CN102930544A - Parameter calibration system of vehicle-mounted camera - Google Patents

Abstract

Disclosed is a parameter calibration method of a vehicle-mounted camera. The method includes steps of self-making a three-dimensional calibration board, and establishing a world coordinate system on the basis of the self-made three-dimensional calibration board; establishing a camera calibration model on the basis of the three-dimensional calibration board, acquiring world coordinates of chessboard corners of the three-dimensional calibration board, and extracting pixel coordinates of the chessboard corners on the basis of a corner detection algorithm; and using a least square method to calibrate inner and outer parameters of a camera in combination of the corner world coordinates and the pixel coordinates.

Description

A kind of parameter calibration system of vehicle-mounted vidicon

Technical field

[01] the present invention relates to intelligent transportation field, relate more specifically to the demarcation of vehicle-mounted vidicon inside and outside parameter in the vehicle DAS (Driver Assistant System).

Background technology

[02] in recent years, intelligent transportation becomes the focus of research, and DAS (Driver Assistant System) receives much concern as the important component part of intelligent transportation.Wherein, lane detection, vehicle detection and tracking and range finding etc. are the gordian techniquies of DAS (Driver Assistant System).These technology all are to rely on vehicle-mounted photography/videography machine collection traffic environment on every side, therefore vehicle-mounted vidicon are demarcated accurately to have very important significance.

[03] camera marking method is divided into traditional camera marking method and self-calibrating method.Common calibrating method has: Tsai (tradition) and Zhang Zhengyou (between tradition and self calibration) etc.Traditional camera calibration method is applied widely, and stated accuracy is high, but calibration process is complicated; From the standardization process is simple but precision is on the low side.

[04] based on the chessboard calibration plate of two dimension video camera is demarcated the very representative property of the method for Zhang Zhengyou.Video camera need to catch the confidential reference items that image more than 2 is found the solution video camera, and the outer ginseng of corresponding every width of cloth image also needs to find the solution according to confidential reference items and the picture of having tried to achieve.The demarcation of vehicle-mounted vidicon, in order to make things convenient for subsequent operation, ginseng is fixed outside wishing.Gu existing vehicle-mounted vidicon scaling method Main Problems is: demarcate the relatively trouble that seems with two-dimentional scaling board, be unfavorable for determining of world coordinate system, and be unfavorable for the detection of back and range finding etc.If demarcate with two-dimentional scaling board, just need two scaling boards, and need to know two world coordinates relations between the scaling board; Perhaps take a scaling board to clap two width of cloth pictures, and need to know the motion track of scaling board.Homemade stereo calibration plate is actual vertically to be comprised of two two-dimentional scaling boards, and the angle point world coordinates is in two planes, and is and all known, easily extraction and the calibrated and calculated of coordinate.

[05] two-dimentional scaling board comparison is simple, and the algorithm of Zhang Zhengyou is comparative maturity also, so a lot of people has adopted two-dimentional scaling board to carry out the demarcation of vehicle-mounted vidicon.Common scheme such as " a kind of simple calibrating method of vehicle-mounted vidicon " (Li Qing etc. in the prior art, " robot " z1 phase in 2003), wherein come to position to two-dimentional scaling board with aids such as vertical, meter ruler and large set squares, video camera is carried out the demarcation of inside and outside parameter.After the method calibrates camera parameters, the perspective transformation matrix that can obtain to fix." based on the single image camera calibration of two quadrature one-dimensional objects " (Xue Junpeng, Su Xianyu, " Acta Optica ", the 1st phase of the 32nd volume, 0115001-1 page or leaf-0115001-7 page or leaf, in January, 2012) in, the T-shape that proposes to form based on two quadrature one-dimensional objects is demarcated target, and set up the scaling method of space coordinates, only need to take the inside and outside parameter that a width of cloth picture just can calibrate distortion parameter and the video camera of camera lens.

[06] still, the vehicles such as lane detection of the prior art, vehicle detection and tracking and range finding are assisted driving technology, need to clap the picture of getting to vehicle-mounted vidicon and carry out perspective transform, therefore need fixing perspective transformation matrix.With two-dimentional scaling board vehicle-mounted vidicon is demarcated, the world coordinate system that can not get fixing, perspective transformation matrix are unfixing yet, inconvenient follow-up perspective transform.Much utilize aid to determine that the scaling method of world coordinate system is also more loaded down with trivial details, easy not, operation is trouble relatively.

[07] terminological interpretation:

Video camera confidential reference items: comprise focal length and the image pixel centre coordinate of video camera, specifically comprise: camera sensor equivalent focal length f in the x and y direction _xAnd f _yImage pixel centre coordinate (u ₀, v ₀); Video camera is joined outward: comprise the installation site of video camera setting angle and the relative world coordinate system of video camera, specifically comprise: the setting angle of video camera: crab angle γ, angle of pitch φ and roll angle

Camera coordinate system ties up to translational movement on x, y and the z direction: t with respect to world coordinates _x, t _yAnd t _z

Summary of the invention

[[08] is for above-mentioned technical matters, the present invention adopts and a kind ofly based on homemade stereo calibration plate the inside and outside parameter of vehicle-mounted vidicon is demarcated, with the stereo calibration plate that homemade two two-dimentional scaling boards form vehicle-mounted vidicon is demarcated, set up fixing world coordinate system and perspective transformation matrix, angle point world coordinate system coordinate and image pixel coordinate conveniently obtain, only need bat to get a width of cloth picture and just can carry out to vehicle-mounted vidicon the demarcation of inside and outside parameter, convenient follow-up lane detection and the operations such as vehicle detection, tracking and range finding.

[09] as shown in Figure 1, the invention provides a kind of vehicle-mounted vidicon scaling method based on the stereo calibration plate, comprise step: 1, self-control stereo calibration plate, set up the camera coordinate system model, set up world coordinate system based on the stereo calibration plate, obtain the world coordinates of stereo calibration plate chessboard angle point; 2, set up the camera calibration model, extract the pixel coordinate of above-mentioned chessboard angle point based on Corner Detection Algorithm; 3, in conjunction with angle point world coordinates and pixel coordinate, utilize least square method that camera interior and exterior parameter is demarcated.

Description of drawings

[10] Fig. 1 is particular flow sheet of the present invention;

[11] Fig. 2 calibrates plate and sets up world coordinate system for self-control is three-dimensional;

[12] Fig. 3 is the foundation of camera coordinate system.

Embodiment

[13] below, by reference to the accompanying drawings, the specific implementation process of the vehicle-mounted vidicon scaling method based on the stereo calibration plate provided by the invention is elaborated.

[14] 1, self-control is three-dimensional calibrates plate and sets up the world coordinate system model

[15] self-control solid calibration plate as shown in Figure 2, this stereo calibration plate becomes 90 degree angles to form by the black and white chessboard scaling board of two 4*4 sizes, and the gridiron pattern size is 150mm*150mm.If ground scaling board is the XOY coordinate system of world coordinate system, endways scaling board is the XOZ coordinate system of world coordinate system, and the tessellated right corner point of first left black and white is world coordinates initial point O on the two plate boundary lines.

[16] 2, set up the camera calibration model

[17] establish P _W(X _W, Y _W, Z _W) be under the world coordinate system a bit, the coordinate under its corresponding camera coordinate system is P _c(x _c, y _c, z _c), the coordinate under the corresponding image physical coordinates system is (x _u, y _u), the coordinate under the corresponding image pixel coordinate system is (u, v), then camera coordinate system is as shown in Figure 3.

[18] under linear pinhole camera modeling, the corresponding relation of four kinds of coordinate systems is as follows:

(1) world coordinates is tied to camera coordinate system:

$\left[\begin{array}{c}{x}_c\\ y_c\\ z_c\\ 1\end{array}\right]=\left[\begin{array}{cc}R& T\\ 0& 1\end{array}\right]\left[\begin{array}{c}{X}_W\\ Y_W\\ Z_W\\ 1\end{array}\right]---\left(1\right)$

In the formula (1): $\left[\begin{array}{ccc}{r}_{11}& r_{12}& r_{13}\\ r_{21}& r_{22}& r_{23}\\ r_{31}& r_{32}& r_{33}\end{array}\right]$ Be rotation matrix, and be orthogonal matrix that by crab angle γ, angle of pitch φ, roll angle ψ, expression formula is as follows

$R=\left[\begin{array}{ccc}\cos \mathrm{\ψ}\cos \mathrm{\γ}& \sin \mathrm{\ψ}\cos \mathrm{\γ}& -\sin \mathrm{\γ}\\ -\sin \mathrm{\ψ}\cos \mathrm{\φ}+\cos \mathrm{\ψ}\sin \mathrm{\γ}\sin \mathrm{\φ}& \cos \mathrm{\ψ}\cos \mathrm{\φ}+\sin \mathrm{\ψ}\sin \mathrm{\γ}\sin \mathrm{\φ}& \cos \mathrm{\γ}\sin \mathrm{\φ}\\ \sin \mathrm{\ψ}\sin \mathrm{\φ}+\cos \mathrm{\ψ}\sin \mathrm{\γ}\cos \mathrm{\φ}& -\cos \mathrm{\ψ}\sin \mathrm{\φ}+\sin \mathrm{\ψ}\sin \mathrm{\γ}\cos \mathrm{\φ}& \cos \mathrm{\γ}\cos \mathrm{\φ}\end{array}\right];$ $T=\left[\begin{array}{c}{t}_x\\ t_y\\ t_z\end{array}\right]$ Be the translation vector of camera coordinate system with respect to world coordinate system.

(2) camera coordinates is tied to desirable non-fault image physical coordinates system:

$x_u=f\frac{x_c}{y_c}$

$y_u=f\frac{y_c}{z_c}$

Wherein f is the focal length of camera lens.

(3) the image physical coordinates is tied to the image pixel coordinate system:

$u=\frac{x_u}{\mathrm{dx}}+u_0$

$v=\frac{y_u}{\mathrm{dy}}+v_0$

(u wherein ₀, v ₀) be the coordinate at image pixel center, dx, dy are respectively the pixel cell distance on camera sensor x and the y direction.

To sum up, object point P in the camera coordinate system _cTransformational relation to image pixel coordinate points (u, v) is:

$\left[\begin{array}{c}u\\ v\\ 1\end{array}\right]=\left[\begin{array}{ccc}{f}_x& 0& u_0\\ 0& f_y& v_0\\ 0& 0& 0\end{array}\right]\left[\begin{array}{c}{x}_c/z_c\\ y_c/z_c\\ 1\end{array}\right]---\left(2\right)$

In the formula (2): f _x=f/dx, f _y=f/dy is respectively camera sensor equivalent focal length in the x and y direction.Order $A=\left[\begin{array}{ccc}{f}_x& 0& u_0\\ 0& f_y& v_0\\ 0& 0& 1\end{array}\right]$ Confidential reference items matrix for video camera.

World coordinate point P _WTransformational relation to image pixel coordinate points (u, v) is:

$z_c\left[\begin{array}{c}u\\ v\\ 1\end{array}\right]=A\left[\begin{array}{cc}R& T\\ 0& 1\end{array}\right]\left[\begin{array}{c}{X}_W\\ Y_W\\ Z_W\\ 1\end{array}\right]=\left[\begin{array}{ccc}{f}_x& o& u_0\\ 0& f_y& v_0\\ 0& 0& 1\end{array}\right]\left[\begin{array}{cccc}{r}_{11}& r_{12}& r_{13}& t_x\\ r_{21}& r_{22}& r_{23}& t_y\\ r_{31}& r_{32}& r_{33}& t_z\\ 0& 0& 0& 1\end{array}\right]\left[\begin{array}{c}{X}_W\\ Y_W\\ Z_W\\ 1\end{array}\right]---\left(3\right)$

[19] 3, find the solution in conjunction with least square method

Order $M=\left[\begin{array}{cccc}{m}_{11}& m_{12}& m_{13}& m_{14}\\ m_{21}& m_{22}& m_{23}& m_{24}\\ m_{31}& m_{32}& m_{33}& m_{34}\end{array}\right]=A\left[\begin{array}{cc}R& T\\ 0& 1\end{array}\right],$ Then

$z_c\left[\begin{array}{c}u\\ v\\ 1\end{array}\right]=M\left[\begin{array}{c}{X}_W\\ Y_W\\ Z_W\\ 1\end{array}\right]---\left(4\right)$

M is the projection matrix of 3*4 in the formula (4), and it is found the solution the inside and outside parameter that namely obtains video camera.

Comprise in the following formula following two about m _IjLinear equation:

X _Wm ₁₁+Y _Wm ₁₂+Z _Wm ₁₃+m ₁₄-u _Wm ₃₁-uY _Wm ₃₂-uZ _Wm ₃₃=um ₃₄

X _Wm ₂₁+Y _Wm ₂₂+Z _Wm ₂₃+m ₂₄-vX _Wm ₃₁-vY _Wm ₃₂-vZ _Wm ₃₃=vm ₃₄

If n world coordinates point coordinate P arranged _Wi(i=1 ... n) and corresponding image pixel coordinate (u _i, v _i), then can obtain a following 2n linear equation:

$\left[\begin{array}{ccccccccccc}{X}_{W1}& Y_{W1}& Z_{W1}& 1& 0& 0& 0& 0& -X_{W1}{u}_1& -Y_{W1}{u}_1& -Y_{W1}{u}_1\\ 0& 0& 0& 0& X_{W1}& Y_{W1}& Z_{W1}& 1& -X_{W1}{v}_1& -Y_{W1}{v}_1& -Z_{W1}{v}_1\\ ...& ...& ...& ...& ...& ...& ...& ...& ...& ...& ...\\ ...& ...& ...& ...& ...& ...& ...& ...& ...& ...& ...\\ X_{\mathrm{Wn}}& Y_{\mathrm{Wn}}& Z_{\mathrm{Wn}}& 1& 0& 0& 0& 0& -X_{\mathrm{Wn}}{u}_n& -Y_{\mathrm{Wn}}{u}_n& -Z_{\mathrm{Wn}}{u}_n\\ 0& 0& 0& 0& X_{\mathrm{Wn}}& Y_{\mathrm{Wn}}& Z_{\mathrm{Wn}}& 1& -X_{\mathrm{Wn}}{v}_n& -Y_{\mathrm{Wn}}{v}_n& -Z_{\mathrm{Wn}}{v}_n\end{array}\right]\×\left[\begin{array}{c}{m}_{11}\\ m_{12}\\ m_{13}\\ m_{14}\\ m_{21}\\ m_{22}\\ m_{23}\\ m_{24}\\ m_{31}\\ m_{32}\\ m_{33}\end{array}\right]=\left[\begin{array}{c}{u}_1{m}_{34}\\ v_1{m}_{34}\\ ...\\ ...\\ u_n{m}_{34}\\ v_n{m}_{34}\end{array}\right]---\left(5\right)$

Be without loss of generality, make m ₃₄=1,2n linear equation of other 11 elements of Metzler matrix then can be abbreviated as:

K _m＝U (6)

M is 11 dimensional vectors that 11 elements form in the formula (6), and K is the 11*2n dimension matrix that world coordinates point coordinate and image pixel point coordinate form, and U is the 2n dimensional vector that the image pixel point coordinate forms.K and U are known vector, as 2n〉11 the time, namely available least square method is found the solution m:

m=K ^-1U (7)

In the formula (7): K ^-1Inverse matrix for K.

Ask for the inside and outside parameter of video camera below by m.

If R=[r ₁r ₂r ₃] ^T, r wherein ₁=[r ₁₁r ₁₂r ₁₃], r ₂=[r ₂₁r ₂₂r ₂₃], r ₃=[r ₃₁r ₃₂r ₃₃].

Then:

$m_{34}\left[\begin{array}{cc}{m}_1^{\′}& m_{14}^{\′}\\ m_2^{\′}& m_{24}^{\′}\\ m_3^{\′}& 1\end{array}\right]=\left[\begin{array}{cccc}{f}_x& 0& u_0& 0\\ 0& f_y& v_0& 0\\ 0& 0& 1& 0\end{array}\right]\left[\begin{array}{cc}{r}_1& t_x\\ r_2& t_y\\ r_3& t_z\\ 0& 1\end{array}\right]=\left[\begin{array}{cc}{f}_x{r}_1+u_0{r}_3& f_x{t}_x+u_0{t}_z\\ f_y{r}_2+v_0{r}_3& f_y{t}_y+v_0{t}_z\\ r_3& t_z\end{array}\right]---\left(8\right)$

In the formula (8): m ' ₁=[m ₁₁m ₁₂m ₁₃]/m ₃₄, m ' ₂=[m ₂₁m ₂₂m ₂₃]/m ₃₄, m ' ₃[m ₃₁m ₃₂m ₃₃]/m ₃₄, m ' ₁₄=m ₁₄/ m ₃₄, m ' ₂₄=m ₂₄/ m ₃₄

By following formula as can be known, m ₃₄M ' ₃=r ₃, be that orthogonal matrix can get by R again | r ₃|=1, so:

$m_{34}=\frac{1}{\left|m_3^{\′}\right|}$

Obtain the calibration result of camera parameters according to above-mentioned calculation procedure:

(a) video camera confidential reference items

Image pixel center horizontal ordinate:

Image pixel center ordinate:

The equivalent focal length of camera sensor on the x direction:

The equivalent focal length of camera sensor on the x direction:

(b) video camera is joined outward

$r_1=\frac{m_{34}}{f_x}(m_1^{\′}-u_0{m}_3^{\′}),$

$r_2=\frac{m_{34}}{f_x}(m_2^{\′}-v_0{m}_3^{\′}),$

r ₃＝m ₃₄m′ ₃，

Crab angle: γ=| arcsin (r ₁₃) |,

The angle of pitch: φ=arcsin (r ₁₂/ cos γ),

Roll angle:

(being defaulted as 0),

Camera coordinate system ties up to translational movement on the z direction: t with respect to world coordinates _z=m ₃₄,

Camera coordinate system ties up to translational movement on the x direction with respect to world coordinates:

Camera coordinate system ties up to translational movement on the y direction with respect to world coordinates:

[20] the present invention at first utilize homemade stereo calibration plate convenient and clear and definite world coordinate system, fixing outer ginseng and perspective transformation matrix is provided, demarcation provides fixing outer ginseng and perspective transformation matrix to vehicle-mounted vidicon, thus the operations such as convenient follow-up lane detection, vehicle detection and tracking and range finding.The stereo calibration plate that wherein adopts is demarcated target than the T-shape that two quadrature one-dimensional objects form, the determining of more convenient world coordinate system.

Claims (4)

1. vehicle-mounted vidicon scaling method based on the stereo calibration plate comprises step: a, self-control stereo calibration plate, set up world coordinate system based on described self-control stereo calibration plate; B, set up the camera calibration model: set up the camera coordinate system model based on the stereo calibration plate, obtain the world coordinates of stereo calibration plate chessboard angle point, and extract the pixel coordinate of above-mentioned chessboard angle point based on Corner Detection Algorithm; C, in conjunction with angle point world coordinates and pixel coordinate, utilize least square method that camera interior and exterior parameter is demarcated.

2. according to claim 1 method, wherein, described self-control stereo calibration plate becomes 90 degree angles to form by the black and white chessboard scaling board of two 4*4 sizes, and the gridiron pattern size is 150mm*150mm; Ground scaling board is the XOY coordinate system of world coordinate system, and endways scaling board is the XOZ coordinate system of world coordinate system, and the tessellated right corner point of first left black and white is world coordinates initial point O on the two plate boundary lines.

3. according to claim 1 and 2 method, wherein,

If P _W(X _W, Y _W, Z _W) be a bit under the world coordinate system, the coordinate under its corresponding camera coordinate system is P _c(x _c, y _c, z _c), the coordinate under the corresponding image physical coordinates system is (x _u, y _u), the coordinate under the corresponding image pixel coordinate system is (u, v),

Under linear pinhole camera modeling, be tied to camera coordinate system, camera coordinates according to world coordinates and be tied to image physical coordinates system and image physical coordinates and be tied to transformational relation between the image pixel coordinate system, obtain world coordinate point P _W(X _W, Y _W, Z _W) to the following transformational relation of image pixel coordinate points (u, v):

$z_c\left[\begin{array}{c}u\\ v\\ 1\end{array}\right]=A\left[\begin{array}{cc}R& T\\ 0& 1\end{array}\right]\left[\begin{array}{c}{X}_W\\ Y_W\\ Z_W\\ 1\end{array}\right]=\left[\begin{array}{ccc}{f}_x& o& u_0\\ 0& f_y& v_0\\ 0& 0& 1\end{array}\right]\left[\begin{array}{cccc}{r}_{11}& r_{12}& r_{13}& t_x\\ r_{21}& r_{22}& r_{23}& t_y\\ r_{31}& r_{32}& r_{33}& t_z\\ 0& 0& 0& 1\end{array}\right]\left[\begin{array}{c}{X}_W\\ Y_W\\ Z_W\\ 1\end{array}\right]$

Wherein, $A=\left[\begin{array}{ccc}{f}_x& 0& u_0\\ 0& f_y& v_0\\ 0& 0& 1\end{array}\right]$ Confidential reference items matrix for video camera; $\left[\begin{array}{ccc}{r}_{11}& r_{12}& r_{13}\\ r_{21}& r_{22}& r_{23}\\ r_{31}& r_{32}& r_{33}\end{array}\right]$ Be rotation matrix, and be orthogonal matrix; $T=\left[\begin{array}{c}{t}_x\\ t_y\\ t_z\end{array}\right]$ Be the translation vector of camera coordinate system with respect to world coordinate system, f _x, f _yBe respectively the equivalent focal length on camera sensor x and the y direction, (u ₀, v ₀) be the coordinate at image pixel center.

4. method one of according to claim 1-3, wherein, the step of utilizing least square method that camera interior and exterior parameter is demarcated comprises:

Order $M=\left[\begin{array}{cccc}{m}_{11}& m_{12}& m_{13}& m_{14}\\ m_{21}& m_{22}& m_{23}& m_{24}\\ m_{31}& m_{32}& m_{33}& m_{34}\end{array}\right]=A\left[\begin{array}{cc}R& T\\ 0& 1\end{array}\right],$ Then

$z_c\left[\begin{array}{c}u\\ v\\ 1\end{array}\right]=M\left[\begin{array}{c}{X}_W\\ Y_W\\ Z_W\\ 1\end{array}\right]---\left(4\right)$

Wherein M is the projection matrix of 3*4, and it is found the solution the inside and outside parameter that can obtain video camera, comprises two about m in the formula (4) _IjLinear equation:

X _Wm ₁₁+Y _Wm ₁₂+Z _Wm ₁₃+m ₁₄-u _Wm ₃₁-uY _Wm ₃₂-uZ _Wm ₃₃=um ₃₄

X _Wm ₂₁+Y _Wm ₂₂+Z _Wm ₂₃+m ₂₄-vX _Wm ₃₁-vY _Wm ₃₂-vZ _Wm ₃₃=vm ₃₄

Then, for n world coordinates point coordinate P _Wi(i=1 ... n) and corresponding image pixel coordinate (u _i, v _i), then can obtain a following 2n linear equation:

$\left[\begin{array}{ccccccccccc}{X}_{W1}& Y_{W1}& Z_{W1}& 1& 0& 0& 0& 0& -X_{W1}{u}_1& -Y_{W1}{u}_1& -Y_{W1}{u}_1\\ 0& 0& 0& 0& X_{W1}& Y_{W1}& Z_{W1}& 1& -X_{W1}{v}_1& -Y_{W1}{v}_1& -Z_{W1}{v}_1\\ ...& ...& ...& ...& ...& ...& ...& ...& ...& ...& ...\\ ...& ...& ...& ...& ...& ...& ...& ...& ...& ...& ...\\ X_{\mathrm{Wn}}& Y_{\mathrm{Wn}}& Z_{\mathrm{Wn}}& 1& 0& 0& 0& 0& -X_{\mathrm{Wn}}{u}_n& -Y_{\mathrm{Wn}}{u}_n& -Z_{\mathrm{Wn}}{u}_n\\ 0& 0& 0& 0& X_{\mathrm{Wn}}& Y_{\mathrm{Wn}}& Z_{\mathrm{Wn}}& 1& -X_{\mathrm{Wn}}{v}_n& -Y_{\mathrm{Wn}}{v}_n& -Z_{\mathrm{Wn}}{v}_n\end{array}\right]\×\left[\begin{array}{c}{m}_{11}\\ m_{12}\\ m_{13}\\ m_{14}\\ m_{21}\\ m_{22}\\ m_{23}\\ m_{24}\\ m_{31}\\ m_{32}\\ m_{33}\end{array}\right]=\left[\begin{array}{c}{u}_1{m}_{34}\\ v_1{m}_{34}\\ ...\\ ...\\ u_n{m}_{34}\\ v_n{m}_{34}\end{array}\right]---\left(5\right)$

Make m ₃₄=1,2n linear equation of other 11 elements of Metzler matrix then can be abbreviated as:

Km=U (6)

M is 11 dimensional vectors that 11 elements form in the formula (6), K is the 11*2n dimension matrix that world coordinates point coordinate and image pixel point coordinate form, and U is the 2n dimensional vector that the image pixel point coordinate forms, and K and U are known vector, as 2n〉11 the time, namely available least square method is found the solution m:

m=K ^-1U (7)

In the formula (7): K ^-1Inverse matrix for K;

Ask for the inside and outside parameter of video camera below by m;

If R=[r ₁r ₂r ₃] ^T, r wherein ₁=[r ₁₁r ₁₂r ₁₃], r ₂=[r ₂₁r ₂₂r ₂₃], r ₃=[r ₃₁r ₃₂r ₃₃];

Then:

$m_{34}\left[\begin{array}{cc}{m}_1^{\′}& m_{14}^{\′}\\ m_2^{\′}& m_{24}^{\′}\\ m_3^{\′}& 1\end{array}\right]=\left[\begin{array}{cccc}{f}_x& 0& u_0& 0\\ 0& f_y& v_0& 0\\ 0& 0& 1& 0\end{array}\right]\left[\begin{array}{cc}{r}_1& t_x\\ r_2& t_y\\ r_3& t_z\\ 0& 1\end{array}\right]=\left[\begin{array}{cc}{f}_x{r}_1+u_0{r}_3& f_x{t}_x+u_0{t}_z\\ f_y{r}_2+v_0{r}_3& f_y{t}_y+v_0{t}_z\\ r_3& t_z\end{array}\right]---\left(8\right)$

In the formula (8): m ' ₁=[m ₁₁m ₁₂m ₁₃]/m ₃₄, m ' ₂=[m ₂₁m ₂₂m ₂₃]/m ₃₄, m ' ₃=[m ₃₁m ₃₂m ₃₃]/m ₃₄, m ' ₁₄=m ₁₄/ m ₃₄, m ' ₂₄=m ₂₄/ m ₃₄,

By following formula as can be known, m ₃₄M ' ₃=r ₃, be that orthogonal matrix can get by R again | r ₃|=1, so:

$m_{34}=\frac{1}{\left|m_3^{\′}\right|}$

Obtain at last the following calibration result of camera parameters:

The video camera confidential reference items:

Image pixel center horizontal ordinate:

Image pixel center ordinate:

The equivalent focal length of camera sensor on the x direction:

The equivalent focal length of camera sensor on the x direction:

Video camera is joined outward:

$r_1=\frac{m_{34}}{f_x}(m_1^{\′}-u_0{m}_3^{\′}),$

$r_2=\frac{m_{34}}{f_x}(m_2^{\′}-v_0{m}_3^{\′}),$

r ₃＝m ₃₄m′ ₃，

Crab angle: γ=| arcsin (r ₁₃) |,

The angle of pitch: φ=arcsin (r ₁₂/ cos γ),

Roll angle:

(being defaulted as 0),

Camera coordinate system ties up to translational movement on the z direction: t with respect to world coordinates _z=m ₃₄,

Camera coordinate system ties up to translational movement on the x direction with respect to world coordinates:

Camera coordinate system ties up to translational movement on the y direction with respect to world coordinates:

Images