CN108986172A - A kind of single-view linear camera scaling method towards small depth of field system - Google Patents

A kind of single-view linear camera scaling method towards small depth of field system Download PDF

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CN108986172A
CN108986172A CN201810824898.2A CN201810824898A CN108986172A CN 108986172 A CN108986172 A CN 108986172A CN 201810824898 A CN201810824898 A CN 201810824898A CN 108986172 A CN108986172 A CN 108986172A
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distortion
point
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matrix
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CN108986172B (en
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齐敏
张博茜
辛红娟
张国安
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Dongguan Andi Precision Machinery Co Ltd
Northwestern Polytechnical University
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Dongguan Andi Precision Machinery Co Ltd
Northwestern Polytechnical University
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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 present invention provides a kind of single-view linear camera scaling methods towards small depth of field system, calculate first order radial distortion coefficient, for carrying out primary correction to original image；Extract control point, carry out the straight line fitting based on orthogonal distance, the accurately straight slope of control point group is obtained, distortion correction target function is established according to the equal constraint condition of collinear points slope, and all distortion parameters are obtained to its optimization processing using optimization algorithm.The present invention carries out video camera linear calibration using individual orthoscopic image on the basis of opening just has calibration algorithm, and principal point simple to operation is demarcated in advance, avoids the complex process and a large amount of calculating of genetic algorithm.Entire calibration process is based on single-view and is demarcated, and can be suitably used for small depth of field system, and use scope is more extensive.

Description

A kind of single-view linear camera scaling method towards small depth of field system
Technical field
The present invention relates to a kind of camera calibration technologies, especially towards small depth of field system, list based on distortion correction View linear camera calibration technique.
Background technique
Camera calibration is the basic problem in 3D vision detection field.As information acquisition unit in detection system The precision of video camera, parameter calibration will directly influence measurement result, thus be the key that in vision measurement and premise.To height For precision vision detection system, using pinhole camera modeling description be it is insufficient, usually also need consider camera lens distortion Model.
Traditional cameras scaling method is taken the photograph using the image coordinate at known target control point and the estimation of corresponding world coordinates The inner parameter of camera and the initial value of external parameter, carry out nonlinear optimization search together with lens distortion parameter, estimate institute There is the optimal solution of parameter, representative method includes that Tsai two-step method and opening based on plane target just have calibration algorithm.This Class method generally requires the uncalibrated image for acquiring several high quality, and has certain limitations to the shooting angle of uncalibrated image.Wherein, Although Tsai two-step method only needs a width uncalibrated image, it assumes that image only has first order radial distortion, limits stated accuracy, Require between camera optical axis and gridiron pattern scaling board plane angle less than 60 degree simultaneously, and need to image principal point coordinate with Scale factor is demarcated in advance.And the uncalibrated image for just having calibration algorithm that at least three width different angles is then needed to shoot, shooting Shi Yaoqiu camera optical axis and gridiron pattern scaling board plane included angle are 45 degree, are floated up and down no more than 5 degree.Such methods will distort The parameter of model and linear pin-hole model, which is coupled, carries out nonlinear optimization search, the complex time-consuming of calibration process, mark Determine result and is also difficult to keep consistency.Simultaneously as scaling board needs big tilt angle when being imaged, the depth of field of video camera is wanted It asks high, therefore the camera calibration of the small depth of field can not be applied to.
Another kind of is non-measurement camera marking method.Such method is still after ideal perspective projection according to space line The property of straight line, establishes the measure function of characterization straight line distortion, and then carries out camera parameter calibration.As Zhang Guangjun et al. proposes Distortion factor scaling method based on cross ratio invariability principle, Chen Ruwen et al. are corrected using autoregressive sequence.Both sides Method is all the distortion correction for only needing single image, but being only completed image, solves distortion coefficients of camera lens, and do not complete and take the photograph phase The solution of machine internal and external parameter.Zhou Fuqiang et al. proposes the distortion correction method of collinear points, and establishes the distortion of video camera Disjunctive model completes camera calibration using the method for non-measurement using single image.But this method is in non-measurement calibration process In do not consider principal point coordinate, directly using the geometric center as plane as principal point processing, while assuming that image only has single order diameter To distortion, stated accuracy is to be improved.Generally, due to the reasons such as assembly, principal point coordinate and as the geometric center of plane is often deposited In difference, and the radial distortion for the main component that distorts is often to be centrosymmetric with principal point coordinate, and picture point is sat further away from principal point Mark, distortion degree is bigger, so cannot ignore the influence of principal point in non-measurement correction course.Zhang Jing et al. considers principal point It influences, deformation parameter and principal point coordinate is obtained by genetic algorithm, but at least two images is required to be corrected and combined respectively Correction, algorithm realization is cumbersome, and calculation amount is larger.
Summary of the invention
In order to overcome, existing camera marking method step complexity, low efficiency, stability is poor and majority may not apply to The problem of small depth of field system, the present invention propose that a kind of single-view towards small depth of field system, based on distortion correction linearly images Machine scaling method completes the distortion correction of image based on gridiron pattern scaling board, is just having calibration algorithm using orthoscopic image Linear calibration is carried out on the basis of basic thought, not only solving traditional cameras scaling method majority can not be under small depth of field system The problem of calibration, while influence of the quantity of parameters coupling to solution also being avoided to mention with the existing non-metric camera scaling method of simplification High stated accuracy.
The technical solution adopted by the present invention to solve the technical problems the following steps are included:
Step 1 defines world coordinate system O using horizontal positioned gridiron pattern scaling board as reference substancew-XwYwZw, origin Ow Positioned at the upper left corner of gridiron pattern scaling board, XwAxis positive direction horizontally to the right, YwAxis positive direction horizontally outward, ZwAxis positive direction is vertical Upwards；Define pixel coordinate system UO0V, origin O0Positioned at the image upper left corner, U axis positive direction horizontally to the right, V axis positive direction vertically to Under；Define image coordinate system XO1Y, origin O1At image geometry center, horizontally to the right, Y-axis positive direction is vertical for X-axis positive direction Downwards；
Horizontal positioned gridiron pattern scaling board keeps scaling board coordinate system parallel with horizontally and vertically distinguishing for image coordinate system, Respective coordinates axle clamp angle vertically shoots a gridiron pattern scaling board original image I less than 10 °orig；
Original image I under pixel coordinate systemorigAccording to vertical relation select three points, respectively gridiron pattern demarcate Point B, a C on plate on the intersection point A and every vertical line of any two orthogonal straight lines, 3 points in distortionless ideograph Position coordinates as in are respectively (u '1, v '1), (u '2, v '2), (u '3, v '3), the actual position coordinate in Iorig is respectively (u1, v1), (u2, v2), (u3, v3)；When only considering first order radial distortion, have:
Wherein, Δ v1=v1-vc, Δ u1=u1-uc,
Δv2=v2-vc, Δ u2=u2-uc,
Δv3=v3-vc, Δ u3=u3-uc,
(uc, vc) it is picture centre；
First order radial distortion coefficient k1One- place 2-th Order solve equation be
Wherein,
N=n1+n2；
ω=(v3-v1)(v2-v1)+(u3-u1)(u2-u1)；
K is solved by three points1Two value k11And k12, qualified value is screened by the following method:
1. enabling k1=k11, take up an official post in straight line AB and take a point D, straight slope k is calculated according to point A, Dad1, similarly according to point A, B Calculate slope kab1, remember the Cha Wei ⊿ of two slopes1=| kad1- kab1|；
2. enabling k1=k12, calculate two slope Zhi Cha ⊿2=| kad2- kab2|；
3. taking the corresponding k of difference smaller of two slopes1Value is used as qualified solution；
To original image according to k1Carry out primary distortion correction, and the pixel generated using bilinear interpolation algorithm to correction Gap is filled, and obtains image I after primary distortion correctionfc-orig；
Step 2, using Harris sub-pix corner detection operator after primary distortion correction image Ifc-origUpper extraction control It is processed, several straight lines are formed, if i-th linear equation is aiu+biv+ci=0, wherein (ai, bi, ci)TFor i-th straight line side Journey coefficient, (uij, vij) it is Harris sub-pix corner detection operator in Ifc-origThe control point coordinates that upper extraction obtains, 0 < i≤ M, 0 < j≤N；M is Harris sub-pix corner detection operator in Ifc-origThe vertical element number of the control point composition of upper extraction, Maximum value is the number of hits of horizontal or vertical direction black and white lattice on gridiron pattern scaling board；N is the control for being fitted i-th straight line Point number, maximum value are the number of hits of horizontal or vertical direction black and white lattice on gridiron pattern scaling board；Solve linear equation coefficient It is as follows:
Wherein:
Obtain the slope k of i-th linear equationi=-ai/bi, as distortionless ideal line slope；With remaining control System point this step of repetition, calculates the slope of the straight line of all control point fittings；
If with (uij, vij) the pixel coordinate of corresponding undistorted ideal image isEnable xd=uij, yd= vij, distortion parameter model is substituted into, is had
The distortion parameter model
WhereinCoordinate (xd, yd) it is the original image I that certain point P has distortion in image coordinate systemorig In imaging position, coordinate (xu, yu) it is position of the P point in distortionless ideal image；k1、k2Respectively single order, second order diameter To distortion factor, p1、p2For tangential distortion coefficient；
Establish distortion correction target functionIt will The solution of distortion parameter is converted into a non-linear optimization problem:
Above-mentioned nonlinearity erron function is solved using LM algorithm, firstly, calculating F to the partial derivative of each parameter, is obtained refined Gram than matrix, the value k of four distortion factors is obtained by several step iteration1、k2、p1、p2Value；
By the single order acquired, second order coefficient of radial distortion k1、k2With tangential distortion coefficient p1、p2Distortion parameter model is substituted into, Obtain the second order distortion model of camera lens；Using the second order distortion model to image I after primary distortion correctionfc-origIt carries out Secondary correction obtains image I after secondary distortion correctionsc-orig；
Step 3 adjusts the relative position of video camera and gridiron pattern scaling board, relative to shooting original image IorigWhen Position only changes object distance, shoots a secondary shooting chessboard table images Isond；Assuming that object distance is by d1Become d2When, same control point Coordinate under image coordinate system is by (u "1, v "1) become (u "2, v "2), then have:
Using the second order distortion model acquired, to secondary shooting chessboard table images IsondDistortion correction is carried out, obtains two Secondary shooting gridiron pattern corrects image Ic-sond；Using Harris sub-pix corner detection operator, in the secondary distortion school of original image Image I after justsc-origImage I is corrected with secondary shooting gridiron patternc-sondIt is upper to extract the corresponding a control point N ", N " > 1 respectively；Benefit Straight line fitting is carried out with image coordinate of the same control point under different object distances, under least square meaning, each fitting a straight line Intersection point is image principal point (u0, v0)；
Transformational relation between the known world coordinate system and image coordinate system is sm=K [R t] T, and wherein s is arbitrary ratio The example factor, m=[u, v, 1]TThe homogeneous coordinates in pixel coordinate system, T=[X are put for certainw, Yw, Zw, 1]TIt is the point in the world Homogeneous coordinates in coordinate system, K are Intrinsic Matrix, and R is spin matrix, and t is translation vector；Since gridiron pattern scaling board is placed In XwOwYwIn plane, therefore its Zw=0, if spin matrix R=[β1 β2 β3], βδ(δ=1,2,3) represents the δ column member of matrix R Element has:
Enable homography matrix H=K [β1 β2T], expression formula is as follows:
If h33It is 1, remembers that homography matrix at this time is H1；
Using Harris sub-pix corner detection operator, M straight line is extracted on image after secondary distortion correction, every straight The N number of control point of line drawing；This M × N number of control point image coordinate and its corresponding world coordinates are substituted into formula to be calculated Matrix H1；
If hσIt indicates homography matrix H column (σ=1,2,3), [h1 h2 h3]=λ H1, wherein λ is H1It is any with H Scale factor；
By the homography matrix H acquired and image principal point (u0, v0) substitute into and acquire parameter fu, fv, λ, to obtain internal reference Matrix number K；
Wherein:
e11=(h11-h13u0)(h21-h23u0)；
e12=(h12-h13v0)(h22-h23v0)；
e21=(h11-h13u0)2-(h21-h23u0)2；
e22=(h12-h13v0)2-(h22-h23v0)2；
The homography matrix H acquired, Intrinsic Matrix K and proportionality factors lambda are substituted into and calculate outer parameter matrix, that is, is rotated Matrix R=[β1 β2 β3] and translation vector t,
β1=λ K-1h1
β2=λ K-1h2
β3=β1×β2
T=λ K-1h3
So far, the gridiron pattern scaling board image for being placed shooting with video camera imaging planar horizontal using one, is completed and is taken the photograph The calibration of camera distortion parameter and inside and outside parameter.
The beneficial effects of the present invention are: using gridiron pattern scaling board, propose it is a kind of it is towards small depth of field system, based on abnormal Become the single-view linear camera scaling method of correction.The present invention calculate first order radial distortion coefficient, for original image into The primary correction of row, avoids influence of a large amount of singular points to subsequent line fitting precision；Extract control point, carry out based on it is orthogonal away from From straight line fitting, obtain the accurately straight slope of control point group, established according to the equal constraint condition of collinear points slope Distortion correction target function, and obtain all distortion parameters to its optimization processing using optimization algorithm, this method is by distortion parameter It is separated from camera model, does not need to bring distortion parameter into camera model into and carry out multiplicating calibration, avoided Traditional cameras scaling method is by the instability problem of distortion parameter and inside and outside parameter coupling bring solution；Lens distortion model Using the form comprising second order radial distortion and tangential distortion, it is more in line with objective fact, improves existing non-metric camera The stated accuracy of scaling method.The present invention carries out video camera on the basis of opening just has calibration algorithm using individual orthoscopic image Linear calibration, principal point simple to operation are demarcated in advance, avoid the complex process and a large amount of calculating of genetic algorithm.It is entire calibrated Journey is based on single-view and is demarcated, and can be suitably used for small depth of field system, and use scope is more extensive.
Detailed description of the invention
Fig. 1 is world coordinate system O of the present inventionw-XwYwZw, pixel coordinate system UO0V and image coordinate system XO1Y schematic diagram；
Fig. 2 is gridiron pattern scaling board original image；
Fig. 3 is camera position assumption diagram；
Fig. 4 is camera calibration method flow diagram.
In figure, 1- image, 2-A point, 3-B point, 4-C point, 5-D point, 6- video camera, 7- camera lens, 8- camera lens optical center, 9- chessboard Case marker fixed board, 10- gridiron pattern scaling board center, 11- object distance.
Specific embodiment
Present invention will be further explained below with reference to the attached drawings and examples, and the present invention includes but are not limited to following implementations Example.
The present invention establishes the isolated camera model that distorts, in conjunction with principal point on the basis of single image non-measurement correction Pre- calibration, proposes a kind of single-view linear camera calibration algorithm applied to the small depth of field, can solve complete parameter.
In traditional camera parameters model, lens distortion parameter and video camera internal and external parameter are interrelated, camera shooting Machine calibration needs to realize using nonlinear optimization method.The present invention separates distortion parameter from camera model, so that Distortion model is mutually indepedent with camera interior and exterior parameter.Firstly, first order radial distortion coefficient is calculated, for gridiron pattern scaling board Original image carries out primary distortion correction；Then control point is extracted, obtained based on the straight line fitting of orthogonal distance constraint condition To the straight slope accurately generated by control point, since all control points are conllinear, according to " different conllinear control points constitute straight Line slope is equal " constraint condition establish distortion correction target function, and optimize processing to it using optimization algorithm, obtain All distortion parameters；Finally, with reference to the thought for just having calibration algorithm is opened, it is linear to carry out video camera using individual orthoscopic image Calibration.
Coordinate system defined in patent and the distortion parameter model used are as follows:
As shown in Figure 1: using horizontal positioned gridiron pattern scaling board as reference substance, world coordinate system O is definedw-XwYwZw, Origin OwPositioned at the upper left corner of gridiron pattern scaling board, XwAxis positive direction horizontally to the right, YwAxis positive direction horizontally outward, ZwAxis is square To straight up；Define pixel coordinate system UO0V, origin O0Positioned at the image upper left corner, U axis positive direction horizontally to the right, V axis positive direction Straight down；Define image coordinate system XO1Y, origin O1It is camera optical axis and imaging plane at image geometry center Intersection point, horizontally to the right, Y-axis positive direction is straight down for X-axis positive direction.
Distortion parameter model uses the form comprising second order radial distortion and second order tangential distortion, specific as follows:
WhereinCoordinate (xd, yd) it is the original image I that certain point P has distortion in image coordinate systemorig In imaging position, coordinate (xu, yu) it is position of the P point in distortionless ideal image.k1、k2Respectively single order, second order diameter To distortion factor, p1、p2For tangential distortion coefficient.
Technical solution is specific as follows:
Step 1: to original image IorigCarry out primary distortion correction.
Horizontal positioned gridiron pattern scaling board keeps scaling board coordinate system parallel with horizontally and vertically distinguishing for image coordinate system, The angle that respective coordinates axis allows to have no more than 10 °.Video camera and gridiron pattern scaling board are adjusted in ZwOpposite position in axis direction It sets, it is vertical to shoot clearly a gridiron pattern scaling board image, referred to as original image Iorig。
(1) first order radial distortion coefficient is solved based on orthogonal straight lines.
Straight line on gridiron pattern scaling board is in the original image I formed by imaging systemorigOn can generate centrifugal distortion (centrifugal distortion includes radial distortion and tangential distortion), straight line thereon bends, and keeps the pixel on straight line different degrees of Ground deviates ideal position, generates a large amount of singular points.It, will certainly if directly carrying out straight line fitting using the pixel on original image Final fitting precision is produced bigger effect.Here " ideal position " of pixel refers to the pixel in distortionless ideal image Position.In order to improve fitting precision, this patent is first to original image IorigIt is corrected, the pixel for participating in being fitted is made to the greatest extent may be used Can ground close to ideal position.
Under ideal image relationship, two orthogonal straight lines also show as vertical relation in the picture.It is sat in pixel In mark system, as shown in Fig. 2, setting A point indicates the intersection point of two vertical lines, B, C are respectively any two in addition to A point on two vertical lines Point.Remember that the position coordinates of A, B, C in distortionless ideal image are respectively (u '1, v '1), (u '2, v '2), (u '3, v '3), Original image IorigIn actual position coordinate be respectively (u1, v1), (u2, v2), (u3, v3), according to the orthogonal property of straight line Matter has:
(v '3- v '1) (v '2- v '1)=- (u '3- u '1) (u '2- u '1) (2)
When only consider first order radial distortion k1When, A point ideal position coordinate are as follows:
Wherein Δ v1=v1-vc, Δ u1=u1-uc,(uc, vc) it is picture centre.And so on, B, C point ideal position coordinate is as follows:
Wherein Δ v2=v2-vc, Δ u2=u2-uc,Δv3=v3-vc, Δ u3=u3-uc,
It will only consider first order radial distortion k1When 3 ideal image coordinates of A, B, C be brought into formula (2), obtain about k1Quadratic equation with one unknown:
Wherein:
N=n1+n2 (8)
ω=(v3-v1)(v2-v1)+(u3-u1)(u2-u1) (11)
Therefore it may only be necessary to 3 points can linear solution go out first order radial distortion coefficient k1, at this time by solving equation to obtain K1There are two solve k11And k12, but only one of them be it is qualified, screening technique is as follows:
1. enabling k1=k11, take up an official post in straight line AB and take a point D, straight slope k is calculated according to point A, Dad1, similarly according to point A, B Calculate slope kab1, remember the Cha Wei ⊿ of two slopes1=| kad1- kab1|。
2. similarly, enabling k1=k12, calculate two slope Zhi Cha ⊿2=| kad2- kab2|。
3. because on the same line, be theoretically by the slope that different two o'clocks are calculated it is equal, therefore, compare ⊿1He ⊿2Size, the wherein corresponding k of smaller1Value is qualified solution.
Here in order to improve k1Precision, multiple groups point can be chosen and calculated, take mean value as k1As a result.
(2) image primary distortion correction is completed by first order radial distortion coefficient.
Calculate first order radial distortion coefficient k1Afterwards, in conjunction with formula (3), according to k1To original image IorigIt carries out primary abnormal Become correction, and be filled using the pixel pitch that bilinear interpolation algorithm generates correction, is schemed after obtaining primary distortion correction Picture is denoted as Ifc-orig。
Step 2: establishing constraint condition according to orthogonal distance, straight line fitting is carried out, solves all distortion using optimization algorithm Parameter.
(1) Harris sub-pix corner detection operator, the image I after primary distortion correction are utilizedfc-origUpper extraction control Point carries out straight line fitting by the constraint condition of orthogonal distance, solves straight slope.
If i-th linear equation is aiu+biv+ci=0, wherein (ai, bi, ci)TFor equation coefficient, (uij, vij) be Harris sub-pix corner detection operator is in Ifc-origUpper to extract obtained control point coordinates, 0 < i≤M, 0 < j < N, M is Harris sub-pix corner detection operator is in Ifc-origThe vertical element number of the control point composition of upper extraction, maximum value are gridiron pattern The number of hits of (or vertical) direction black and white lattice horizontal on scaling board；N is the control point number for being fitted i-th straight line, most Big value is the number of hits of (or horizontal) direction black and white lattice vertical on gridiron pattern scaling board.If M takes horizontal direction, N is exactly Vertical Square To；If M takes vertical direction, N is just horizontally oriented.Then point (uij, vij) arrive straight line orthogonal distance are as follows:
Straight line fitting is carried out with the minimum principle of orthogonal distance quadratic sum, the coefficient of i-th linear equation solves scheme such as Under, note:
Then:
So far, the slope k of i-th linear equation can be obtainedi=-ai/bi, as distortionless ideal line slope.It is similar Ground is repeated the above process with remaining control point, is fitted to (i+1) article straight line, until it is quasi- to calculate all control points The slope of M straight line of conjunction.
(2) distortion correction target function is established, distortion parameter is solved by nonlinear optimization algorithm.
In order to measure the degree that bending straight line approaches ideal line after distortion correction, distortion correction target function is introduced To characterize the effect of distortion correction.If with (uij, vij) the pixel coordinate of corresponding undistorted ideal image is Enable xd=uij, yd=vij, substitute into formula (1), haveAccording to " space line is under ideal perspective projection The property of straight line, and collinear points slope is equal ", if bending straight line is corrected, the slope of adjacent point-to-point transmission should be equal to ideal Straight slope, therefore it is as follows to establish distortion correction target function F:
Finally, converting a non-linear optimization problem for the solution of distortion parameter:
Above-mentioned nonlinearity erron letter is solved using literary Burger-Ma Kuaerte (Levenberg-Marquardt, LM) algorithm is arranged Four distortion factors can be obtained in number.LM algorithm is a kind of nonlinear optimization algorithm, using gradient maximizing or minimum value, it Have the advantages that gradient method and Newton method simultaneously, when step-length very little, step-length is equal to Newton method step-length；When step-length is very big, step The long step-length for being approximately equal to gradient descent method.Here, F is calculated first to the partial derivative of each parameter, is obtained Jacobian matrix, is passed through Several step iteration obtain the value of four distortion factors.
(3) image secondary correction is completed by second order distortion model.
By the single order acquired, second order coefficient of radial distortion k1、k2With tangential distortion coefficient p1、p2Formula (1) is substituted into be taken the photograph The second order distortion model of camera lens.Using the second order distortion model to image I after primary distortion correctionfc-origCarry out secondary school Just, original image I is obtainedorigSecondary distortion correction after image, be denoted as Isc-orig。
Step 3: video camera linear calibration is carried out using individual orthoscopic image.
Video camera linear calibration image I after secondary distortion correctionsc-origUpper progress.
(1) image principal point (u is solved0, v0)。
Single image can only obtain two constraint equations of intrinsic parameter, can solve 2 parameters.Opening just is having method to need to mark Fixed intrinsic parameter has 5, including image principal point (u0, v0) and u, v axis scale factor fu, fvAnd obliquity factor γ, therefore The number of unknown quantity must be reduced.Since present manufacturing process is higher, general ccd sensor unit is all standard rectangular, base The case where out of plumb is not present in this, it may therefore be assumed that obliquity factor γ is 0.The intrinsic parameter for needing to demarcate at this time is four remaining, this In the scheme taken be to (u0, v0) demarcated in advance.
Object distance refers to object to the distance of optical center of lens, as shown in figure 3, object distance is defined as gridiron pattern scaling board in the present invention Vertical range of the center to camera lens optical center.It is photosensitive in video camera when the focal length of video camera or object distance change The picture range formed on component will generate scaled.Since camera optical axis is constant, optical axis and imaging plane Intersection point it is constant, this point is exactly image principal point, that is, center of distortion.Assuming that object distance is by d1Become d2When, same control point exists Coordinate under image coordinate system is by (u "1, v "1) become (u "2, v "2), under a proportional relationship, have:
Matrix form are as follows:
The relative position for adjusting video camera and gridiron pattern scaling board, relative to shooting original image IorigWhen position, only Change object distance, then shoot a clear gridiron pattern scaling board image, is called " secondary shooting chessboard table images ", is denoted as Isond, This image is only used for principal point and demarcates in advance.Using the second order distortion model acquired, to secondary shooting chessboard table images IsondIt carries out Distortion correction obtains " secondary shooting gridiron pattern corrects image ", is denoted as Ic-sond.Using Harris sub-pix corner detection operator, The image I after the secondary distortion correction of original imagesc-origAnd secondary shooting gridiron pattern corrects image Ic-sondIt is upper to extract respectively The corresponding a control point N ", N " > 1.Straight line is carried out using image coordinate of the same control point under different object distances according to formula (20) Fitting, under least square meaning, the intersection point of each fitting a straight line is image principal point (u0, v0)。
(2) linear solution camera interior and exterior parameter and world coordinates and image coordinate.
1. solving homography matrix H.
The solution procedure of camera interior and exterior parameter is just having the basic thought of calibration algorithm, first solution homography square using opening Battle array.Homography is a concept in geometry, and in computer vision, the homography of plane is defined as from plane E to plane F Projection mapping.In camera calibration, it can be understood as the mapping on point to imaging plane on gridiron pattern scaling board.
Transformational relation between world coordinate system and image coordinate system are as follows:
Sm=K [R t]T (21)
Wherein s is arbitrary scale factor, m=[u, v, 1]TThe homogeneous coordinates in pixel coordinate system, T=are put for certain [Xw, Yw, Zw, 1]TFor the homogeneous coordinates in world coordinate system of the point, K is Intrinsic Matrix, and R is spin matrix, and t is flat The amount of shifting to.
Since gridiron pattern scaling board is placed on XwOwYwIn plane, i.e., in imaging plane, so its ZwCoordinate is zero.Rotation Matrix R=[β1 β2 β3], wherein βδThe δ column element that (δ=1,2,3) represents matrix R, then have following expression:
Enable H=K [β1 β2T], be homography matrix, expression formula is as follows:
During calculating homography matrix H, without loss of generality, h can be set33It is 1, remembers that homography matrix at this time is H1.By formula (22) it is found that a pair of control point can provide two constraint conditions, two parameters, H are solved1There are eight independent ginsengs Number can be calculated H by the method for solving over-determined systems by four pairs or more of control points1。
Due to assuming h when solving H33It is 1, H at this time1A scale factor is differed between real homography matrix H.If hσIt indicates homography matrix H column (σ=1,2,3), following expression is had according to formula (23):
[h1 h2 h3]=λ H1 (24)
Wherein λ is H1With the arbitrary scale factor of H.
2. solving Intrinsic Matrix.
Since spin matrix R is unit orthogonal matrix, then β1And β2There is following the constraint relationship:||β1| |= ||β2||.And due to det (K) ≠ 0, then matrix K is reversible, is had according to formula (24):
Formula (25) is constraint condition of the homography matrix H to intrinsic parameter K.
When obliquity factor γ is 0, Intrinsic Matrix K:
Wherein as previously mentioned, (u0, v0) it is image principal point, fu, fvThe respectively scale factor of u, v axis.
Enable G=K-TK-1, due to GT=G is obtained so G is symmetrical matrix:
It can be obtained by formula (25):
Due to introducing proportionality factors lambda, therefore have constraint equation during calculating homography matrix H:
Bringing formula (28) into above formula can obtain:
Wherein Ω1=fu/ λ, Ω2=fv/λ.Then combinatorial formula (28) and formula (30) obtain following equation group:
According to the homography matrix H and image principal point (u acquired0, v0), parameter can be obtained by solving above-mentioned equation group fu, fvAnd λ.
For convenience of description, enable:
e11=(h11-h13u0)(h21-h23u0)；
e12=(h12-h13v0)(h22-h23v0)；
e21=(h11-h13u0)2-(h21-h23u0)2；
e22=(h12-h13v0)2-(h22-h23v0)2；
Then
3. solving outer parameter matrix
It is available by formula (24) in conjunction with the homography matrix H of every image according to the Intrinsic Matrix K solved The corresponding external parameter matrix of every image, i.e. spin matrix R=[β1 β2 β3] and translation vector t:
So far, it using one and the gridiron pattern scaling board image of the horizontal positioned shooting of video camera imaging plane approximation, completes The calibration of distortion of camera parameter and inside and outside parameter.
Following instance uses image known to one group of distortion factor and partial interior parameter to carry out stated accuracy verifying first, The calibration of distortion of camera parameter and inside and outside parameter is then completed using the real scene shooting image of three groups of video cameras.
Example 1: using known distortion factor and part calibrating parameters image to the correctness of this patent scaling method into Row verifying.
Drawing digital chessboard table images size is 640 × 480, and unit is pixel；Distortion parameter is k1=-2.18 × 10-6, k2=7.32 × 10-13, p1=2.47 × 10-6, p2=-2.02 × 10-6, image principal point is (320,240).By original image It is wide and it is high be enlarged into original 1.2 times, distortion emulation is carried out to digital gridiron pattern image, obtain emulation distortion chessboard trrellis diagram Picture, emulation distortion chessboard table images peak excursion is 8 pixels, is located at emulating image grid edge, and smallest offset is 0 picture Element is located near picture centre.Using emulation distortion chessboard table images as original image IorigCarry out camera calibration.
In original image IorigMiddle three selected point for intersection point A (108,183) and another two point B (165,124) and C (164,241), is calculated first order radial distortion coefficient k1Two solution be respectively k11=9.530 × 10-6、k12=-2.167 ×10-6.A point D (220,65) is taken on straight line AB, screening obtains first order radial distortion coefficient k1=k12=-2.167 × 10-6。
20 straight lines are extracted on image after primary distortion correction using Harris sub-pix corner detection operator, every straight 20 control points are selected on line, obtain four distortion factors, respectively k1=-2.178 × 10-6、k2=1.1 × 10-13、p1= 1.46×10-6、p2=-1.14 × 10-6.Very close with the distortion factor that initially sets up, distortion factor solves correct.
20 straight lines are extracted on secondary shooting gridiron pattern correction image using Harris sub-pix corner detection operator, often 20 control points of lines detection, and corresponding 400 control points are extracted on image after the secondary distortion correction of original image, it asks Obtaining image principal point is (320.015,240.021), and unit is pixel, consistent with the image principal point initially set up.
Using Harris sub-pix corner detection operator, 10 straight lines of extraction on image after secondary distortion correction, every 10 control points of lines detection.Acquire homography matrix H:
Intrinsic Matrix K:
Outer parameter matrix R:
Translation vector t:
T=[- 26.162-25.277 295.745]T
So far, the solution for completing video camera whole parameter, completes camera calibration.
Camera used in following example 2-4 is RX 130CD-GE monochrome industrial camera, and imaging resolution is 1280 × 960 Pixel, pixel dimension are 6 × 6 μm.Camera lens be Japan's Computar MP2514-MP2 industrial lens, focal length 25mm, clearly at As when far and near range of the lens edge apart from subject be 10~14mm, i.e., field depth is 4mm.The captured calibration of experiment Plate is high-precision ceramic gridiron pattern scaling board, and lattice actual size is 1 × 1mm.
Example 2: it is demarcated using the real scene shooting image 1 of video camera.
By gridiron pattern scaling board fixed placement, the position of video camera is adjusted, keeps gridiron pattern scaling board and video camera imaging flat Face is parallel, and object distance is that 14mm shoots a clear image, as original image IorigFor distortion correction and camera calibration；Change Become object distance to 12mm, takes the photograph a clearly secondary shooting chessboard table images Isond, demarcated in advance for principal point.
Three points selected in original image are intersection point A (605,544) and B (369,548), and C (598,193) is obtained First order radial distortion coefficient k1Two solution be respectively k11=1.452 × 10-5、k12=9.833 × 10-9.One is taken on straight line AB Point D (838,540), screening obtain first order radial distortion coefficient k1=k12=9.833 × 10-9。
8 straight lines are extracted on image after primary distortion correction using Harris sub-pix corner detection operator, every straight 10 control points are selected on line, and four distortion factors: k are calculated1=-5.08 × 10-10、k2=2.32 × 10-16、p1= 1.37×10-7、p2=-6.00 × 10-9。
8 straight lines are extracted on secondary shooting gridiron pattern correction image using Harris sub-pix corner detection operator, often 10 control points of lines detection, and corresponding 80 control points are extracted on image after the secondary distortion correction of original image, it asks Obtaining image principal point is (638.2,485.6), and unit is pixel.
Using Harris sub-pix corner detection operator, 8 straight lines are extracted on image after secondary distortion correction, every straight 10 control points of line drawing.Acquire homography matrix H:
Intrinsic Matrix K:
Outer parameter matrix R:
Translation vector t:
T=[- 429.1484-249.3853 33316.12]T
So far, the solution for completing video camera whole parameter, completes camera calibration.
Example 3: it is demarcated using the real scene shooting image 2 of video camera.
By gridiron pattern scaling board fixed placement, side is slightly padded, adjusts the position of video camera, make gridiron pattern scaling board with Video camera imaging plane has 9 degree of angle, and object distance is that 10mm shoots a clear image, as original image IorigFor distorting Correction and camera calibration；Change object distance to 12mm, takes the photograph a clearly secondary shooting chessboard table images Isond, pre- for principal point Calibration.
Three points selected in original image are intersection point A (843,774) and B (608,778), and C (835,423) is obtained First order radial distortion coefficient k1Two solution be respectively k11=-1.742 × 10-8、k12=-4.388 × 10-6.It is taken on straight line AB One point D (372,783), screening obtain first order radial distortion coefficient k1=k11=-1.742 × 10-8。
8 straight lines are extracted on image after primary distortion correction using Harris sub-pix corner detection operator, every straight 10 control points are selected on line, and four distortion factors: k are calculated1=-4.58 × 10-9、k2=1.35 × 10-16、p1=9.36 ×10-8、p2=-4.90 × 10-9。
8 straight lines are extracted on secondary shooting gridiron pattern correction image using Harris sub-pix corner detection operator, often 10 control points of lines detection, and corresponding 80 control points are extracted on image after the secondary distortion correction of original image, it asks Obtaining image principal point is (637.5,485.2), and unit is pixel.
Using Harris sub-pix corner detection operator, 8 straight lines are extracted on image after secondary distortion correction, every straight 10 control points of line drawing.Acquire homography matrix H:
Intrinsic Matrix K:
Outer parameter matrix R:
Translation vector t:
T=[9.0579-30.0086 300.187]T
So far, the solution for completing video camera whole parameter, completes camera calibration.
Example 4: it is demarcated using the real scene shooting image 3 of video camera.
By gridiron pattern scaling board fixed placement, side is slightly padded, adjusts the position of video camera, make gridiron pattern scaling board with Video camera imaging plane has 5 degree of angle, and object distance is that 12mm shoots a clear image, as original image IorigFor distorting Correction and camera calibration；Change object distance to 14mm, takes the photograph a clearly secondary shooting chessboard table images Isond, pre- for principal point Calibration.
Three points selected in original image are intersection point A (722,542) and B (488,547), and C (718,310) is obtained First order radial distortion coefficient k1Two solution be respectively k11=4.180 × 10-5、k12=-3.574 × 10-8.It is taken on straight line AB One point D (955,539), screening obtain first order radial distortion coefficient k1=k12=-3.574 × 10-8。
8 straight lines are extracted on image after primary distortion correction using Harris sub-pix corner detection operator, every straight 10 control points are selected on line, and four distortion factors, k can be obtained1=-4.78 × 10-9、k2=2.15 × 10-16、p1=1.24 × 10-7、p2=-5.40 × 10-9。
8 straight lines are extracted on secondary shooting gridiron pattern correction image using Harris sub-pix corner detection operator, often 10 control points of lines detection, and corresponding 80 control points are extracted on image after the secondary distortion correction of original image, it asks Obtaining image principal point is (638.6,485.9), and unit is pixel.
Using Harris sub-pix corner detection operator, 8 straight lines are extracted on image after secondary distortion correction, every straight 10 control points of line drawing.Acquire homography matrix H:
Intrinsic Matrix K:
Outer parameter matrix R:
Translation vector t:
T=[18.5368 0.6428 285.367]T
So far, the solution for completing video camera whole parameter, completes camera calibration.

Claims (1)

1. a kind of single-view linear camera scaling method towards small depth of field system, it is characterised in that include the following steps:
Step 1 defines world coordinate system O using horizontal positioned gridiron pattern scaling board as reference substancew-XwYwZw, origin OwIt is located at The upper left corner of gridiron pattern scaling board, XwAxis positive direction horizontally to the right, YwAxis positive direction horizontally outward, ZwAxis positive direction is straight up； Define pixel coordinate system UO0V, origin O0Positioned at the image upper left corner, horizontally to the right, V axis positive direction is straight down for U axis positive direction；It is fixed Adopted image coordinate system XO1Y, origin O1At image geometry center, horizontally to the right, Y-axis positive direction is straight down for X-axis positive direction；
Horizontal positioned gridiron pattern scaling board keeps scaling board coordinate system parallel with horizontally and vertically distinguishing for image coordinate system, corresponding Reference axis angle vertically shoots a gridiron pattern scaling board original image I less than 10 °orig；
Original image I under pixel coordinate systemorigAccording to vertical relation select three points, respectively on gridiron pattern scaling board Point B, a C on the intersection point A and every vertical line of any two orthogonal straight lines, 3 points in distortionless ideal image Position coordinates be respectively (u '1, v '1), (u '2, v '2), (u '3, v '3), the actual position coordinate in Iorig is respectively (u1, v1), (u2, v2), (u3, v3)；When only considering first order radial distortion, have:
Wherein, Δ v1=v1-vc, Δ u1=u1-uc,
Δv2=v2-vc, Δ u2=u2-uc,
Δv3=v3-vc, Δ u3=u3-uc,
(uc, vc) it is picture centre；
First order radial distortion coefficient k1One- place 2-th Order solve equation be
Wherein,
N=n1+n2；
ω=(v3-v1)(v2-v1)+(u3-u1)(u2-u1)；
K is solved by three points1Two value k11And k12, qualified value is screened by the following method:
1. enabling k1=k11, take up an official post in straight line AB and take a point D, straight slope k is calculated according to point A, Dad1, similarly calculated according to point A, B Slope kab1, remember the Cha Wei ⊿ of two slopes1=| kad1- kab1|；
2. enabling k1=k12, calculate two slope Zhi Cha ⊿2=| kad2- kab2|；
3. taking the corresponding k of difference smaller of two slopes1Value is used as qualified solution；
To original image according to k1Carry out primary distortion correction, and the pixel pitch generated using bilinear interpolation algorithm to correction It is filled, obtains image I after primary distortion correctionfc-orig；
Step 2, using Harris sub-pix corner detection operator after primary distortion correction image Ifc-origUpper extraction control point, Several straight lines are formed, if i-th linear equation is aiu+biv+ci=0, wherein (ai, bi, ci)TFor i-th linear equation system Number, (uij, vij) it is Harris sub-pix corner detection operator in Ifc-origIt is upper to extract obtained control point coordinates, 0 < i≤M, 0 < j≤N；M is Harris sub-pix corner detection operator in Ifc-origThe vertical element number of the control point composition of upper extraction, it is maximum Value is the number of hits of horizontal or vertical direction black and white lattice on gridiron pattern scaling board；N is for being fitted the control point of i-th straight line Number, maximum value are the number of hits of horizontal or vertical direction black and white lattice on gridiron pattern scaling board；It is as follows to solve linear equation coefficient:
Wherein:
Obtain the slope k of i-th linear equationi=-ai/bi, as distortionless ideal line slope；With remaining control point This step is repeated, the slope of the straight line of all control point fittings is calculated；
If with (uij, vij) the pixel coordinate of corresponding undistorted ideal image isEnable xd=uij, yd=vij, generation Enter distortion parameter model, has
The distortion parameter model
WhereinCoordinate (xd, yd) it is the original image I that certain point P has distortion in image coordinate systemorigIn at Image position, coordinate (xu, yu) it is position of the P point in distortionless ideal image；k1、k2Respectively single order, second order radial distortion Coefficient, p1、p2For tangential distortion coefficient；
Establish distortion correction target functionIt will distortion The solution of parameter is converted into a non-linear optimization problem:
Above-mentioned nonlinearity erron function is solved using LM algorithm, firstly, calculating F to the partial derivative of each parameter, obtains Jacobi Matrix obtains the value k of four distortion factors by several step iteration1、k2、p1、p2Value；
By the single order acquired, second order coefficient of radial distortion k1、k2With tangential distortion coefficient p1、p2Distortion parameter model is substituted into, is obtained The second order distortion model of camera lens；Using the second order distortion model to image I after primary distortion correctionfc-origIt carries out secondary Correction, obtains image I after secondary distortion correctionsc-orig；
Step 3 adjusts the relative position of video camera and gridiron pattern scaling board, relative to shooting original image IorigWhen position, Only change object distance, shoots a secondary shooting chessboard table images Isond；Assuming that object distance is by d1Become d2When, same control point is being schemed As the coordinate under coordinate system is by (u "1, v "1) become (u "2, v "2), then have:
Using the second order distortion model acquired, to secondary shooting chessboard table images IsondDistortion correction is carried out, secondary shooting is obtained Gridiron pattern corrects image Ic-sond；Using Harris sub-pix corner detection operator, scheme after the secondary distortion correction of original image As Isc-origImage I is corrected with secondary shooting gridiron patternc-sondIt is upper to extract the corresponding a control point N ", N " > 1 respectively；Using same Image coordinate of the control point under different object distances carries out straight line fitting, and under least square meaning, the intersection point of each fitting a straight line is For image principal point (u0, v0)；
Transformational relation between the known world coordinate system and image coordinate system is sm=K [R t] T, wherein s be arbitrary ratio because Son, m=[u, v, 1]TThe homogeneous coordinates in pixel coordinate system, T=[X are put for certainw, Yw, Zw, 1]TIt is the point in world coordinates Homogeneous coordinates in system, K are Intrinsic Matrix, and R is spin matrix, and t is translation vector；Since gridiron pattern scaling board is placed on XwOwYwIn plane, therefore its Zw=0, if spin matrix R=[β1 β2 β3], βδ(δ=1,2,3) represents the δ column element of matrix R, Have:
Enable homography matrix H=K [β1 β2T], expression formula is as follows:
If h33It is 1, remembers that homography matrix at this time is H1；
Using Harris sub-pix corner detection operator, M straight line is extracted on image after secondary distortion correction, every straight line mentions Take N number of control point；This M × N number of control point image coordinate and its corresponding world coordinates are substituted into formula, matrix is calculated H1；
If hσIt indicates homography matrix H column (σ=1,2,3), [h1 h2 h3]=λ H1, wherein λ is H1With the arbitrary proportion of H The factor；
By the homography matrix H acquired and image principal point (u0, v0) substitute into and acquire parameter fu, fv, λ, to obtain intrinsic parameter square Battle array K；
Wherein:
e11=(h11-h13u0)(h21-h23u0)；
e12=(h12-h13v0)-(h22-h23v0)；
e21=(h11-h13u0)2-(h21-h23u0)2；
e22=(h12-h13v0)2-(h22-h23v0)2；
The homography matrix H acquired, Intrinsic Matrix K and proportionality factors lambda are substituted into and calculate outer parameter matrix, i.e. spin matrix R=[β1 β2 β3] and translation vector t,
β1=λ K-1h1
β2=λ K-1h2
β3=β1×β2
T=λ KK-1h3
So far, the gridiron pattern scaling board image for placing shooting with video camera imaging planar horizontal using one, completes video camera The calibration of distortion parameter and inside and outside parameter.
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