CN101021947A - Double-camera calibrating method in three-dimensional scanning system - Google Patents

Abstract

This invention relates to a double-vidicon calibration method in a three-D scan system including: calibrating aberration coefficient first, then correcting the pick-up image utilizing the aberration coefficient to calibrate the internal parameter of the vidicon combined with an deal pinhole perspective model, and the parameter includes an imaging center, slant factors among axeses and equivalent focuses, finally calibrating the outside parameters of the right and left vidicons based on the internal parameter and further utilizing the outer model of the double vidicons to calibrate relative outside parameters of the two vidicons to get the internal and outside parameters.

Description

Double-camera calibrating method in the 3 D scanning system

Technical field

The present invention relates to the demarcation problem of the twin camera in the vision system, relate in particular to the double-camera calibrating method in a kind of 3 D scanning system.

Background technology

One of basic task of computer vision is to take the image that obtains from video camera, calculates the three-dimensional information of object in the visual field, comes thus three-dimensional body is rebuild and discerned.The three-dimensional geometric information of body surface point and its mutual relationship between the corresponding point on the image are that in fact the process of setting up this geometric model is exactly the solution procedure of camera parameters by the decision of the imaging model of video camera.Therefore, the demarcation to camera parameters is the prerequisite and the key of this modeling process.Solution procedure to camera parameters is called camera calibration.

Document " Image Processing; Analysis; and Machine Vision " (M.Sonka, V.Hlavac, R.Boyle, International Thomson Publishing, 1998) set forth a kind of comparatively general video camera imaging model in, this imaging model can be described with following formula:

$\left[\begin{array}{c}u\\ v\\ 1\end{array}\right]=\mathrm{\λA}\left[\mathrm{RT}\right]\left[\begin{array}{c}{X}_w\\ Y_w\\ Z_w\\ 1\end{array}\right]$

Wherein, X _w, Y _w, Z _wBe the spatial point coordinate of demarcating thing, u, v are the two-dimensional coordinates on image, and λ is a scalar, and R, T are the external parameter matrix of video camera, have defined video camera respectively in three-dimensional attitude and position, $A=\left[\begin{array}{ccc}\mathrm{\α}& s& u_0\\ 0& \mathrm{\β}& v_0\\ 0& 0& 1\end{array}\right]$ Be the intrinsic parameters of the camera matrix, α wherein, β are illustrated respectively in the scale-up factor of the physical coordinates of picture point on x direction and the y direction to image coordinate, or are called the equivalent focal length on x direction and the y direction, also comprise other intrinsic parameter between centers inclination factors s, imaging center (u ₀, v ₀).

Camera calibration is exactly a process of calculating intrinsic parameters of the camera and external parameter.The camera calibration technology roughly can be divided into two classes: traditional camera marking method and camera self-calibration method.

In recent years, video camera obtained very big progress from calibration algorithm, delivered a considerable amount of documents, the some of them algorithm has obtained comparatively widely to use.But because poor with respect to traditional calibration algorithm precision, be not suitable for accuracy of detection being required very high occasion such as 3-D scanning etc. from calibration algorithm.

Traditional calibration algorithm has also obtained using comparatively widely, has also obtained effect preferably simultaneously.Document " A versatile camera calibration technique for high accuracy 3Dmachine vision metrology using off-the-shelf TV cameras and lenses " (Tsai R Y.IEEE Robotics Automation for example, 1987,3 (4): disclose a kind of utilize radial alignment to retrain to obtain external parameter, focal length and the linear solution of distortion once radially pages324-344).This method iteration parameter is less, and initial value preferably can be provided automatically, and it is fast to find the solution speed, has considered the radial distortion of camera lens simultaneously, and precision is higher.Shortcoming is in this method, and the horizontal spacing of sensitization unit and longitudinal pitch are considered to known in the ccd array, imaging center are not revised.

Summary of the invention

Technical matters: the purpose of this invention is to provide and a kind ofly can carry out double-camera calibrating method in the 3 D scanning system of complete demarcation, have and make simple, high, the fireballing advantage of precision to the inside and outside parameter of camera chain.

Technical scheme: double-camera calibrating comprises in the 3 D scanning system of the present invention: earlier distortion factor is demarcated; After utilizing distortion factor that captured image is carried out image rectification then, associated ideal pin hole perspective model, the calibrating camera inner parameter, wherein intrinsic parameters of the camera mainly comprises imaging center, between centers inclination factor and equivalent focal length; Demarcate the external parameter of left and right cameras at last according to intrinsic parameters of the camera, further utilize the twin camera external model, demarcate the relative external parameter of left and right cameras, thereby obtain all internal and external parameters of video camera.

The main operational steps of this method is:

1.) the sign round dot on one group of parallel lines that are positioned on the scaling board of use, and, utilize parallel lines projection intersection point (x on the picture plane according to geometrical perspective projection ultimate principle _c, y _c) constraint condition and distortion of camera model, obtain one group and cross intersection point (x _c, y _c) straight-line equation: y-y _c=k _i(x-x _c) (i=1,2 ..., N), k wherein _iIt is the slope of i bar straight line; The parallel lines of choosing on n (n 〉=3) the group scaling board just can obtain n above-mentioned straight-line equation, and the individual straight-line equation of said n (n 〉=3) is combined into a system of equations, is tried to achieve by least square method: W=[A (k) A ^t(k)] ^-1A ^t(k) B (k), wherein A and B matrix are the functions about distortion factor k, utilize variable step-size search method search distortion factor k in the one-dimensional space, when $\left|\right|\stackrel{\‾}{A}\stackrel{\‾}{W}-B\left|\right|=\underset{k}{\min }\left|\right|\mathrm{AW}-B\left|\right|$ The time, the k value is distortion factor;

Above-mentioned step-length adopts following method to determine: the distortion parameter value of camera lens is all smaller, and the region of search can just elect (10 as ^-6, 10 ^-6), when the precision of distortion parameter reaches 10 ^-9The time, the correction precision of pixel is reached O.02 about a pixel.

2.) after trying to achieve the distortion factor of video camera, captured image is carried out image distortion correction, obtain undistorted uncalibrated image, utilize desirable pin hole perspective model to demarcate intrinsic parameters of the camera except that distortion factor then, mainly comprise the demarcation of imaging center, the demarcation of between centers inclination factor and the demarcation of equivalent focal length, make the z of world coordinate system _wComponent is 0, and desirable pin hole perspective model is:

sp _u，i＝Hp _w，i

P wherein _{U, i}=[u v 1] ^T, p _{W, i}=[x _wy _w1] ^T, H=λ A[r ₁r ₂T]=[h ₁h ₂h ₃], r _i(i=1～3) and h _iThe column vector of (i=1～3) expression rotation matrix R and matrix H, matrix A is the intrinsic parameter matrix, λ is a scalar:

The H matrix representation homography between calibrating template plane and the plane of delineation, degree of freedom is 8, therefore needs at least 4 above non-colinear corresponding point, just can obtain the H matrix of band scale factor, because rotation matrix R is the unit orthogonal matrix, so r ₁, r ₂Be the unit orthogonal vector, can get two constraints thus, form an equation of constraint, the image of every bat n (n 〉=3) width of cloth plane reference plate just can obtain n above-mentioned equation of constraint, utilize least-squares algorithm just can calibrate the intrinsic parameter matrix A, mainly comprise imaging center, between centers inclination factor and equivalent focal length.

3.) calibrate the intrinsic parameter matrix A after, according to camera model, just can demarcate the external parameter of every width of cloth image, be video camera attitude and location parameter, the rotation matrix of initially trying to achieve does not satisfy orthogonality, therefore adopts singular value decomposition method with its orthogonalization, obtains the external parameter of video camera;

Behind attitude that calibrates left and right cameras respectively and location parameter, just can calibrate the relative external parameter of left and right cameras according to the twin camera external model, promptly relative attitude and location parameter are:

$R=R_r{R}_l^{-1},$ $T=T_r-R_r{R}_l^{-1}{T}_l$

R wherein, T is the attitude and the location matrix of the left relatively video camera of right video camera, R _r, T _rBe the attitude and the location matrix of the relative world coordinate system of right video camera, R _l, T _lBe the attitude and the location matrix of the relative world coordinate system of left video camera.

Specific as follows:

(1) demarcation of distortion factor

Use one group of sign round dot on the parallel lines that are positioned on the scaling board, and, utilize parallel lines projection intersection point (x on the picture plane according to geometrical perspective projection ultimate principle _c, y _c) constraint condition and distortion model, obtain one group and cross intersection point (x _c, y _c) straight-line equation: y-y _c=k _i(x-x _c) (i=1,2 ..., N), k wherein _iBe the slope of i bar straight line,

Above-mentioned straight-line equation group is combined into: AW=B

Wherein

$W=\left[\begin{array}{c}{k}_1\\ k_2\\ .\\ .\\ .\\ k_N\\ y_c\\ k_1{x}_c\\ k_2{x}_c\\ .\\ .\\ .\\ k_N{x}_c\end{array}\right]$ $\left[\begin{array}{c}{y}_{11}\\ y_{12}\\ .\\ .\\ .\\ y_{{1M}_1}\\ y_{21}\\ .\\ .\\ .\\ y_{{2M}_2}\\ y_{31}\\ .\\ .\\ .\end{array}\right]$

Solve by least square method: W=(AA ^t) ^-1A ^tB, wherein A and B matrix are the functions about distortion factor k, and then obtain W=[A (k) A ^t(k)] ^-1A ^t(k) B (k) utilizes variable step-size search method search distortion factor k in the one-dimensional space, when $\left|\right|\stackrel{\‾}{A}\stackrel{\‾}{W}-B\left|\right|=\underset{k}{\min }\left|\right|\mathrm{AW}-B\left|\right|$ The time, the k value is distortion factor.

Above-mentioned step-length adopts following method to determine: the distortion parameter value of camera lens is all smaller, and the region of search can just elect (10 as ^-6, 10 ^-6), when the precision of distortion parameter reaches 10 ^-9The time, the correction precision of pixel has been reached about 0.02 pixel, this generally speaking, this has reached the limit of the bearing accuracy in the monumented point center of circle, therefore further search is nonsensical.

(2) intrinsic parameters of the camera is demarcated

After trying to achieve the distortion factor of camera lens, just can carry out image distortion correction to photographic images, obtain undistorted uncalibrated image.Utilize desirable pin hole perspective model to demarcate intrinsic parameters of the camera except that distortion factor then, mainly comprise the demarcation of imaging center, the demarcation of between centers inclination factor and the demarcation of equivalent focal length.Make the z of world coordinate system _wComponent is 0, and desirable pin hole perspective model just can be rewritten as:

sp _u，i＝H _pw，l

P wherein _{U, i}=[u v 1] ^T, p _{W, i}=[x _wy _w1] ^T, H=λ A[r ₁r ₂T]=[h ₁h ₂h ₃], r _i(i=1～3) and h _iThe column vector of (i=1～3) rotation matrix R and matrix H, matrix A are the intrinsic parameter matrix, and λ is a scalar.

The H matrix representation homography between calibrating template plane and the plane of delineation, degree of freedom is 8, therefore needs at least 4 above non-colinear corresponding point, just can obtain the H matrix of band scale factor.Because rotation matrix R is the unit orthogonal matrix, so r ₁, r ₂Be the unit orthogonal vector, can get two constraints thus:

$\left\{\begin{array}{c}{h}_1^T{A}^{-T}{A}^{-1}{h}_2=0\\ h_1^T{A}^{-T}{A}^{-1}{h}_1=h_2^T{A}^{-T}{A}^{-1}{h}_2\end{array}\right.$

Order $B=A^{-T}{A}^{-1}=\left[\begin{array}{ccc}{b}_1& b_2& b_4\\ b_2& b_3& b_5\\ b_4& b_5& b_6\end{array}\right],$ Define vectorial b=[b ₁b ₂b ₃b ₄b ₅b ₆] ^T, then go up

Formula can be written as again:

$\left[\begin{array}{c}{v}_{12}^T\\ {(v_{11}-v_{12})}^T\end{array}\right]b=\mathrm{Vb}=0$

V wherein _Ij=[h _I1h _J1, h _I1h _J2+ h _I2h _J1, h _I2h _J2, h _I3h _J1+ h _I1h _J3, h _I3h _J2+ h _I2h _J3, h _I3h _J3] ^T, h wherein _IjFor the i of matrix H is capable, the j column element.The image of every bat n (n 〉=3) width of cloth plane reference plate just can obtain n above-mentioned system of equations, thereby solves matrix B.After solving B, just can calibrate the intrinsic parameter matrix A by the Qiao Lisiji decomposition, comprise imaging center, between centers inclination factor and equivalent focal length.

(3) demarcation of the relative external parameter of left and right cameras

After calibrating the intrinsic parameter matrix A, just can determine the external parameter of every width of cloth image, promptly video camera attitude and location parameter are:

$\left\{\begin{array}{c}{r}_1=\mathrm{\ρ}{A}^{-1}{h}_1,r_2=\mathrm{\ρ}{A}^{-1}{h}_2,r_3=r_1\×r_2\\ T=\mathrm{\ρ}{A}^{-1}{h}_3\\ \mathrm{\ρ}=1/\left|\right|A^{-1}{h}_1\left|\right|=1/\left|\right|A^{-1}{h}_2\left|\right|\end{array}\right.$

The rotation matrix R that is determined by following formula does not satisfy orthogonality, therefore adopts singular value decomposition method with its orthogonalization, obtains the external parameter of video camera.

Behind attitude that calibrates left and right cameras respectively and location parameter, just can calibrate the relative attitude and the location parameter of left and right cameras according to the twin camera external model:

$R=R_r{R}_l^{-1},$ $T=T_r-R_r{R}_l^{-1}{T}_l$

R wherein, T is the attitude and the position of the left relatively video camera of right video camera, R _r, T _rBe the attitude and the location matrix of the relative world coordinate system of right video camera, R _l, t _lBe the attitude and the location matrix of the relative world coordinate system of left video camera.

Beneficial effect: the present invention is mainly used in the various application scenarios of video camera being demarcated real-time based on the plane reference plate.Utilize each parameter of calibration algorithm calibrating camera of this patent, mainly contain following advantage:

(1) the present invention has more intactly marked each parameter of desirable video camera, comprise imaging center, between centers inclination factor, equivalent focal length, attitude parameter and translation parameters, mark the distortion parameter of camera lens simultaneously, the follow-up image that photographs can carry out distortion in images according to this parameter and proofread and correct.

(2) computing among the present invention is linear operation, do not use and nonlinear operation such as recall, thereby the full linear that has realized video camera is demarcated.This method speed is fast, can be applied to various to the demanding occasion of real-time.

(3) used plane reference object to demarcate among the present invention, plane reference object is three-dimensional demarcate thing have make simple, the precision advantages of higher, this has just reduced in the calibration process the dependence of high-precision calibrating thing, has simplified calibration process.

Description of drawings

Fig. 1 is scaling board figure,

Fig. 2 is that vanishing point forms schematic diagram,

Fig. 3 is the process flow diagram of search distortion factor,

Fig. 4 is the 3 D scanning system structural drawing,

Fig. 5 is twin camera external model figure,

Fig. 6 is the parameter calibration process flow diagram.

Embodiment

Double-camera calibrating comprises in the 3 D scanning system: earlier distortion factor is demarcated; After utilizing distortion factor that captured image is carried out image rectification then, associated ideal pin hole perspective model, the calibrating camera inner parameter, wherein intrinsic parameters of the camera mainly comprises imaging center, between centers inclination factor and equivalent focal length; Demarcate the external parameter of left and right cameras at last according to intrinsic parameters of the camera, further utilize the twin camera external model, demarcate the relative external parameter of left and right cameras, it is characterized in that:

(1) demarcation of distortion factor

Use one group of sign round dot on the parallel lines that are positioned on the scaling board, and, utilize parallel lines projection intersection point (x on the picture plane according to geometrical perspective projection ultimate principle _c, y _c) constraint condition and distortion model, obtain one group and cross intersection point (x _c, y _c) straight-line equation:

Y-y _c=k _i(x-x _c) (i=1,2 ..., N), k wherein _iBe the slope of i bar straight line,

Above-mentioned straight-line equation group is combined into: AW=B

Wherein

$W=\left[\begin{array}{c}{k}_1\\ k_2\\ .\\ .\\ .\\ k_N\\ y_c\\ k_1{x}_c\\ k_2{x}_c\\ .\\ .\\ .\\ k_N{x}_c\end{array}\right],$ $B=\left[\begin{array}{c}{y}_{11}\\ y_{12}\\ .\\ .\\ .\\ y_{1M_1}\\ y_{21}\\ .\\ .\\ .\\ y_{2M_2}\\ y_{31}\\ .\\ .\\ .\end{array}\right]$

Solve by least square method: W=(AA ^t) ^-1A ^tB, wherein A and B matrix are the functions about distortion factor k, and then obtain W=[A (k) A ^t(k) ^-1A ^t(k) B (k) utilizes variable step-size search method search distortion factor k in the one-dimensional space, when $\left|\right|\stackrel{\‾}{A}\stackrel{\‾}{W}-B\left|\right|=\underset{k}{\min }\left|\right|\mathrm{AW}-B\left|\right|$ The time, the k value is distortion factor.

Above-mentioned step-length adopts following method to determine: the distortion parameter value of camera lens is all smaller, and the region of search can just elect (10 as ^-6, 10 ^-6), when the precision of distortion parameter reaches 10 ^-9The time, the correction precision of pixel has been reached about 0.02 pixel, this generally speaking, this has reached the limit of the bearing accuracy in the monumented point center of circle, therefore further search is nonsensical.

(2) intrinsic parameters of the camera is demarcated

After trying to achieve the distortion factor of camera lens, just can carry out distortion correction to photographic images, obtain undistorted uncalibrated image.The intrinsic parameters of the camera that utilizes desirable pin hole perspective model to demarcate except that distortion factor is then demarcated (comprising the demarcation of imaging center, the demarcation of between centers inclination factor and the demarcation of equivalent focal length).Make the z of world coordinate system _wComponent is 0, and desirable pin hole perspective model just can be rewritten as:

sp _u，i＝Hp _w，i

P wherein _{U, i}=[u v 1] ^T, p _{W, i}=[x _wy _w1] ^T, H=λ A[r ₁r ₂T]=[h ₁h ₂h ₃], r _i(i=1～3) and h _iThe column vector of (i=1～3) rotation matrix R and matrix H, matrix A are the intrinsic parameter matrix, and λ is a scalar.

The H matrix representation homography between calibrating template plane and the plane of delineation, degree of freedom is 8, therefore needs at least 4 above non-colinear corresponding point, just can obtain the H matrix of band scale factor.Because rotation matrix R is the unit orthogonal matrix, so r ₁, r ₂Be the unit orthogonal vector, can get two constraints thus:

$\left\{\begin{array}{c}{h}_1^T{A}^{-T}{A}^{-1}{h}_2=0\\ h_1^T{A}^{-T}{A}^{-1}{h}_1=h_2^T{A}^{-T}{A}^{-1}{h}_2\end{array}\right.$

Order $B=A^{-T}{A}^{-1}=\left[\begin{array}{ccc}{b}_1& b_2& b_4\\ b_2& b_3& b_5\\ b_4& b_5& b_6\end{array}\right],$ Define vectorial b=[b ₁b ₂b ₃b ₄b ₅b ₆] ^T, then following formula can be written as again:

$\left[\begin{array}{c}{v}_{12}^T\\ {(v_{11}-v_{22})}^T\end{array}\right]b=\mathrm{Vb}=0$

V wherein _Ij=[h _I1h _J1, h _I1h _J2+ h _I2h _J1, h _I2h _J2, h _I3h _J1+ h _I1h _J3, h _I3h _J2+ h _I2h _J3, h _I3h _J3] ^T, h wherein _IjFor the i of matrix H is capable, the j column element.The image of every bat n (n 〉=3) width of cloth plane reference plate just can obtain n above-mentioned system of equations, thereby solves matrix B.After solving B, just can calibrate the intrinsic parameter matrix A by the Qiao Lisiji decomposition, comprise imaging center, between centers inclination factor and equivalent focal length.

(3) demarcation of the relative external parameter of left and right cameras

After calibrating the intrinsic parameter matrix A, just can determine the external parameter of every width of cloth image, promptly video camera attitude and location parameter are:

$\left\{\begin{array}{c}{r}_1=\mathrm{\ρ}{A}^{-1}{h}_1,r_2=\mathrm{\ρ}{A}^{-1}{h}_2,r_3=r_1\×r_2\\ T=\mathrm{\ρ}{A}^{-1}{h}_3\\ \mathrm{\ρ}1/\left|\right|A^{-1}{h}_1\left|\right|=1/\left|\right|A^{-1}{h}_2\left|\right|\end{array}\right.$

The rotation matrix R that is determined by following formula does not satisfy orthogonality, therefore adopts singular value decomposition method with its orthogonalization, obtains the external parameter of video camera.

Behind attitude that calibrates left and right cameras respectively and location parameter, just can calibrate the relative attitude and the location parameter of left and right cameras according to the twin camera external model:

$R=R_r{R}_l^{-1},$ $T=T_r-R_r{R}_l^{-1}{T}_l$

R wherein, T is the attitude and the position of the left relatively video camera of right video camera, R _r, T _rBe the attitude and the location matrix of the relative world coordinate system of right video camera, R _l, T _lBe the attitude and the location matrix of the relative world coordinate system of left video camera.

With reference to the accompanying drawings, specific embodiments of the present invention are made more detailed description:

The present invention utilizes plane reference object---and scaling board carries out camera parameters to be demarcated, and array distribution has round monumented point on the plate, and as Fig. 1, the circle monumented point can be arranged in the straight line that is parallel to each other.Handle by video camera is taken the image that obtains, obtain the picture side's coordinate and the object coordinates of monumented point.Calibration algorithm in this patent utilizes these center of circle data, and camera interior and exterior parameter is demarcated.

Concrete steps are as follows:

(1) demarcation of distortion factor

Document " a kind of new hand-held cameras Camera self-calibration based " (Chen Zezhi, Wu Chengke. Chinese image graphics journal, 2003,8 (A version) (3), 241-346) a kind of new video camera Camera self-calibration based based on linear model has been proposed, this method is at first to utilize the character of three-point perspective projection figure, vanishing point and vectorial quadrature to obtain one group of nonlinear equation, is converted into the Solving Linear calibrating parameters then.Adopted cubic block as scaling reference in the document with three-point perspective, and the maximum feasible one-tenth two-point perspectiveness of the plane reference plate that we use in calibration process, this just needs the scaling board image of different angles to remedy this restriction.

Calibration point on our the employed plane reference is array distribution, selects suitable dotted line can form the some groups of straight lines that are parallel to each other.Here we only choose the crosswise spots of array or vertically put and constitute one group of parallel lines, and as shown in Figure 2, according to the character of perspective projection, the one group of parallel lines in space intersect at a point on image.In shooting process, projection plane and scaling board plane keep certain included angle, make this group parallel lines projection on imaging plane intersect at a point.

The actual imaging model

Desirable lens imaging is the pin hole perspective imaging model, but owing to many-sided reasons such as manufacturing installations, on imaging plane, there be certain departing from the more satisfactory picture point of actual image point, and this departing from is exactly distortion of camera.Therefore, when the desirable pin hole perspective model of application carries out the mapping conversion of picture point and physical points, must at first proofread and correct the distortion of picture point.Calibration model is as follows:

$\left\{\begin{array}{c}{X}_u=(1+\stackrel{\‾}{k}{r}^2)X_d\\ Y_u=(1+\stackrel{\‾}{k}{r}^2)Y_d\end{array}\right.---\left(1\right)$

Wherein $r^2=X_d^2+Y_d^2,$

Be distortion factor, when barrel distortion

For just, during pincushion distortion

For negative.

If

Be image actual pixels point coordinate, (u v) is the desirable pixel coordinate of image.The transformational relation of image pixel point coordinate and image physical coordinates is:

$\left\{\begin{array}{c}u=\mathrm{\α}{X}_u+u_0\\ v=\mathrm{\β}{Y}_u+v_0\end{array}\right.---\left(2\right)$

Convolution (1) and (2) can get:

Wherein

Consider the raising of video camera manufacturing technology level in recent years, the aspect ratio of video camera

Be in close proximity to 1.Therefore can get α ≈ β, (3) formula can be rewritten at this moment:

Wherein

$k=\frac{\stackrel{\‾}{k}}{{\mathrm{\α}}^2}.$

The present invention proposes the constraint that a kind of projection that utilizes one group of parallel lines intersects at a point, find the solution distortion parameter, this method has been used all points that are positioned on one group of line that is parallel to each other simultaneously, utilize the constraint condition that meets at vanishing point of parallel lines projection to list one group of linear equation, find the solution distortion parameter by linear search.

If the straight line that world coordinates exists the N bar to be parallel to each other, there is M in each straight line _i(i=1,2 ... N) individual monumented point, the desirable pixel coordinate of j point is (u on the i bar straight line _Ij, v _Ij), the distorted image vegetarian refreshments is a coordinate

Then have according to formula (4):

Wherein,

x _Ij=u _Ij-u ₀, y _Ij=v _Ij-v ₀

If the intersection point of each straight line is (x _c, y _c), then the The Representation Equation of each straight line is:

y-y _c＝k _i(x-x _c)(i＝1，2，…，N) (6)

K wherein _iIt is the slope of i bar straight line.Formula (6) easily changes into

k _ix+v ₁-k _iu ₁＝y

Each calibration point coordinate substitution can be got satisfies following equation between the ideal image point:

AW＝B

Wherein

$W=\left[\begin{array}{c}{k}_1\\ k_2\\ .\\ .\\ .\\ k_N\\ y_c\\ k_1{x}_c\\ k_2{x}_c\\ .\\ .\\ .\\ k_N{x}_c\end{array}\right],$ $B=\left[\begin{array}{c}{y}_{11}\\ y_{12}\\ .\\ .\\ .\\ y_{1M_1}\\ y_{21}\\ .\\ .\\ .\\ y_{2M_2}\\ y_{31}\\ .\\ .\\ .\end{array}\right]$

Solve by least square method:

W＝(AA ^t) ^-1A ^tB

Each non-constant element of A and B matrix is that the ideal coordinates value by calibration point constitutes, and the ideal coordinates value is to carry out revised result by the distortional point coordinate figure through distortion model.Therefore, after having selected parallel lines and corresponding calibration point, can think that A and B matrix are the functions about distortion factor k, B then is normal column vector, correspondingly:

W＝[A(k)A ^t(k) ^-1A ^t(k)B

Utilize step length searching method search distortion factor k in the one-dimensional space, make:

$\left|\right|\stackrel{\‾}{A}\stackrel{\‾}{W}-B\left|\right|=\underset{k}{\min }\left|\right|\mathrm{AW}-B\left|\right|$

At this moment k is the distortion parameter that we will find the solution.Concrete steps are as follows:

1) region of search can just elect (10 as ^-6, 10 ^-6), at first with 10 ^-7Be step-length, search for the k as a result of this time search ¹

2) with interval (k ¹-10 ^-7, k ¹+ 10 ^-7) be the region of search, with 10 ^-8Be step-length, search for

The k as a result of this time search ²

3) with interval (k ²-10 ^-8, k ²+ 10 ^-8) be the region of search, with 10 ^-9Be step-length, search for the k as a result of this time search ³

k ³Be the distortion parameter of being found the solution, see accompanying drawing 3.

The distortion parameter value of camera lens is all smaller, and the region of search can just elect (10 as ^-6, 10 ^-6), when the precision of distortion parameter reaches 10 ^-9The time, the correction precision of pixel has been reached about 0.02 pixel, this generally speaking, this has reached the limit of the bearing accuracy in the monumented point center of circle, therefore further search is nonsensical.

In the practical application two ccd video cameras are fixed on the top of the shelf by shown in Figure 4.The left and right sides mirror that requires according to calibration algorithm is respectively taken 10 original scaling board image informations, handle by above-mentioned steps, according to each width of cloth image find the solution the distortion factor of left and right sides mirror, obtain distortion factor and the results are shown in Table 1:

The calibration result of table 1 left and right sides mirror distortion factor

Sequence number	Left side mirror distortion factor (10 -5)	Right mirror distortion factor (10 -5)
			1	0.0049	0.0056
2	0.0048	0.0059
			3	0.0052	0.0063
4	0.0051	0.0053
			5	0.0052	0.0050
6	0.0053	0.0062
			7	0.0052	0.0062
8	0.0052	0.0062
			9	0.0051	0.0059
10	0.0056	0.0059

(2) intrinsic parameters of the camera is demarcated

Trying to achieve after camera lens gets distortion factor, just can carry out image distortion correction to photographic images.As long as distortion factor k substitution formula (5), just can determine that the ideal image pixel coordinate of each point on the straight line is:

$\left\{\begin{array}{c}{u}_{\mathrm{ij}}=x_{\mathrm{ij}}+u_0\\ v_{\mathrm{ij}}=y_{\mathrm{ij}}+v_0\end{array}\right.$

Utilize desirable pin hole perspective model to come other inside and outside parameter of calibrating camera then, comprise imaging center, between centers inclination factor, effective focal length and external parameter.Document " A Flexible New Technique forCamera Calibration " (Zhang Z Y, IEEE Transactions on Pattern Analysisand Machine Intelligence, 2000,20 (11): 1330-1334) propose a kind of calibration algorithm that is called as the plane template method, it mainly is the inside and outside parameter except that distortion factor of at first coming the linear solution video camera with desirable pin hole perspective model, utilize the actual imaging model to find the solution distortion factor then, utilize the nonlinear optimization algorithm to optimize all camera interior and exterior parameters at last.Used first step algorithm in the document in this patent, but difference is that algorithm is that imaging model is used as desirable pin hole perspective model in the document, in fact owing to the existence that distorts in the image, therefore this hypothesis is irrational to the high precision occasion.Therefore this patent algorithm is to find the solution distortion factor earlier, image is proofreaied and correct eliminated the influence that distortion brings then, utilizes desirable pin hole perspective model to find the solution camera parameters again.

Make the z of world coordinate system _wComponent is 0, and desirable pin hole perspective model just can be rewritten as:

$s\left[\begin{array}{c}u\\ v\\ 1\end{array}\right]=A\left[\mathrm{RT}\right]\left[\begin{array}{c}{x}_w\\ y_w\\ 0\\ 1\end{array}\right]=A\left[r_1{r}_{2}T\right]\left[\begin{array}{c}{x}_w\\ y_w\\ 1\end{array}\right]---\left(7\right)$

Make p _{U, i}=[u v 1] ^T, p _{W, i}=[x _wy _w1] ^T, H=λ A[r ₁r ₂T]=[h ₁h ₂h ₃], r wherein _i(i=1～3) and h _iThe column vector of (i=1～3) rotation matrix R and matrix H, matrix A are the intrinsic parameter matrix, and λ is a scalar.Therefore formula (7) can be write as:

sP _u，i＝Hp _w，i (8)

The H matrix representation homography between calibrating template plane and the plane of delineation, by formula (8) as can be known, the degree of freedom of matrix H is 8, therefore needs at least 4 above non-colinear corresponding point, just can obtain the H matrix of band scale factor.Because rotation matrix R is the unit orthogonal matrix, so r ₁, r ₂Be the unit orthogonal vector, can get two constraints thus:

$\left\{\begin{array}{c}{h}_1^T{A}^{-T}{A}^{-1}{h}_2=0\\ h_1^T{A}^{-T}{A}^{-1}{h}_1=h_2^T{A}^{-T}{A}^{-1}{h}_2\end{array}\right.---\left(9\right)$

Order $B=A^{-T}{A}^{-1}=\left[\begin{array}{ccc}{b}_1& b_2& b_4\\ b_2& b_3& b_5\\ b_4& b_5& b_6\end{array}\right],$ Obviously B is a positive definite symmetric matrices.Define a vector

B=[b ₁b ₂b ₃b ₄b ₅b ₆] ^T, then two constraints of formula (9) can be written as again:

$\left[\begin{array}{c}{v}_{12}^T\\ {(v_{11}-v_{22})}^T\end{array}\right]b=\mathrm{Vb}=0---\left(10\right)$

V wherein _Ij=[h _I1h _J1, h _I1h _J2+ h _I2h _J1, h _I2h _J2, h _I3h _J1+ h _I1h _J3, h _I3h _J2+ h _I2h _J3, h _I3h _J3] ^T, h wherein _IjFor the i of matrix H is capable, the j column element.The image of every bat n (n 〉=3) width of cloth plane reference plate just can obtain n above-mentioned system of equations, and V is the matrix of 2n * 6.Separating of formula (10) is matrix V ^TThe minimal eigenvalue characteristic of correspondence vector of V.After solving B, but decompose just calibrating camera intrinsic parameter matrix A, comprise imaging center, between centers inclination factor and equivalent focal length by Qiao Lisiji.

(3) demarcation of the relative external parameter of left and right cameras

After calibrating the intrinsic parameter matrix A, just can determine the external parameter of every width of cloth image, promptly attitude and location parameter are:

$\left\{\begin{array}{c}{r}_1=\mathrm{\ρ}{A}^{-1}{h}_1,r_2=\mathrm{\ρ}{A}^{-1}{h}_2,r_3=r_1\×r_2\\ T=\mathrm{\ρ}{A}^{-1}{h}_3\\ \mathrm{\ρ}=1/\left|\right|A^{-1}{h}_1\left|\right|=1/\left|\right|A^{-1}{h}_2\left|\right|\end{array}\right.---\left(11\right)$

The rotation matrix R that is determined by formula (11) does not satisfy orthogonality, therefore adopts singular value decomposition method with its orthogonalization, obtains the external parameter of video camera.All inside and outside parameter of video camera have so just been determined.

Behind attitude of demarcating left and right cameras respectively and location parameter, press the twin camera external model of Fig. 5, just can calibrate the relative attitude and the location parameter of left and right cameras according to following formula:

$R=R_r{R}_l^{-1},$ $T=T_r-R_r{R}_l^{-1}{T}_l,$ R, T are the attitude and the positions of the left relatively video camera of right video camera, R _r, T _rBe the attitude and the location matrix of the relative world coordinate system of right video camera, R _l, T _lBe the attitude and the location matrix of the relative world coordinate system of left video camera.

In the practical application two ccd video cameras are fixed on the top of the shelf by shown in Figure 4.The left and right sides mirror that requires according to calibration algorithm is respectively taken 10 original scaling board image informations, handle by above-mentioned steps, utilize desirable pin hole perspective model to find the solution all inside and outside parameter except that distortion factor, utilize following formula to find the solution the relative attitude and the location parameter of left and right sides mirror then.Camera intrinsic parameter sees Table 2, and video camera relative attitude and location parameter see Table 3.

Table 2 left and right sides mirror intrinsic parameter calibration result

	α	β	u o	v o	s
						Left side mirror	1501.001	1489.956	376.800	297.560	-0.826
Right mirror	1477.471	1467.680	389.012	281.778	0.203

Table 3 left and right sides mirror relative attitude and location position result

Whole calibrating procedure is carried out according to the flow process among Fig. 6, demarcates distortion factor, camera intrinsic parameter (equivalent focal length, imaging center, between centers inclination factor), left and right cameras relative position parameter and attitude parameter successively.

Claims (3)

1. double-camera calibrating method in the 3 D scanning system is characterized in that double-camera calibrating method mainly comprises in the 3 D scanning system: earlier distortion factor is demarcated; After utilizing distortion factor that captured image is carried out image rectification then, associated ideal pin hole perspective model, the calibrating camera inner parameter, wherein intrinsic parameters of the camera mainly comprises imaging center, between centers inclination factor and equivalent focal length; Demarcate the external parameter of left and right cameras at last according to intrinsic parameters of the camera, further utilize the twin camera external model, demarcate the relative external parameter of left and right cameras, thereby obtain all internal and external parameters of video camera.

2. double-camera calibrating method in the 3 D scanning system according to claim 1 is characterized in that the main operational steps of this method is:

1.) the sign round dot on one group of parallel lines that are positioned on the scaling board of use, and, utilize parallel lines projection intersection point (x on the picture plane according to geometrical perspective projection ultimate principle _c, y _c) constraint condition and distortion of camera model, obtain one group and cross intersection point (x _c, y _c) straight-line equation: y-y _c=k _i(x-x _c) (i=1,2 ..., N), k wherein _iIt is the slope of i bar straight line; The parallel lines of choosing on n (n 〉=3) the group scaling board just can obtain n above-mentioned straight-line equation, and the individual straight-line equation of said n (n 〉=3) is combined into a system of equations, is tried to achieve by least square method: W=[A (k) A ^t(k)] ^-1A ^t(k) B (k), wherein A and B matrix are the functions about distortion factor k, utilize variable step-size search method search distortion factor k in the one-dimensional space, when $\text{||}\stackrel{\‾}{\mathrm{AW}}\text{-B||=}\underset{k}{\min }\text{||AW-B||}$ The time, the k value is distortion factor;

2.) after trying to achieve the distortion factor of video camera, captured image is carried out image distortion correction, obtain undistorted uncalibrated image, utilize desirable pin hole perspective model to demarcate intrinsic parameters of the camera except that distortion factor then, mainly comprise the demarcation of imaging center, the demarcation of between centers inclination factor and the demarcation of equivalent focal length, make the z of world coordinate system _wComponent is 0, and desirable pin hole perspective model is:

sp _u，i＝Hp _w，i

P wherein _{U, i}=[uv1] ^T, p _{W, i}=[x _wy _w1] ^T, H=λ A[r ₁r ₂T]=[h ₁h ₂h ₃], r _i(i=1～3) and h _iThe column vector of (i=1～3) expression rotation matrix R and matrix H, matrix A is the intrinsic parameter matrix, λ is a scalar;

The H matrix representation homography between calibrating template plane and the plane of delineation, degree of freedom is 8, therefore needs at least 4 above non-colinear corresponding point, just can obtain the H matrix of band scale factor, because rotation matrix R is the unit orthogonal matrix, so r ₁, r ₂Be the unit orthogonal vector, can get two constraints thus, form an equation of constraint, the image of every bat n (n 〉=3) width of cloth plane reference plate just can obtain n above-mentioned equation of constraint, utilize least-squares algorithm just can calibrate the intrinsic parameter matrix A, mainly comprise imaging center, between centers inclination factor and equivalent focal length;

3.) calibrate the intrinsic parameter matrix A after, according to camera model, just can demarcate the external parameter of every width of cloth image, be video camera attitude and location parameter, the rotation matrix of initially trying to achieve does not satisfy orthogonality, therefore adopts singular value decomposition method with its orthogonalization, obtain the external parameter of video camera, behind attitude that calibrates left and right cameras respectively and location parameter, just can calibrate the relative external parameter of left and right cameras according to the twin camera external model, promptly relative attitude and location parameter are:

$R=R_r{R}_l^{-1},$ $T=T_r-R_r{R}_l^{-1}{T}_l$

R wherein, T is the attitude and the location matrix of the left relatively video camera of right video camera, R _r, T _rBe the attitude and the location matrix of the relative world coordinate system of right video camera, R _l, T _lBe the attitude and the location matrix of the relative world coordinate system of left video camera.

3. double-camera calibrating method in the 3 D scanning system according to claim 2, it is characterized in that described step-length adopts following method to determine: the distortion parameter value of camera lens is all smaller, and the region of search can just elect (10 as ^-6, 10 ^-6), when the precision of distortion parameter reaches 10 ^-9The time, the correction precision of pixel has been reached about 0.02 pixel.

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