CN108805935A - It is a kind of based on orthogonal pixel equivalent than line-scan digital camera distortion correction method - Google Patents
It is a kind of based on orthogonal pixel equivalent than line-scan digital camera distortion correction method Download PDFInfo
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Abstract
It is a kind of based on orthogonal pixel equivalent than line-scan digital camera distortion correction method, by analyze line-scan digital camera imaging model, the theory of orthogonal direction pixel equivalent Ratio invariableness under ideal camera lens is deduced out, to finally obtain the distortion parameter of line-scan digital camera.Comprise the concrete steps that the angle point sought first on gridiron pattern picture, secondly appoint the angle point for taking adjacent rows, derive their undistorted coordinate expressions, then the x-axis and y-axis direction pixel equivalent value at lattice diagonal line midpoint are sought, object function to be optimized is subsequently obtained according to the theory of orthogonal direction pixel equivalent Ratio invariableness under ideal camera lens, finally can be obtained distortion parameter using nonlinear optimization method.The method of the present invention can obtain the longitudinal stretching ratio of picture simultaneously, and without carrying out secondary correction, therefore calculation amount smaller, Simultaneous Stabilization is good, and implementation condition easily reaches.
Description
Technical field
The invention belongs to technical field of image processing, are related to the aberration correction technique of camera, specially a kind of based on orthogonal
Pixel equivalent than line-scan digital camera distortion correction method.
Background technology
Line-scan digital camera is simple in structure, at low cost and high resolution, in contactless real-time measurement system, surface defects detection system
More and more applications are obtained in system and high-speed moving object attitude measurement system.In high-precision dimensional measurement and linear array binocular
In the applications such as vision, the presence of lens distortion can seriously affect system performance.Therefore, in more demanding line-scan digital camera vision system
It must distort to camera lens in system and be demarcated and compensated.
More mature to the research of area array cameras lens distortion theory at present, the classical standardization of either Zhang Zhengyou is also
Being individual distortion standardization has good precision to show, but the distortion model theory of line-scan digital camera is perfect not enough.Currently, line
Array camera lens distortion scaling method has method, polynomial fitting method and precision angle method based on cross ratio invariability theory etc..It hands over
It is the property based on cross ratio invariability in perspective projection than constant theory, this theory is used in result in area array cameras distortion calibration
It is not very stable, is easily trapped into local optimum, similarly, there is also same problems in line-scan digital camera distortion calibration.It is multinomial
Formula fitting process does not account for the actual imaging model of camera, only draws up the distortion characteristics in scene using polynomial module, this
Its adaptation sex expression in different scenes of sample is not fine, and calculation amount is very big.Precision angle method relies on additionally high-precision
Calibration tool is spent, it is inconvenient for operation.
In addition, the typical case of line-scan digital camera is to do continuous scanning line by line to the object of uniform motion, due to scan frequency
The rate mismatch advanced with target can frequently result in meeting in the longitudinal direction, and there are one stretch ratios, and going based on cross ratio invariability is abnormal
Change method can not carry out the correction of longitudinal stretching.
Invention content
The problem to be solved in the present invention is：A kind of new method of correction line-scan digital camera distortion is provided, and can be obtained simultaneously
To the longitudinal stretching ratio of picture.
The technical scheme is that：It is a kind of based on orthogonal pixel equivalent than line-scan digital camera distortion correction method, according to
The imaging characteristics of line-scan digital camera, the pixel equivalent for listing the both direction of line-scan digital camera scanning direction and vertical scanning direction are public
Formula is derived by the conclusion of orthogonal direction pixel equivalent Ratio invariableness under ideal camera lens, thus designs distortion parameter solved function,
The distortion correction for carrying out line-scan digital camera, includes the following steps：
Step 1：The multi-party lattice gridiron pattern of a plane is designed, the length and width of unit square is recorded, gridiron pattern is allowed at the uniform velocity to pass through
The lower section of line-scan digital camera is to carry out Image Acquisition；
Step 2：The chessboard table images of acquisition are pre-processed, the angle point of all grids of gridiron pattern is extracted；
Step 3：Appoint the angle point for taking adjacent rows, the distortion model of line-scan digital camera obtained by the distortion model of area array cameras,
The undistorted coordinate expressions of angle point are derived according to the distortion model of line-scan digital camera；
Step 4：Calculate the x-axis and y-axis direction pixel equivalent value at lattice clinodiagonal midpoint；
Step 5：According to the conclusion design object function of orthogonal direction pixel equivalent Ratio invariableness under ideal camera lens, utilize
Nonlinear optimization method optimization object function, solution obtain distortion parameter, and obtained distortion parameter is adopted for line-scan digital camera to be practical
Distortion correction when collection.
Further, it in step 5, is also solved to obtain the longitudinal stretching ratio of image by optimization object function, is used for linear array phase
The longitudinal stretching of machine corrects.
Preferably, in step 2, the angle point of extraction is sub-pix rank, and the angular coordinate the accurate more is conducive to distortion ginseng
Several seeks.
Step 3 is specially：
The distortion model of area array cameras is：
Wherein, xuAnd yuIndicate undistorted coordinate, xdAnd ydIndicate distortion coordinate, δxAnd δyIt is lens distortion in the direction x, y
Component,
In above formula(cx,cy) be center of distortion pixel coordinate, k1For radial distortion
Coefficient,
p1,p2For centrifugal distortion coefficient, s1,s2For thin prism distortion factor；
The master pattern of line-scan digital camera lens distortion is
Wherein, b=k1；
In the image of line-scan digital camera acquisition, the undistorted coordinate for obtaining angle point is：
Wherein, b is coefficient of radial distortion, cxFor the center of distortion of line-scan digital camera.
In step 4, the pixel equivalent at grid clinodiagonal midpoint seek for：Calculate two angle point A (x of clinodiagonal1,
y1), B (x2,y2) midpoint pixel equivalent：
Wherein, | A0B0|xIndicate value of gridiron pattern feature angle point A and the B space length in scanning line direction, | A0B0|yTable
Show gridiron pattern feature angle point A and B space length in the value in scanning line direction.
Step 5 is specially：Orthogonal direction pixel equivalent Ratio invariableness under ideal camera lens, i.e., the directions x picture in orthoscopic image
Plain equivalent Dx(xu) and the directions y pixel equivalent Dy(xu) locate all to be equal in any position, there is Dx(xu)/Dy(xu)=C, C mono-
A constant indicates image longitudinal stretching ratio, sets object function：
L is the number of lateral collinear feature point in formula；The solution of distortion coefficients of camera lens b is just converted into minimum formula at this time
(5) process.
For the present invention on the basis of fully analysis line-scan digital camera imaging characteristics, deduction obtains line-scan digital camera by ideal camera lens
This theory of pixel equivalent Ratio invariableness on orthogonal direction after imaging, it is proposed that a kind of correction line-scan digital camera fault image newly
Method, and the method can obtain longitudinal stretching coefficient simultaneously, the experiment proved that the distortion correction effect of the method for the present invention is fine.
Compared with precision angle method, this programme needs not rely on additional high-precision calibrating tool, more convenient operation, in different applications
Better adaptability in scene.Compared with cross ratio invariability method, the stability of this programme is more preferable, and while obtaining distortion factor into
Row longitudinal stretching corrects, without carrying out secondary correction, calculation amount smaller.In addition, the prior art《A kind of line-scan digital camera lens distortion
Scaling method》(Fang Suping, Xia Xiaohua, Xiao Yan, Guo Rui,《XI AN JIAOTONG UNIVERSITY Subject Index》, in January, 2013, the 1st phase of volume 47)
The distortion scaling method that also proposed line-scan digital camera, with《A kind of scaling method of line-scan digital camera lens distortion》One text passes through reduction
The scaling method for demarcating the equidistant conllinear feature extraction of object is compared, the stated accuracy higher of the method for the present invention, the method for the present invention
0.2 pixel can be reached,《A kind of scaling method of line-scan digital camera lens distortion》The method of one text is 0.5 pixel, and of the invention
Scheme also can get longitudinal stretching coefficient while distortion correction, no longer need to carry out secondary correction, this is prior art institute nothing
What method was completed.
Description of the drawings
Fig. 1 be the present invention is based on orthogonal pixel equivalent than line-scan digital camera distortion correction method flow chart.
Fig. 2 is the gridiron pattern scaling board experimental image 1 of the embodiment of the present invention.
Fig. 3 is the gridiron pattern scaling board experimental image 2 of the embodiment of the present invention.
Fig. 4 is the gridiron pattern scaling board experimental image 3 of the embodiment of the present invention.
Fig. 5 is that the straight line that characteristic point to these characteristic points fits is put down after carrying out distortion correction using the method for the present invention
The figure of equal distance.
Fig. 6 is the ratio of unit lattice length-width ratio after the longitudinal stretching correction using the method for the present invention progress line-scan digital camera
Compared with.
Specific implementation mode
In order to make those skilled in the art more fully understand the technical solution in the present invention, below in conjunction with of the invention real
The attached drawing in example is applied, technical scheme in the embodiment of the invention is clearly and completely described, it is clear that described implementation
Example is only a part of the embodiment of the present invention, instead of all the embodiments.Based on the embodiments of the present invention, the common skill in this field
The every other embodiment that art personnel are obtained without making creative work should all belong to what the present invention protected
Range.
As shown in Fig. 1, be the present invention is based on orthogonal pixel equivalent than line-scan digital camera distortion correction method flow chart,
Distortion parameter is sought using orthogonal direction pixel equivalent Ratio invariableness in the case of undistorted, is illustrated below.
It allows a gridiron pattern scaling board with equidistant collinear feature point at the uniform velocity to pass through line-scan digital camera, obtains a figure
Picture, image coordinate (x, y).Calculate the directions x of corresponding position by chessboard table images, i.e. line-scan digital camera scanning line direction
Pixel equivalent DxAnd the directions y, i.e., perpendicular to the pixel equivalent D of line-scan digital camera scanning line directiony。
Through inventor the study found that can obtain following 3 conclusions by the imaging characteristics of line-scan digital camera：
(1) in a column direction, i.e., vertical scan line direction, the influence of lens distortion can be ignored, and the directions y are (vertical
In line-scan digital camera scanning line direction) pixel equivalent only distance dependent with object point to camera in the direction of the optical axis, i.e., and object distance
Related, since line-scan digital camera only scans a line every time, object distance is only related with x, so the directions y pixel equivalent is the letter of independent variable x
Number, enables Dy(x)=F (x), wherein F (x) characterize influence of the object distance to pixel equivalent.
(2) directions the x pixel equivalent in different lines is also influenced, by mirror by lens distortion in addition to related with object distance
Head distortion model is it is found that amount of distortion is only related with coordinate x, therefore can enable Dx(x)=CG (x) F (x), wherein G (x) characterization distortion pair
The influence of pixel equivalent, constant C are to cause pixel equivalent in x with object rate travel Incomplete matching due to camera scanning frequency
There are a fixed ratios on the directions y, are also longitudinal stretching ratio.
(3) D on same column positionxAnd DyAll it is steady state value, because coordinate x is to determine at this time.
Often camera not exclusively faces objective plane in practical application, i.e., objective plane is not orthogonal to optical axis, and leads to
Reason condition can all have lens distortion, then on a certain row, the ratio D of the directions x pixel equivalent and the directions y pixel equivalentx
(xi)/Dy(xi)=CG (xi) only influenced by distorting, in other words, the D that certain in image arrangesx/DyCharacterize lens distortion at this
Amount.It as a result, in the case of ideal camera lens, does not distort, G (x is not presenti), then orthogonal direction pixel equivalent ratio is Dx(xu)/
Dy(xu)=C, value is constant, this is the theoretical foundation that the present invention goes distortion method.
The present invention's comprises the concrete steps that：
Step 1：Design and the making multi-party lattice gridiron pattern of one plane, record the length and width of unit square, allow it in guide rail
On at the uniform velocity by the lower section of line-scan digital camera to carry out Image Acquisition, wherein three representative width figures are respectively such as Fig. 2-4；
Step 2：Picture is pre-processed, X-comers are extracted, the angle point extracted here is sub-pix rank, more
Accurate angular coordinate can obtain more accurate distortion parameter；
Step 3：Appoint the angle point for taking adjacent rows, derives their undistorted coordinate expressions, preferably take centre here
The relational expression of the angle point of line number, ideal undistorted coordinate and actual coordinate is：
xu=xd+b(xd-cx)3
yu=yd
Wherein, (xu, yu) it is ideal coordinates, (xd, yd) it is actual coordinate.
Step 4：The pixel equivalent at the midpoint of grid clinodiagonal can be sought in this way：Two angle point A (x1,y1),B(x2,
y2) the pixel equivalent at midpoint can be approximately considered
Wherein, | A0B0|xIndicate value of gridiron pattern feature angle point A and the B space length in scanning line direction, | A0B0|yTable
Show gridiron pattern feature angle point A and B space length in the value in scanning line direction.
Step 5：Target letter to be optimized is obtained according to the theory of orthogonal direction pixel equivalent Ratio invariableness under ideal camera lens
Number solves distortion parameter and longitudinal stretching ratio, specially using nonlinear optimization method：
In undistorted, Dx(xu)/Dy(xu)=C, C are a constant.Therefore object function can be set
L is the number of lateral collinear feature point in formula.Therefore, the solution of distortion coefficients of camera lens is just converted into minimum above formula
Process, i.e.,
F(b*,cx *,C*)=minF (b, cx,C)
b*, cx *The as distortion factor of camera lens, and C can be utilized for the flexible correction of scale of image longitudinal direction, utilize Lay text
Bei Ge-Marquart method (Levenberg-Marquardt algorithm) can carry out nonlinear optimization, obtain distortion factor
With vertical scale magnification.
Line-scan digital camera lens distortion size only carries out nonlinear change with image coordinate x, and this non-linear relation makes
Angled straight lines on image become curve, then, after completing distortion correction, fitting a straight line are carried out to collinear points on gridiron pattern, special
The average distance of sign point to the straight line fitted with them is smaller to illustrate that the effect of distortion correction is better.It is straight due to Different Slope
Line is different by the deformation extent of distortion effects, therefore point set on the leading diagonal of scaling board is unanimously selected test in testing
Card.The variation of the average distance value for the straight line that sampling point is fitted to it before and after distortion correction is as shown in Figure 5.After carrying out distortion correction
The average distance of characteristic point to straight line is stablized within 0.2 pixel, and distortion correction works well.
The coefficient C that the method for the present invention acquires can be used for the longitudinal stretching correction of line-scan digital camera, by the artwork of acquisition and be
The length-width ratio of the no unit lattice for carrying out longitudinal stretching correction compares, as shown in fig. 6, not correcting unit in picture completely
Least close to length-width ratio 1.005025 (long 6.00mm, wide 5.97mm) in kind, average value is the length-width ratio of lattice
0.971649；The length-width ratio of lateral aberration correction is only carried out relative to not correcting completely, closer to actual value 1.005025, is put down
Mean value is 0.989952；The length-width ratio of lateral aberration correction and longitudinal stretching correction is carried out at the same time closest to actual value
1.005025 average value 1.004943.
The present invention fully analyzes line-scan digital camera imaging characteristics, using line-scan digital camera after ideal lens imaging orthogonal side
This feature of upward pixel equivalent Ratio invariableness, has carried out distortion correction, effect is fine.Compared with existing known technology, no
It needing to rely on additional high-precision calibrating tool, the better adaptability in different application scenarios is easy to operate, and stability is good,
And longitudinal stretching coefficient can be obtained, without carrying out secondary correction, calculation amount is small while obtaining distortion factor.
Although embodiment describes the invention in detail, it will be understood by those of ordinary skill in the art that, to this hair
Bright technical solution is modified or replaced equivalently, and without departure from the spirit and scope of technical solution of the present invention, should all be contained
Lid is in the scope of the claims of the present invention.
Claims (6)
1. it is a kind of based on orthogonal pixel equivalent than line-scan digital camera distortion correction method, it is characterized in that according to the imaging of line-scan digital camera
Feature lists the pixel equivalent formula of the both direction of line-scan digital camera scanning direction and vertical scanning direction, is derived by ideal
Thus the conclusion of orthogonal direction pixel equivalent Ratio invariableness under camera lens designs distortion parameter solved function, carries out line-scan digital camera
Distortion correction includes the following steps：
Step 1：The multi-party lattice gridiron pattern of a plane is designed, the length and width of unit square is recorded, gridiron pattern is allowed at the uniform velocity to pass through linear array
The lower section of camera is to carry out Image Acquisition；
Step 2：The chessboard table images of acquisition are pre-processed, the angle point of all grids of gridiron pattern is extracted；
Step 3：Appoint the angle point for taking adjacent rows, the distortion model of line-scan digital camera is obtained by the distortion model of area array cameras, according to
The distortion model of line-scan digital camera derives the undistorted coordinate expressions of angle point；
Step 4：Calculate the x-axis and y-axis direction pixel equivalent value at lattice clinodiagonal midpoint；
Step 5：According to the conclusion design object function of orthogonal direction pixel equivalent Ratio invariableness under ideal camera lens, utilization is non-thread
Property optimization method optimization object function, solution obtain distortion parameter, obtained distortion parameter be used for line-scan digital camera actual acquisition when
Distortion correction.
2. it is according to claim 1 it is a kind of based on orthogonal pixel equivalent than line-scan digital camera distortion correction method, feature
It is also to be solved to obtain the longitudinal stretching ratio of image by optimization object function in step 5, is used for the longitudinal stretching school of line-scan digital camera
Just.
3. it is according to claim 1 or 2 it is a kind of based on orthogonal pixel equivalent than line-scan digital camera distortion correction method, it is special
Sign is in step 2, and the angle point of extraction is sub-pix rank, and the angular coordinate the accurate more is conducive to seeking for distortion parameter.
4. it is according to claim 1 or 2 it is a kind of based on orthogonal pixel equivalent than line-scan digital camera distortion correction method, it is special
Sign is that step 3 is specially：
The distortion model of area array cameras is：
Wherein, xuAnd yuIndicate undistorted coordinate, xdAnd ydIndicate distortion coordinate, δxAnd δyPoint for lens distortion in the direction x, y
Amount,
In above formula(cx,cy) be center of distortion pixel coordinate, k1For coefficient of radial distortion,
p1,p2For centrifugal distortion coefficient, s1,s2For thin prism distortion factor；
The master pattern of line-scan digital camera lens distortion is
Wherein, b=k1；
In the image of line-scan digital camera acquisition, the undistorted coordinate for obtaining angle point is：
Wherein, b is coefficient of radial distortion, cxFor the center of distortion of line-scan digital camera.
5. it is according to claim 1 or 2 it is a kind of based on orthogonal pixel equivalent than line-scan digital camera distortion correction method, it is special
Sign is in step 4, the pixel equivalent at grid clinodiagonal midpoint seek for：Calculate two angle point A (x of clinodiagonal1,y1), B
(x2,y2) midpoint pixel equivalent：
Wherein, | A0B0|xIndicate value of gridiron pattern feature angle point A and the B space length in scanning line direction, | A0B0|yIndicate chess
Disk lattice feature angle point A and B space length is in the value in scanning line direction.
6. it is according to claim 1 or 2 it is a kind of based on orthogonal pixel equivalent than line-scan digital camera distortion correction method, it is special
Sign is that step 5 is specially：Orthogonal direction pixel equivalent Ratio invariableness under ideal camera lens, i.e., the directions x pixel is worked as in orthoscopic image
Measure Dx(xu) and the directions y pixel equivalent Dy(xu) locate all to be equal in any position, there is Dx(xu)/Dy(xu)=C, C are one normal
Number indicates image longitudinal stretching ratio, sets object function：
L is the number of lateral collinear feature point in formula；The solution of distortion coefficients of camera lens b at this time is just converted into minimum formula (5)
Process.
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| CN110927965A (en) * | 2019-12-20 | 2020-03-27 | 易思维（杭州）科技有限公司 | Design method of compensation lens for compensating error caused by light deflection |
| CN111047586A (en) * | 2019-12-26 | 2020-04-21 | 中国矿业大学 | Pixel equivalent measuring method based on machine vision |
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| CN112529792A (en) * | 2020-11-20 | 2021-03-19 | 暨南大学 | Distortion correction method for distortion-free model camera |
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| CN110310340B (en) * | 2019-07-05 | 2022-10-11 | 河南科技大学 | Single linear array distortion calibration method based on collinear characteristic |
| CN110927965A (en) * | 2019-12-20 | 2020-03-27 | 易思维（杭州）科技有限公司 | Design method of compensation lens for compensating error caused by light deflection |
| CN111047586A (en) * | 2019-12-26 | 2020-04-21 | 中国矿业大学 | Pixel equivalent measuring method based on machine vision |
| CN111242858A (en) * | 2020-01-07 | 2020-06-05 | 曲建涛 | Distortion correction method and system for camera lens |
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| CN112529792B (en) * | 2020-11-20 | 2022-03-29 | 暨南大学 | Distortion correction method for distortion-free model camera |
| CN112529792A (en) * | 2020-11-20 | 2021-03-19 | 暨南大学 | Distortion correction method for distortion-free model camera |
| CN112950493B (en) * | 2021-02-01 | 2022-11-01 | 中车青岛四方车辆研究所有限公司 | Method and device for correcting image distortion of linear array camera of rail train |
| CN112950493A (en) * | 2021-02-01 | 2021-06-11 | 中车青岛四方车辆研究所有限公司 | Method and device for correcting image distortion of linear array camera of rail train |
| CN112985265B (en) * | 2021-04-20 | 2021-07-30 | 苏州维嘉科技股份有限公司 | Linear array camera, precision compensation method thereof and storage medium |
| CN112985265A (en) * | 2021-04-20 | 2021-06-18 | 苏州维嘉科技股份有限公司 | Linear array camera, precision compensation method thereof and storage medium |
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| CN113808049B (en) * | 2021-09-23 | 2023-06-02 | 成都货安计量技术中心有限公司 | Train line image distortion correction method and electronic equipment |
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