y∑y 1.13
-z′1=Aa1+Bb1 1.14
-z′2=Aa2+Bb2 1.15
Third step according to the datum plane Ax+By+z+C=0 that solves, Calculation Plane target characteristic point z-axis direction it is inclined
Shifting amount Δ znFor：
Δzn=zn+(Axn+Byn+C)。 1.19
4th step demarcates target or circular index point plane target drone according to Zhang Zhengyou calibration principles by plane gridiron pattern
Calibrating procedure is write out in OpenCV.Initial parameter calibration process is as shown in Fig. 2, with binocular camera while camera plane target
Image several, from image and calibration target on characteristic point position coordinate relationship solve camera initial parameter.In Zhang Zhengyou schemes
Reaction image pixel coordinates and target on relationship between feature point coordinates mathematical model it is as follows：
The coordinate (u, v) of pixel and corresponding spatial point on image according to the Zhang Zhengyou plane target drone camera parameter models
Coordinate (x, y, z) relationship be：
Wherein s is scale factor, and H is homography matrix, and H=A [R | T] wherein R is spin matrix, and T is translation vector, A
For camera intrinsic parameter.Assuming that above-mentioned formula can be converted into the point on target in a plane：
5th step setting Optimized Iterative number is N (N>0), the process number of repetition of N representing optimizeds iteration, for optimizing journey
Sequence finally determines whether to complete optimization output result.Iterations flag bit n often carries out an iteration n and adds 1 automatically, every time repeatedly
The magnitude relationship of iteration flag bit n and N is judged after the completion of generation, is exported after n is more than or equal to the iterations N of initial user setting
Camera parameter after iteration optimization is as final result.
6th step goes out the pixel coordinate after correction according to camera parameter Derivation of Mathematical Model, and specific derivation process is：
Assume that target is separately as shown in figure 3, representing the relationship between pixel coordinate and target co-ordinates system, in Zhang Zhengyou models
Plane target drone, but practical target is since plane target drone out-of-flatness causes target z-axis direction coordinate value to be not zero, above-mentioned steps meter
The offset in target z-axis direction relative datum face is calculated.In fig. 4, it is assumed that plane target drone is three-dimensional coordinate, target passes through phase
Machine lens imaging is projected in image plane, and according to imaging model, there are certain mathematics passes for point and point in correspondence image on target
System.R, T represent the spin matrix and translation vector between target co-ordinates system and photo coordinate system respectively in figure.Feature on target
Subpoints of the point A in image plane is A '.
For the plane target drone of out-of-flatness, picture on the corresponding image with error of coordinate (x, y, z) of characteristic point thereon
Coordinate (the u of vegetarian refreshmentse, ve) between correspondence, can be expressed as：
Wherein homography matrix and scale factor be by Zhang Zhengyou scaling methods, by out-of-flatness target calibrate Lai just
Initial value.It can be obtained by upper 1.21 and 1.22 formulas：
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 znIf the pixel coordinate in the corresponding image of n-th of characteristic point is (un, vn), the pixel after correction
Coordinate is (u 'n, v 'n), from 1.23-1.26 formulas：
u′n=un-h3Δzn 1.27
v′n=vn-h7Δzn 1.28
1.19 formulas are substituted into obtain to 1.27 and 1.28 formulas：
u′n=un-h3(zn+(Axn+Byn+C)) 1.29
v′n=vn-h7(zn+(Axn+Byn+C)) 1.30
7th step is the pixel coordinate (u ' after correctionn, v 'n) and corresponding flat target on known to the coordinate (x, y) put is used as
Condition substitutes into equation：
The inside and outside parameter of camera is solved according to Zhang Zhengyou plane target drone scaling methods, wherein s is scale factor, and A is interior
Ginseng, R is spin matrix, and T is translation vector.
8th step is complete primary per Optimization Solution, and iteration flag bit n is automatically plus one, n represents iteration optimization and carried out n times.
9th step judges iteration flag bit n and sets relationship of the Optimized Iterative number between N, if n<N obtains the 8th step
To n-th compensation after camera parameter bring back to the 6th step as initial value, computed repeatedly again from the 6th step to the 8th step.
Using by solved after error compensation come camera parameter as initial value, substitute into the pixel coordinate (u ' after correction againn, v 'n)
With in the coordinate (x, y) to above-mentioned formula put on corresponding flat target, new camera parameter is solved.Then judged again.
The precision that the step repeats n times optimum results can improve.Until n is more than or equal to N, the result after n times are optimized is as final
Correcting camera parameter.Complete the compensation to camera calibration parameter error caused by plane target drone flatness error.
This document describes various operations or functions, can be realized or be defined as software generation as software code or instruction
Code or instruction.Such content can be (" object " or " executable " form) source code or differential code that can directly perform
(" increment " or " patch " code).The software of embodiment as described herein is realized can be via being wherein stored with code or instruction
Product is provided via operation communication interface in method via communication interface transmission data.Machine computer-readable is deposited
Storage media can make machine perform described function or operation, and including with can be by machine (for example, computing device, electronics
System etc.) any mechanism of form storage information for accessing, such as recordable/non-recordable medium is (for example, read-only memory
(ROM), random access memory (RAM), magnetic disk storage medium, optical storage media, flash memory device, etc.).Communication interface includes
It is joined to any mechanism of any one of the media such as hardwired, wireless, optics to communicate with another equipment, such as memory
Bus interface, processor bus interface, internet connection, Magnetic Disk Controler etc..Can parameter and/or transmission be configured by offer
Communication interface is configured to get out the communication interface to provide the data-signal of description software content by signal.It can be via
One or more orders or the signal of communication interface are sent to access communication interface.
The foregoing is merely illustrative of the preferred embodiments of the present invention, is not intended to limit the scope of the present invention.It is all
Within the spirit and principles in the present invention, any modification, equivalent replacement and improvement for being made etc. should be included in the guarantor of the present invention
Within the scope of shield.
Claims (4)
1. a kind of error compensating method for photogrammetric camera calibration parameter, including：
S1, the offset of the relative datum plane in z-axis direction for measuring and calculating the plane target drone characteristic point；
S2, the initial value for not adding camera parameter under error compensation is calibrated；
S3, according to the initial value, show that the offset of the relative datum plane in the z-axis direction of the plane target drone characteristic point is drawn
Play the offset of character pair point pixel coordinate in the plane target drone correspondence image；
S4, pass through the pixel coordinate in the characteristic point correspondence image described in offset correction course corrections on plane target drone；
S5, camera parameter calibration is re-started with the image coordinate after the correction.
2. it to be used for the error compensating method of photogrammetric camera calibration parameter as described in claim 1, which is characterized in that step
Rapid S1, including：The z-axis direction coordinate of any one of characteristic point on the plane target drone is set first as 0, next is measured
The z-axis direction coordinate value of the relatively any one of characteristic point of other described characteristic points, above-mentioned to measure on the plane target drone
The feature point coordinates that journey is measured is (xn,yn,zn), obtain the datum plane equation ax+by+z+c=0 with least square method,
The offset Δ zn=zn+(axn+byn+c)。
3. it to be used for the error compensating method of photogrammetric camera calibration parameter as described in claim 1, which is characterized in that step
The offset correction processes in rapid S4, including：According to the initial value and the offset, homography matrix is obtainedPixel coordinate in the corresponding image of the characteristic point is (un, vn), the pixel after correction
Coordinate is (u 'n, v 'n), wherein the pixel coordinate compensation formula is u 'n=un-h3ΔznWith v 'n=vn-h7Δzn。
4. it to be used for the error compensating method of photogrammetric camera calibration parameter as described in claim 1, which is characterized in that step
Rapid S5 and then S4 and S5 step n times are repeated, the n is the integer more than 0.
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| CN110202581A (en) * | 2019-06-28 | 2019-09-06 | 南京博蓝奇智能科技有限公司 | Compensation method, device and the electronic equipment of end effector of robot operating error |
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| WO2021208369A1 (en) * | 2020-04-17 | 2021-10-21 | 嘉楠明芯(北京)科技有限公司 | Image correction method and apparatus |
| CN114061472A (en) * | 2021-11-03 | 2022-02-18 | 常州市建筑科学研究院集团股份有限公司 | Method for correcting measurement coordinate error based on target |
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