CN1323547C - Three-line calibration method for external parmeters of camera carried by car - Google Patents

Abstract

The present invention discloses a three-line calibration method for external parameters of a vehicle-mounted camera. The method aims at the calibration problem of a vehicle-mounted camera of an intelligent vehicle on the basis of visual navigation; a ready-made tool box is used for carrying out the calibration of internal parameters; three parallel lines have the same vanishing point and different slope rates on a picture plane according to the principle of perspective projection; the external parameters of the camera have internal relation with the vanishing point and the slope rates; the expression of the external parameters of the camera in pixels can be established through mathematical derivation and coordinate transformation. In a pixel coordinate system, after the coordinates of the intersection points of the parallel lines and the other three points are manually or automatically determined, parameters needed can be directly calculated. The process can be realized under different environment such as roads, playground tracks or special delineated parallel lines. Experimental results verify the feasibility and the correctness of the method.

Description

The three-way scaling method of a kind of vehicle-mounted vidicon external parameter

Technical field

The invention belongs to computer vision field, relate to camera calibration in the computer vision, the three-way scaling method of particularly a kind of vehicle-mounted vidicon external parameter.

Background technology

Along with popularizing of development of urbanization and automobile, the communications and transportation problem is serious day by day, and the notion of intelligent vehicle navigation is arisen at the historic moment.Road tracking based on vision is paid attention to most, according to the data-searching that the applicant carries out, finds following document:

[1]Bertozzi M，Broggi A，Cellario M，et al.ArtificialVision in road vehicles[C].In：Proceedings of the IEEE on IntelligentTransmission System，2002，90(7)：1258-1271

[2] Yang Ming, Lu Jianye, Wang Hong opens cymbals etc. and the road based on vision is followed the tracks of [J]. " pattern recognition and artificial intelligence ", 2001,14 (2): 186-193

[3] Qiu Maolin, Ma Songde, Li Yi. camera calibration summary in the computer vision. " automation journal ", 2000,26 (1): 43-55

[4]Bertozzi M，Broggi A.GOLD：a parallel real-time stereovision system for generic obstacle and lane detection [J].IEEEtransactions on image processing，1998，7(1)：62-81

[5]Bertozzi M，Broggi A，Fascioli A.Self-calibration of astereo vision system for automotive applications[C].In：Proceedingsof IEEE International Conference on Robotics and Automation，2001，4：3698-3703

[6]Southall B，Taylor C J. Stochastic road shapeestimation[C].In：Proceedings of Eighth IEEE InternationalConference on Computer Vision，2001，1：205-212

[7] Song Xuefeng, Yang Ming, Wang Hong. based on the simple and easy camera marking method of latticed texture. " computer engineering and application [J] " .2002,7:72-74

In many complexity of intelligent vehicle navigation and challenging task, the most valued road that is based on vision is followed the tracks of ^{[1] [2]}In this process, need calculate the geological information of object in the three dimensions according to the image information that video camera obtains usually, and rebuild thus or recognition object, thereby camera calibration is absolutely necessary ^[3]For the demarcation problem of vehicle-mounted vidicon, have a lot of people to study: the inner parameter of the ARGO system supposition video camera of Parma university is known, draws the grid of known dimensions on the ground, utilizes the intersection point of grid to demarcate external parameter ^[4]They have also adopted a kind of so-called self-calibrating method in addition ^[5], the gauge point on the use hood is as spotting, and these calibration points are known with respect to the position of bodywork reference frame; The breadboard researcher of the GRASP of the University of Pennsylvania has used the calibration tool case of University of Southern California's exploitation to carry out the demarcation of inner parameter, utilizes and represents the straight line in track to carry out the demarcation of external parameter ^[6]The researcher of Tsing-Hua University utilizes ground grid to demarcate ^[7]Also have other researchers to use the function library of Intel to carry out the demarcation of intrinsic parameters of the camera, use the method that is similar to the ARGO system to demarcate external parameter.Though above-mentioned scaling method can be dealt with problems preferably, all there is weak point: complicated operating process, higher to environment requirement, or the parameter of demarcating is less.

To the research of intelligent vehicle, mainly concentrate on more smooth zone, road surface at present, therefore can make ground flatness hypothesis.Because vehicle is to travel on the road surface, the deviation in the certain limit can not cause too big problem, so the precision of demarcating can be significantly less than the precision in the applications such as Robot Hand-eye demarcation, three-dimensional reconstruction.

Summary of the invention

These characteristics at above-mentioned vehicle-mounted vidicon is demarcated the objective of the invention is to, and the method for the three-way demarcation of a kind of vehicle-mounted vidicon external parameter is provided.

Realize that foregoing invention purpose technical solution is, the three-way scaling method of vehicle-mounted vidicon external parameter, be characterized in, on smooth ground, draw three straight lines parallel to each other, or utilize existing parallel lines, or look for one section straight road that three markings are arranged, and make the car body longitudinal axis of the automobile that is loaded with video camera be parallel to these straight lines, record the distance of they and the car body longitudinal axis; Foundation is that the video camera external parameter expression formula of unit is determined the vehicle-mounted vidicon external parameter with the pixel, through mathematical derivation and coordinate transform, obtain the angle of heel ψ, pitching angle theta, deflection of the relative car body of video camera _, video camera in car body overhead height h and the video camera photocentre apart from the lateral separation d of the car body longitudinal axis.

Method of the present invention only needs three parallel straight lines on the smooth ground, just can carry out the video camera calibrating external parameters, need not special-purpose place, even can finish in the driving process of vehicle.

Description of drawings

Fig. 1 is the schematic diagram that concerns between car body of the present invention and the video camera, also is one embodiment of the present of invention; Wherein (a) is end view, (b) is vertical view, (c) is rearview;

Fig. 2 is the schematic diagram that concerns of camera coordinate system, plane of delineation coordinate system and pixel coordinate system;

Fig. 3 is straight highway and the superincumbent straight line picture of manual stack of demarcating usefulness;

Fig. 4 is sports filed track and the superincumbent straight line picture of manual stack of demarcating usefulness.

Embodiment

The present invention is described in further detail below in conjunction with embodiment that accompanying drawing and inventor provide.

According to technique scheme, the three-way scaling method of vehicle-mounted vidicon external parameter may further comprise the steps:

1) on smooth ground, draws three straight lines parallel to each other, or utilize existing parallel lines, or look for one section straight road that three markings are arranged, make the car body longitudinal axis of the automobile that is loaded with video camera be parallel to these straight lines, record the distance of they and the car body longitudinal axis;

2) the vehicle-mounted vidicon external parameter determines

The vehicle-mounted vidicon external parameter comprise the angle of heel ψ, pitching angle theta, deflection of the relative car body of video camera _, video camera in car body overhead height h and video camera apart from car centre distance d;

3) setting up with the pixel is the video camera external parameter expression formula of unit

As shown in Figure 1, adopt left-handed coordinate system, establishing in the bodywork reference frame certain any coordinate is p _v=(x _v, y _v, z _v), its coordinate at camera coordinate system is p _c=(x _c, y _c, z _c).The angle of heel of the relative car body of video camera is ψ (observing to tilt clockwise for just along vehicle heading), and the angle of pitch is θ (points upwards for just), deflection is _ (sensing vehicle body axis left for just), the position of the photocentre of video camera in bodywork reference frame is t=(l, d, h), then

p _v＝R·p _c+t

p _c＝R ^-1·p _v-R ^-1·t＝R ^T·p _v-R ^T·t (1)

Wherein

$=$ $\left[\begin{array}{ccc}{r}_{11}& r_{12}& r_{13}\\ r_{21}& r_{32}& r_{23}\\ r_{31}& r_{32}& r_{33}\end{array}\right]$

Wherein

Suppose that ground is smooth, optical axis o is at plane z _vThe vector that projection on=0 forms is η, η and X _vThe angle that axle forms is _, optical axis o is θ with the angle that η forms, the angle of heel of the relative car body of video camera (or roll angle of title video camera) is ψ, l ₁, l ₂, l ₃For three straight lines that are parallel to the vehicle body longitudinal axis on the smooth ground, apart from X _vDistance be respectively a, b, c;

For on the smooth ground one be parallel to the vehicle body longitudinal axis X _v, and arriving it apart from being the straight line l of k, its parametric equation is

$\left\{\begin{array}{cc}{x}_v=s& \\ y_v=k,& s\∈R\\ z_v=0& \end{array}\right.---\left(2\right)$

According to formula (1), the parametric equation of l in camera coordinate system is

$\left(\begin{array}{c}{x}_c\\ y_c\\ z_c\end{array}\right)=\left[\begin{array}{ccc}{r}_{11}& r_{21}& r_{31}\\ r_{12}& r_{22}& r_{32}\\ r_{13}& r_{23}& r_{33}\end{array}\right]\·\left(\begin{array}{c}s\\ k\\ 0\end{array}\right)-\left[\begin{array}{ccc}{r}_{11}& r_{21}& r_{31}\\ r_{12}& r_{22}& r_{32}\\ r_{13}& r_{23}& r_{33}\end{array}\right]\·\left(\begin{array}{c}l\\ d\\ h\end{array}\right)$

$=\left(\begin{array}{c}s\·r_{11}+k\·r_{21}-l\·r_{11}-d\·r_{21}-h\·r_{31}\\ s\·r_{12}+k{\·r}_{22}-l\·r_{12}-d\·r_{22}-h\·r_{32}\\ s\·r_{13}+k\·r_{23}-l\·r_{13}-d\·r_{23}-h\·r_{33}\end{array}\right)---\left(3\right)$

Correlation (Fig. 2) according between camera coordinate system, plane of delineation coordinate system and the pixel coordinate system of this paper definition has

u＝y _c，v＝-z _c，u＝(i-c _i)·dx，v＝(j-c _j)·dy (4)

Wherein dx, dy and c _i, c _jBe respectively laterally, proportionality coefficient and principal point position longitudinally.

According to the pinhole imaging system model, convolution (3), formula (4), the parametric equation of l on plane of delineation coordinate system is (focal length is unit representation with the pixel)

$\left\{\begin{array}{c}u=f_i\·\mathrm{dx}\·\frac{y_c}{x_c}=f_i\·\mathrm{dx}\·\frac{s\·r_{12}+k\·r_{22}-l\·r_{12}-d\·r_{22}-h\·r_{32}}{s\·r_{11}+k\·r_{21}-l\·r_{11}-d\·r_{21}-h\·r_{31}}\\ v=-f_j\·\mathrm{dy}\·\frac{z_c}{x_c}=-f_j\·\mathrm{dy}\·\frac{s\·r_{13}+k\·r_{23}-l\·r_{13}-d\·r_{23}-h\·r_{33}}{s\·r_{11}+k\·r_{21}-l\·r_{11}-d\·r_{21}-h\·r_{31}}\end{array}\right.---\left(5\right)$

Because s is any real number, and and l on same direction, formula (5) is rewritten into

$\left\{\begin{array}{c}u=f_i\·\mathrm{dx}\·\frac{y_c}{x_c}=f_i\·\mathrm{dx}\·\frac{s\·r_{12}+k\·r_{22}-d\·r_{22}-h\·r_{32}}{s\·r_{11}+k\·r_{21}-d\·r_{21}-h\·r_{31}}\\ v=-f_j\·\mathrm{dy}\·\frac{z_c}{x_c}=-f_j\·\mathrm{dy}\·\frac{s\·r_{13}+k\·r_{23}-d\·r_{23}-h\·r_{33}}{s\·r_{11}+k\·r_{21}-d\·r_{21}-h\·r_{31}}\end{array}\right.---\left(6\right)$

When s → ∞, straight line l extends to infinite distant place, and its end point on plane of delineation coordinate system is

$u_h={\underset{s\→\∞}{\lim }}^u$

$=\underset{s\→\∞}{\lim }{f}_i\·\mathrm{dx}\·\frac{s\·r_{12}+k\·r_{22}-d\·r_{22}-h\·r_{32}}{s\·r_{11}+k\·r_{21}-d\·r_{21}-h\·r_{31}}$

$=f_i\·\mathrm{dx}\·\frac{r_{12}}{r_{11}}---\left(7a\right)$

$v_h={\underset{s\→\∞}{\lim }}^v$

$=\underset{s\→\∞}{\lim }-f_j\·\mathrm{dy}\·\frac{s\·r_{13}+k\·r_{23}-d\·r_{23}-h{r}_{33}}{s\·r_{11}+k\·r_{21}-d\·r_{21}-h\·r_{31}}---\left(7b\right)$

$=-f_j\·\mathrm{dy}\·\frac{r_{13}}{r_{11}}$

Because the family of straight lines that is parallel to each other in the space has identical end point at view plane, so straight line l ₁, l ₂, l ₃The end point of imaging is

u _h1＝u _h2＝u _h3＝u _h

v _h1＝v _h2＝v _h3＝v _h

$g=\frac{\mathrm{du}}{\mathrm{dv}}=\frac{\frac{\mathrm{du}}{\mathrm{ds}}}{\frac{\mathrm{dv}}{\mathrm{ds}}}---\left(8\right)$

$=-\frac{f_i\·\mathrm{dx}}{f_j\·\mathrm{dy}}\·\frac{k\·r_{12}\·r_{21}-d\·r_{12}\·r_{21}-h\·r_{12}\·r_{31}-k\·r_{11}\·r_{22}+d\·r_{11}\·r_{22}+h\·r_{11}{r}_{32}}{k\·r_{13}\·r_{21}-d\·r_{13}\·r_{21}-h\·r_{13}\·r_{31}-k\·r_{11}\·r_{23}+d\·r_{11}\·r_{23}+h\·r_{11}{r}_{33}}$

For 3 parallel lines l ₁, l ₂, l ₃, have respectively

$g_1=-\frac{f_i\·\mathrm{dx}}{f_j\·\mathrm{dy}}\·\frac{a\·r_{12}\·r_{21}-d\·r_{12}\·r_{21}-h\·r_{12}\·r_{31}-a\·r_{11}\·r_{22}+d\·r_{11}\·r_{22}+h\·r_{11}{r}_{32}}{a\·r_{13}\·r_{21}-d\·r_{13}\·r_{21}-h\·r_{13}\·r_{31}-a\·r_{11}\·r_{23}+d\·r_{11}\·r_{23}+h\·r_{11}{r}_{33}}$

$g_2=-\frac{f_i\·\mathrm{dx}}{f_j\·\mathrm{dy}}\·\frac{b\·r_{12}\·r_{21}-d\·r_{12}\·r_{21}-h\·r_{12}\·r_{31}-b\·r_{11}\·r_{22}+d\·r_{11}\·r_{22}+h\·r_{11}{r}_{32}}{b\·r_{13}\·r_{21}-d\·r_{13}\·r_{21}-h\·r_{13}\·r_{31}-b\·r_{11}\·r_{23}+d\·r_{11}\·r_{23}+h\·r_{11}{r}_{33}}---\left(9\right)$

$g_3=-\frac{f_i\·\mathrm{dx}}{f_j\·\mathrm{dy}}\·\frac{c\·r_{12}\·r_{21}-d\·r_{12}\·r_{21}-h\·r_{12}{r}_{31}-c\·r_{11}\·r_{22}+d\·r_{11}\·r_{22}+h\·r_{11}{r}_{32}}{c\·r_{13}\·r_{21}-d\·r_{13}\·r_{21}-h\·r_{13}\·r_{31}-c\·r_{11}\·r_{23}+d\·r_{11}\·r_{23}+h\·r_{11}{r}_{33}}$

According to formula (9), solve

$\mathrm{tg\ψ}=\frac{(r_1-r_3)(a-b)-(r_1-r_2)(a-c)}{(r_1-r_3)(r_{1}a-r_{2}b)-(r_1-r_2)(r_{1}a-r_{3}c)}---\left(10\right)$

According to formula (7a), (7b)

$\mathrm{tg\θ}=\frac{u_h\·\sin \mathrm{\ψ}}{f_i\·\mathrm{dx}}+\frac{v_h\·\cos \mathrm{\ψ}}{f_j\·\mathrm{dy}}---\left(11\right)$

According to formula (9), solve

$h=\frac{(b-a)\mathrm{AC}}{\mathrm{BC}-\mathrm{AD}}---\left(13\right)$

$d=\frac{B}{A}\·\frac{(b-a)\mathrm{AC}}{\mathrm{BC}-\mathrm{AD}}+a$

Wherein:

A＝r ₁·sinψ·cosθ-cosθcos ψ

B＝-(cos_sinψ+sin_cosψsinθ)-r ₁(cos_cosψ-sin_sinψsinθ)

C＝r ₂·sinψcosθ-cosθcosψ

D＝-(cos_sinψ+sin_cosψsinθ)-r ₂(cos_cosψ-sin_sinψsinθ)

$r_n=-\frac{g_n}{\frac{f_i}{f_j}\·\frac{\mathrm{dx}}{\mathrm{dy}}},n=\mathrm{1,2,3}$

4) parameter calibration

The inner parameter of video camera use the calibration tool case of University of Southern California's exploitation demarcate (J.Y.Bouget.Matlab camera calibration toolbox.http: //www.vision.caltech.edu/bougetj/calib_doc/index.html), from the image of one group of demarcation thing different azimuth, extract the characteristic point of known geological information, then it is sent into optimizing process, just can obtain the principal point and the effective focal length of video camera.

Utilize the present invention on smooth ground, to draw three straight lines parallel to each other, or utilize existing parallel lines (as hundred meters racing tracks of sports ground), or look for one section straight road that three lane lines are arranged, make the longitudinal axis of automobile be parallel to these straight lines, the distance (being a, b, c) that records they and the car body longitudinal axis just can be carried out the video camera calibrating external parameters easily.

Embodiment:

This method is tested on the instruction carriage of Jilin University and Xi'an Communications University with different forms.What at first select for use is one section straight highway with three lane lines.Fig. 3 is the frame in the video gathered of laboratory vehicle, camera is the TMC-9700 of U.S. PULNIX company, capture card and transaction card are respectively the Viper RGB and the Python of Canadian CORECO company, camera lens is selected Computar 8mm for use, image resolution ratio is set at 256 * 240, and video camera is installed in the front upper place of copilot station.This frame picture is saved as the file of bmp form, utilizes the paintbrush of Windows to handle then, with the straight line tool of the paintbrush l that draws ₁ ^c, l ₂ ^c, l ₃ ^cArticle three, straight line is superimposed upon on the lane line, represents the center line of markings imaging.H (i _h, j _h) expression three parallel lines intersection point, P ₁(i ₁, j ₁) be l _{1 c}Go up and remove H (i _h, j _h) outer more arbitrarily, P ₂(i ₂, j ₂) be l ₂ ^cGo up and remove H (i _h, j _h) outer more arbitrarily, P ₃(i ₃, j ₃) be l ₃ ^cGo up and remove H (i _h, j _h) outer more arbitrarily.Utilize the image coordinate positioning function of paintbrush, find out the pixel coordinate of four Chosen Points, record a=-3.2m in addition, b=0.3m, c=3.8m.In pixel coordinate system,

$g_n=\frac{\mathrm{dx}}{\mathrm{dy}}\·\frac{i_h-i_n}{j_h-j_n},n=\mathrm{1,2,3}---\left(14\right)$

In formula (14) substitution formula (10), (11), (12), (13), can try to achieve ψ, θ, _, d, the value of h.

Table 1 PULNIX intrinsic parameters of the camera and calibrating external parameters result

Parameter	f i	f j	c i	c j	ψ	θ	_	d	h
										Value	599 pixels	605 pixels	89 pixels	150 pixels	0.034rad	-0.219rad	0.053rad	0.29m	1.70m

Above-mentioned experimental technique is a kind of implementation of this scaling method, can also carry out in another mode.As shown in Figure 4, the 100-metre dash road (can directly utilize the known geological information of racing track markings like this and setting-out again, and satisfy ground flatness hypothesis) of plastic sports ground is selected in the place for use, makes the longitudinal axis of automobile be parallel to the runway marking line.Used camera is SONY DSR-PD150P, and zoom is set at the maximum of the mode of looking in the distance, Manual focusing, resolution setting is 640 * 480, records a=-1.25m, b=0m, c=1.25m, demarcation the results are shown in Table 2.

Table 2 SONY intrinsic parameters of the camera and calibrating external parameters result

Parameter	f i	f j	c i	c j	ψ	θ	_	d	h
										Value	789 pixels	806 pixels	322 pixels	218 pixels	0.039rad	-0.026rad	-0.028rad	0.25m	1.37m

Can in the vehicle ' process, demarcate in addition.For example under steam, the driver makes a certain sign aligning middle lane line of reserving in advance on the car body, and direct of travel is parallel with lane line, just can determine the value of a, b, c, thereby finishes demarcation.

Parallel lines imaging location in the three-way scaling method of vehicle-mounted vidicon external parameter of the present invention is manual the realization, if introduce image processing techniques in calibration process, just can realize the automatic demarcation of vehicle-mounted vidicon external parameter.Even vehicle under steam like this,, just can demarcate at any time as long as run into suitable highway section.

Obviously, three-way scaling method of the present invention can not be demarcated the length travel l of the relative bodywork reference frame of video camera photocentre, needs extra this parameter of measuring, and makes l introduce measure error, but generally not too large.In the ordinary course of things, the preview distance of automobile is 30m～70m, and it is negligible therefore measuring the error of introducing, and other CALCULATION OF PARAMETERS does not rely on this parameter fortunately.

In addition, calibration process can produce error inevitably, and its main cause can be summed up as follows:

● can not satisfy ground flatness hypothesis;

● three straight lines exist crooked or not parallel each other;

● the longitudinal axis of vehicle body does not have and straight line parallel;

● the straight line of manual stack is not the center line of markings;

● three straight lines are bigger with respect to the range measurement error of vehicle body longitudinal axis;

● the demarcation of inner parameter is inaccurate.

Theory analysis and experimental result show that trilinear method only needs three parallel lines, just can finish the calibrating external parameters of vehicle-mounted vidicon, existing relatively certain methods, it is simple to have principle, easy to operate, highly versatile, implementation is various, and is easy of integration in the medium advantage of on-vehicle machines vision system.After introducing image processing techniques, whole calibrating procedure can full automation, even can carry out in vehicle ', thereby has solved the drifting problem of vehicle-mounted vidicon parameter to a certain extent.In addition, trilinear method can also be simplified to 6 methods, and promptly six points with rectangular distribution replace three parallel lines.6 methods are particularly suitable for demarcating in a fixed venue, only need six points of picture, but are not suitable for demarcating on highway.

Attached:

The proof of some formula in " vehicle-mounted vidicon calibrating external parameters trilinear method "

1. the derivation of civilian Chinese style (8)

$\frac{\mathrm{du}}{\mathrm{ds}}=f_i\·\mathrm{dx}\·\frac{r_{12}(s\·r_{11}+k\·r_{21}-d\·r_{21}-h\·r_{31})-(s\·r_{12}+k\·r_{22}-d\·r_{22}-h\·r_{32})\·r_{11}}{{(s\·r_{11}+k\·r_{21}-d\·r_{21}-h\·r_{31})}^2}\·r_{11}$

$=f_i\·\mathrm{dx}\·\frac{k\·r_{12}\·r_{21}-d\·r_{12}\·r_{21}-h\·r_{12}\·r_{31}-k\·r_{11}\·r_{22}+d\·r_{11}\·r_{22}+h\·r_{11}{r}_{32}}{{(s\·r_{11}+k\·r_{21}-d\·r_{21}-h\·r_{31})}^2}\·r_{11}$

$\frac{\mathrm{dv}}{\mathrm{ds}}=-f_j\·\mathrm{dy}\·\frac{r_{13}\·(s\·r_{11}+k\·r_{21}-d\·r_{21}-h\·r_{31})-(s\·r_{13}+k\·r_{23}-d\·r_{23}-h\·r_{32})\·r_{11}}{{(s\·r_{11}+k\·r_{21}-d\·r_{21}-h\·r_{31})}^2}\·r_{11}$

$=-f_i\·\mathrm{dy}\·\frac{k\·r_{13}\·r_{21}-d\·r_{13}\·r_{21}-h\·r_{13}\·r_{31}-k\·r_{11}\·r_{23}+d\·r_{11}\·r_{23}+h\·r_{11}{r}_{33}}{{(s\·r_{11}+k\·r_{21}-d\·r_{21}-h\·r_{31})}^2}\·r_{11}$

Have then

$g=\frac{\mathrm{du}}{\mathrm{dv}}=\frac{\frac{\mathrm{du}}{\mathrm{ds}}}{\frac{\mathrm{dv}}{\mathrm{ds}}}$

$=-\frac{f_i\·\mathrm{dx}}{f_j\·\mathrm{dy}}\·\frac{k\·r_{12}\·r_{21}-d\·r_{12}\·r_{21}-h\·r_{12}\·r_{31}-k\·r_{11}\·r_{22}+d\·r_{22}\·r_{22}+h\·r_{11}{r}_{32}}{k\·r_{13}\·r_{21}-d\·r_{13}\·r_{21}-h\·r_{13}\·r_{31}-k\·r_{11}\·r_{23}+d\·r_{11}\·r_{23}+h\·r_{11}{r}_{33}}$

2. the derivation of civilian Chinese style (10)

According to civilian Chinese style (9)

$g_1=-\frac{f_i\·\·\mathrm{dx}}{f_j\·\mathrm{dy}}\·\frac{a\·r_{12}\·r_{21}-d\·r_{12}\·r_{21}-h\·r_{12}\·r_{31}-a\·r_{11}\·r_{22}+d\·r_{11}\·r_{22}+h\·r_{22}{r}_{32}}{a\·r_{13}\·r_{21}-d\·r_{13}\·r_{21}-h\·r_{13}\·r_{31}-a\·r_{11}\·r_{23}+d\·r_{11}\·r_{23}+h\·r_{11}{r}_{33}}$

$g_2=-\frac{f_i\·\mathrm{dx}}{f_j\·\mathrm{dy}}\·\frac{b\·r_{12}\·r_{21}-d\·r_{12}\·r_{21}-h\·r_{12}\·r_{31}-b\·r_{11}\·r_{22}+d\·r_{11}\·r_{22}+h\·r_{11}{r}_{32}}{b\·r_{13}\·r_{21}-d\·r_{13}\·r_{21}-h\·r_{13}\·r_{31}-b\·r_{11}\·r_{23}+d\·r_{11}\·r_{23}+h\·r_{11}{r}_{33}}$

$g_3=-\frac{f_i\·\mathrm{dx}}{f_j\·\mathrm{dy}}\·\frac{c\·r_{12}\·r_{21}-d\·r_{12}\·r_{21}-h\·r_{12}\·r_{31}-c\·r_{11}\·r_{22}+d\·r_{11}\·r_{22}+h\·r_{11}{r}_{32}}{c\·r_{13}\·r_{21}-d\·r_{13}\·r_{21}-h\·r_{13}\·r_{31}-c\·r_{11}\·r_{23}+d\·r_{11}\·r_{23}+h\·r_{11}{r}_{33}}$

Order $r_n=-\frac{g_n}{\frac{f_i}{f_j}\·\frac{\mathrm{dx}}{\mathrm{dy}}},n=\mathrm{1,2,3}$

Then

$r_1=\frac{a(r_{12}\·r_{21}-r_{11}\·r_{22})+d(r_{11}\·r_{22}-r_{12}\·r_{21})+h(r_{11}\·r_{32}-r_{12}\·r_{31})}{a\·(r_{13}\·r_{21}-r_{11}\·r_{23})+d(r_{11}\·r_{23}-r_{13}\·r_{21})+h(r_{11}\·r_{33}-r_{13}\·r_{31})}$

Launch

r ₁·a·(r ₁₃·r ₂₁-r ₁₁·r ₂₃)+r ₁·d·(r ₁₁·r ₂₃-r ₁₃·r ₂₁)+r ₁·h·(r ₁₁r ₃₃-r ₁₃·r ₃₁)＝a·(r ₁₂·r ₂₁-r ₁₁·r ₂₂)+d·(r ₁₁·r ₂₂-r ₁₂·r ₂₁)+h·(r ₁₁r ₃₂-r ₁₂·r ₃₁) (A1)

In like manner can get

r ₂·b·(r ₁₃·r ₂₁-r ₁₁r ₂₃)+r ₂·d·(r ₁₁·r ₂₃-r ₁₃·r ₂₁)+r ₂·h·(r ₁₁r ₃₃-r ₁₃·r ₃₁)＝b·(r ₁₂·r ₂₁-r ₁₁·r ₂₂)+d·(r ₁₁·r ₂₂-r ₁₂·r ₂₁)+h·(r ₁₁r ₃₂-r ₁₂·r ₃₁) (A2)

r ₃·c·(r ₁₃·r ₂₁-r ₁₁·r ₂₃)+r ₃·d·(r ₁₁·r ₂₃-r ₁₃·r ₂₁)+r ₃·h·(r ₁₁r ₃₃-r ₁₃·r ₃₁)＝c·(r ₁₂·r ₂₁-r ₁₁·r ₂₂)+d·(r ₁₁·r ₂₂-r ₁₂·r ₂₁)+h·(r ₁₁r ₃₂-r ₁₂·r ₃₁) (A3)

Formula (A1) deducts formula (A2) and gets

(r ₁·a-r ₂·b)·(r ₁₃·r ₂₁-r ₁₁·r ₂₃)+d·(r ₁-r ₂)·(r ₁₁·r ₂₃-r ₁₃·r ₂₁)+h·(r ₁-r ₂)·(r ₁₁·r ₃₃-r ₁₃·r ₃₁)＝(a-b)·(r ₁₂·r ₂₁-r ₁₁·r ₂₂) (A4)

Formula (A1) deducts formula (A3) and gets

(r ₁·a-r ₃·c)·(r ₁₃·r ₂₁-r ₁₁·r ₂₃)+d·(r ₁-r ₃)·(r ₁₁·r ₂₃-r ₁₃·r ₂₁)+h·(r ₁-r ₃)·(r ₁₁·r ₃₃-r ₁₃·r ₃₁)＝(a-c)·(r ₁₂·r ₂₁-r ₁₁·r ₂₂) (A5)

Formula (A2) deducts formula (A3) and gets

(r ₂·b-r ₃·c)·(r ₁₃·r ₂₁-r ₁₁·r ₂₃)+d·(r ₂-r ₃)·(r ₁₁·r ₂₃-r ₁₃·r ₂₁)+h·(r ₂-r ₃)·(r ₁₁·r ₃₃-r ₁₃·r ₃₁)＝(b-c)·(r ₁₂·r ₂₁-r ₁₁·r ₂₂) (A6)

Get by (A4)

d·(r ₁-r ₂)·(r ₁₁·r ₂₃-r ₁₃·r ₂₁)＝(a-b)·(r ₁₂·r ₂₁-r ₁₁·r ₂₂)-(r ₁·a-r ₂·b)·(r ₁₃·r ₂₁-r ₁₁·r ₂₃)-h·(r ₁-r ₂)·(r ₁₁·r ₃₃-r ₁₃·r ₃₁) (A7)

Get by (A5)

d·(r ₁-r ₃)·(r ₁₁·r ₂₃-r ₁₃·r ₂₁)＝(a-c)·(r ₁₂·r ₂₁-r ₁₁·r ₂₂)-(r ₁·a-r ₃·c)·(r ₁₃·r ₂₁-r ₁₁·r ₂₃)-h·(r ₁-r ₃)·(r ₁₁·r ₃₃-r ₁₃·r ₃₁) (A8)

Get by (A6)

d·(r ₂-r ₃)·(r ₁₁·r ₂₃-r ₁₃·r ₂₁)＝(b-c)·(r ₁₂·r ₂₁-r ₁₁·r ₂₂)-(r ₂·b-r ₃·c)·(r ₁₃·r ₂₁-r ₁₁·r ₂₃)-h·(r ₂-r ₃)·(r ₁₁·r ₃₃-r ₁₃·r ₃₁) (A9)

(A7) divided by (A8),

$\frac{r_1-r_2}{r_1-r_3}=\frac{(a-b)\·(r_{12}\·r_{21}-r_{11}\·r_{32})-(r_1\·a-r_2\·a)\·(r_{13}\·r_{21}-r_{11}\·r_{23})-h\·(r_1-r_2)\·(r_{11}\·r_{33}-r_{13}\·r_{33})}{(a-c)\·(r_{12}\·r_{21}-r_{11}\·r_{22})-(r_1\·a-r_3\·c)\·(r_{13}\·r_{21}-r_{11}\·r_{23})-h\·(r_1-r_3)\·(r_{11}\·r_{33}-r_{13}\·r_{31})}---\left(A10\right)$

Put in order:

(r ₁-r ₂)·(a-c)·(r ₁₂·r ₂₁-r ₁₁·r ₂₂)-(r ₁-r ₂)·(r ₁·a-r ₃·c)·(r ₁₃·r ₂₁-r ₁₁·r ₂₃)＝(r ₁-r ₃)·(a-b)·(r ₁₂·r ₂₁-r ₁₁·r ₂₂)-(r ₁-r ₃)·(r ₁·a-r ₂·b)·(r ₁₃·r ₁₁-r ₁₁·r ₂₃) (A11)

Because

r ₁₂·r ₂₁-r ₁₁·r ₂₂＝(sin_cosψ+cos_sinψsinθ)·(-sin_cosθ)-cosθcos_·(cos_cosψ-sin_sinψsinθ)＝-cosψcosθ

r ₁₃R ₂₁-r ₁₁R ₂₃=(sin_sin ψ-cos_cos ψ sin θ) (sin_cos θ)-cos θ cos_ (cos_sin ψ+sin_cos ψ sin θ)=-sin_cos θ formula (A11) is rewritten as

(r ₁-r ₂)·(a-c)·(-cos_cosθ)-(r ₁-r ₂)·(r ₁·a-r ₃·c)·(-sinψcosθ)＝(r ₁-r ₃)·(a-b)·(-cosψcosθ)-(r ₁-r ₃)·(r ₁·a-r ₂·b)·(-sinψcosθ) (A12)

The both members cos θ that divides out has

-(r ₁-r ₂)·(a-c)·cosψ+(r ₁-r ₃)·(a-b)·cosψ＝(r ₁-r ₃)·(r ₁·a-r ₂·b)·sinψ-(r ₁-r ₂)·(r ₁·a-r ₃·c)·sin_

So have

$\mathrm{tg\ψ}=\frac{(r_1-r_3)(a-b)-(r_1-r_2)(a-c)}{(r_1-r_3)(r_{1}a-r_{2}b)-(r_1-r_2)(r_{1}a-r_{3}c)}---\left(A13\right)$

3. the derivation of civilian Chinese style (11)

According to civilian Chinese style (7a) and (7b), have

Formula (A14) solves at last divided by formula (A15)

$\mathrm{tg\θ}=\frac{u_h\·\sin \mathrm{\ψ}}{f_i\·\mathrm{dx}}+\frac{v_h\·\cos \mathrm{\ψ}}{f_j\·\mathrm{dy}}---\left(A16\right)$

4. the derivation of civilian Chinese style (12)

According to formula (A14), solve

5. the derivation of civilian Chinese style (13)

Get by formula (A1)

d·[r ₁·(r ₁₁·r ₂₃-r ₁₃·r ₂₁)-(r ₁₁·r ₂₂-r ₁₂·r ₂₁)]＝h·[(r ₁₁·r ₃₂-r ₁₂·r ₃₁)-r ₁·(r ₁₁r ₃₃-r ₁₃·r ₃₁)]+a·(r ₁₂·r ₂₁-r ₁₁·r ₂₂)-r ₁·a·(r ₁₃·r ₂₁-r ₁₁·r ₂₃) (A18)

Get by formula (A2)

d·[r ₂·(r ₁₁·r ₂₃-r ₁₃·r ₂₁)-(r ₁₁·r ₂₂-r ₁₂·r ₂₁)]＝h·[(r ₁₁·r ₃₂-r ₁₂·r ₃₁)-r ₂·(r ₁₁r ₃₃-r ₁₃·r ₃₁)]+b·(r ₁₂·r ₂₁-r ₁₁·r ₂₂)-r ₂·b·(r ₁₃·r ₂₁-r ₁₁·r ₂₃) (A19)

Wherein

r ₁₁·r ₂₂-r ₁₂·r ₂₁＝cosθcos_·(cos_cosψ-sin_sinψsinθ)-(sin_cosψ+cos_sinψsinθ)·(-sin_cosθ)

＝cosθcosψ

r ₁₁·r ₂₃-r ₁₃·r ₂₁＝cosθcos_·(cos_sinψ+sin_cosψsinθ)-(sin_sinψ-cos_cosψsinθ)·(-sin_cosθ)

＝sinψcosθ

r ₁₁·r ₃₂-r ₁₂·r ₃₁＝cosθcos_·(-cosθsinψ)-(sin_sinψ-cos_cosψsinθ)·sinθ

＝-cos_·sinψ-sin_·cosψ·sinθ

r ₁₁·r ₃₃-r ₁₃·r ₃₁＝cosθcos_·cosθcosψ-(sin_sinψ-cos_cosψsinθ)·sinθ

＝cos_·cosψ-sin_·sin·sinθ

Order

A＝r ₁·(r ₁₁·r ₂₃-r ₁₃·r ₂₁)-(r ₁₁·r ₂₂-r ₁₂·r ₂₁)＝r ₁·sinψ·cosθ-cosθcos_

B＝[(r ₁₁·r ₃₂-r ₁₂·r ₃₁)-r ₁·(r ₁₁r ₃₃-r ₁₃·r ₃₁)]＝-(cos_sinψ+sin_cosψsinθ)-r ₁(cos_cosψ-sin_sinψsinθ)

C＝r ₂(r ₁₁·r ₂₃-r ₁₃·r ₂₁)-(r ₁₁·r ₂₂-r ₁₂·r ₂₁)＝r ₂·sinψcosθ-cosθcosψ

D＝(r ₁₁·r ₃₂-r ₁₂·r ₃₁)-r ₂·(r ₁₁r ₃₃-r ₁₃·r ₃₁)＝-(cos_sinψ+sin_cosψsinθ)-r ₂(cos_cosψ-sin_sinψsinθ)

Formula (A18) gets divided by (A19)

$\frac{A}{C}=\frac{\mathrm{hB}+\mathrm{aA}}{\mathrm{hD}+\mathrm{bC}}$

So

$h=\frac{(b-a)\mathrm{AC}}{\mathrm{BC}-\mathrm{AD}}$

By formula (A18), get again

$d=\frac{B}{A}\·\frac{(b-a)\mathrm{AC}}{\mathrm{BC}-\mathrm{AD}}+a$

Claims (1)

1. the three-way scaling method of vehicle-mounted vidicon external parameter is characterized in that, may further comprise the steps:

1) on smooth ground, draws three straight lines parallel to each other, or utilize existing parallel lines, or look for one section straight road that three markings are arranged, the car body longitudinal axis that is loaded with the automobile of video camera is parallel to these straight lines, record the distance of these straight lines and the car body longitudinal axis;

2) the vehicle-mounted vidicon external parameter determines

The vehicle-mounted vidicon external parameter comprise the angle of heel ψ, pitching angle theta, deflection of the relative car body of video camera _, video camera in car body overhead height h and the video camera photocentre apart from the lateral separation d of the car body longitudinal axis;

Bodywork reference frame adopts left-handed coordinate system, and the initial point of bodywork reference frame is the barycenter of vehicle, and car body longitudinal axis directed forward is X _vAxle, pointing to right-hand is Y _v, points upwards is Z _v

(1) setting up with the pixel is the video camera external parameter expression formula of unit, adopts left-handed coordinate system, and establishing in the bodywork reference frame certain any coordinate is p _v=(x _v, y _v, z _v), its coordinate at camera coordinate system is p _c=(x _c, y _c, z _c); The angle of heel of the relative car body of video camera is ψ, and this angle of heel is observed to tilt clockwise for just along vehicle heading; The angle of pitch is θ, and this angle of pitch points upwards is for just; Deflection is _, this deflection points to vehicle body axis left for just; The position of the photocentre of video camera in bodywork reference frame be t=(l, d, h), then

p _v＝R·p _c+t

p _c＝R ^-1·p _v-R ^-1·t＝R ^T·p _v-R ^T·t (1)

Wherein

$=\left[\begin{array}{ccc}{r}_{11}& r_{12}& r_{13}\\ r_{21}& r_{22}& r_{23}\\ r_{31}& r_{32}& r_{33}\end{array}\right]$

(2) suppose that ground is smooth, optical axis ο is at plane z _vThe vector that projection on=0 forms is η, η and X _vThe angle that axle forms is _, optical axis ο is θ with the angle of η formation, the angle of heel of video camera is ψ, l ₁, l ₂, l ₃For three straight lines that are parallel to the vehicle body longitudinal axis on the smooth ground, apart from X _vDistance be respectively a, b, c;

For on the smooth ground one be parallel to the vehicle body longitudinal axis X _v, and arriving it apart from being the straight line l of k, its parametric equation is

$\left\{\begin{array}{c}{x}_v=s\\ y_v=k,s\∈R\\ z_v=0\end{array}\right.---\left(2\right)$

(3) according to formula (1), the parametric equation of l in camera coordinate system is

$\left(\begin{array}{c}{x}_c\\ y_c\\ z_c\end{array}\right)=\left[\begin{array}{ccc}{r}_{11}& r_{21}& r_{31}\\ r_{12}& r_{22}& r_{32}\\ r_{13}& r_{23}& r_{33}\end{array}\right]\·\left(\begin{array}{c}s\\ k\\ 0\end{array}\right)-\left[\begin{array}{ccc}{r}_{11}& r_{21}& r_{31}\\ r_{12}& r_{22}& r_{32}\\ r_{13}& r_{23}& r_{33}\end{array}\right]\·\left(\begin{array}{c}l\\ d\\ h\end{array}\right)$

$=\left(\begin{array}{c}s\·r_{11}+k\·r_{21}-l\·r_{11}-d\·r_{21}-h\·r_{31}\\ s\·r_{12}+k\·r_{22}-l\·r_{12}-d\·r_{22}-h\·r_{32}\\ s\·r_{13}+k\·r_{23}-l\·r_{13}-d\·r_{23}-h\·r_{33}\end{array}\right)---\left(3\right)$

(4) according to the camera coordinate system of above-mentioned definition, the correlation between its plane of delineation coordinate system, pixel coordinate system and the camera coordinate system has:

u＝y _c，v＝-z _c，u＝(i-c _i)·dx，v＝(j-c _j)·dy (4)

Wherein u, v are the coordinate of plane of delineation coordinate system, and i, j are the coordinate of pixel coordinate system, dx, dy and c _i, c _jBe respectively laterally, proportionality coefficient and principal point position longitudinally; Wherein dx, dy are constant;

(5) according to the pinhole imaging system model, convolution (3), formula (4), the parametric equation of l on plane of delineation coordinate system is

$\left\{\begin{array}{c}u=f_i\·\mathrm{dx}\·\frac{y_c}{x_c}=f_i\·\mathrm{dx}\·\frac{s\·r_{12}+k\·r_{22}-l\·r_{12}-d\·r_{22}-h\·r_{32}}{s\·r_{11}+k\·r_{21}-l\·r_{11}-d\·r_{21}-h\·r_{31}}\\ v=-f_j\·\mathrm{dy}\·\frac{z_c}{x_c}=-f_j\·\mathrm{dy}\·\frac{s\·r_{13}+k\·r_{23}-l\·r_{13}-d\·r_{23}-h\·r_{33}}{s\·r_{11}+k\·r_{21}-l\·r_{11}-d\·r_{21}-h\·r_{31}}\end{array}\right.---\left(5\right)$

F in the formula _i, f _jBe focal length of camera, its unit is a pixel; Because s is any real number, and and l on same direction, formula (5) is rewritten into

$\left\{\begin{array}{c}u=f_i\·\mathrm{dx}\·\frac{y_c}{x_c}=f_i\·\mathrm{dx}\·\frac{s\·r_{12}+k\·r_{22}-d\·r_{22}-h\·r_{32}}{s\·r_{11}+k\·r_{21}-d\·r_{21}-h\·r_{31}}\\ v=-f_j\·\mathrm{dy}\·\frac{z_c}{x_c}=-f_j\·\mathrm{dy}\·\frac{s\·r_{13}+k\·r_{23}-d\·r_{23}-h\·r_{33}}{s\·r_{11}+k\·r_{21}-d\·r_{21}-h\·r_{31}}\end{array}\right.---\left(6\right)$

(6) when s → ∞, straight line l extends to infinite distant place, and its end point on plane of delineation coordinate system is

$u_h=\underset{s\→\∞}{\lim }u$

$=\underset{s\→\∞}{\lim }{f}_i\·\mathrm{dx}\·\frac{s\·r_{12}+k\·r_{22}-d\·r_{22}-h\·r_{32}}{s\·r_{11}+k\·r_{21}-d\·r_{21}-h\·r_{31}}$

$=f_i\·\mathrm{dx}\·\frac{r_{12}}{r_{11}}---\left(7a\right)$

$v_h=\underset{s\→\∞}{\lim }v$

$=\underset{s\→\∞}{\lim }-f_j\·\mathrm{dy}\·\frac{s\·r_{13}+k\·r_{23}-d\·r_{23}-h\·r_{33}}{s\·r_{11}+k\·r_{21}-d\·r_{21}-h\·r_{31}}$

$=-f_j\·\mathrm{dy}\·\frac{r_{13}}{r_{11}}---\left(7b\right)$

Because the family of straight lines that is parallel to each other in the space has identical end point at view plane, so straight line l ₁, l ₂, l ₃The end point of imaging is

u _h1＝u _h2＝u _h3＝u _h

v _h1＝v _h2＝v _h3＝v _h

(7) slope according to the image plane cathetus gets

$g=\frac{\mathrm{du}}{\mathrm{dv}}=\frac{\frac{\mathrm{du}}{\mathrm{ds}}}{\frac{\mathrm{dv}}{\mathrm{ds}}}---\left(8\right)$

$=-\frac{f_i\·\mathrm{dx}}{f_j\·\mathrm{dy}}\·\frac{k\·r_{12}\·r_{21}-d\·r_{12}\·r_{21}-h\·r_{12}\·r_{31}-k\·r_{11}\·r_{22}+d\·r_{11}\·r_{22}+h\·r_{11}{r}_{33}}{k\·r_{13}\·r_{21}-d\·r_{13}\·r_{21}-h\·r_{13}{\·r}_{31}-k\·r_{11}\·r_{23}+d\·r_{11}\·r_{23}+h\·r_{11}{r}_{33}}$

For 3 parallel lines l ₁, l ₂, l ₃, have respectively

$g_1=-\frac{f_i\·\mathrm{dx}}{f_j\·\mathrm{dy}}\·\frac{a\·r_{12}\·r_{21}-d\·r_{12}\·r_{21}-h\·r_{21}\·r_{31}-a\·r_{11}\·r_{22}+d\·r_{11}\·r_{22}+h\·r_{11}{r}_{32}}{a\·r_{13}\·r_{21}-d\·r_{13}\·r_{21}-h\·r_{13}\·r_{31}-a\·r_{11}\·r_{23}+d\·r_{11}\·r_{23}+h\·r_{11}{r}_{33}}$

$g_2=-\frac{f_i\·\mathrm{dx}}{f_j\·\mathrm{dy}}\·\frac{b\·r_{12}\·r_{21}-d\·r_{12}\·r_{21}-h\·r_{12}\·\·r_{31}-b\·r_{11}\·r_{22}+d\·r_{11}\·r_{22}+h\·r_{11}{r}_{32}}{b\·r_{13}{\·r}_{21}-d\·r_{13}\·r_{21}-h\·r_{13}\·r_{31}-b\·r_{11}\·r_{23}+d\·r_{11}\·r_{23}+h{\·r}_{11}{r}_{33}}---\left(9\right)$

$g_3=-\frac{f_i\·\mathrm{dx}}{f_j\·d}\·\frac{c\·r_{12}\·r_{21}-d\·r_{12}\·r_{21}-h\·r_{12}\·r_{31}-c\·r_{11}\·r_{22}+d\·r_{11}\·r_{22}+h{\·r}_{11}{r}_{32}}{c\·r_{13}\·r_{21}-d\·r_{13}\·r_{21}-h\·r_{13}\·r_{31}-c\·r_{11}\·r_{23}+d\·r_{11}\·r_{23}+h\·r_{11}{r}_{33}}$

(8) according to formula (9), solve

$\mathrm{tg\ψ}=\frac{(r_1-r_3)(a-b)-(r_1-r_2)(a-c)}{(r_1-r_3)(r_{1}a-r_{2}b)-(r_1-r_2)(r_{1}a-r_{3}c)}---\left(10\right)$

(9), obtain the expression formula of the angle of pitch according to formula (7a), (7b)

$\mathrm{tg\θ}=\frac{u_h\·\sin \mathrm{\ψ}}{f_i\·\mathrm{dx}}+\frac{v_h\·\cos \mathrm{\ψ}}{f_j\·\mathrm{dy}}---\left(11\right)$

(10), can also obtain the expression formula of deflection according to formula (7a), (7b)

(11) according to formula (9), can solve

$h=\frac{(b-a)\mathrm{AC}}{\mathrm{BC}-\mathrm{AD}}$

$d=\frac{B}{A}\·\frac{(b-a)\mathrm{AC}}{\mathrm{BC}-\mathrm{AD}}+a---\left(13\right)$

Wherein:

A＝r ₁·sinψ·cosθ-cosθcosψ

B＝-(cos_sinψ+sin_cosψsinθ)-r ₁(cos_cosψ-sin_sinψsinθ)

C＝r ₂·sinψcosθ-cosθcosψ

D＝-(cos_sinψ+sin_cosψsinθ)-r ₂(cos_cosψ-sin_sinψsinθ)

$r_n=-\frac{g_n}{\frac{f_i}{f_j}\·\frac{\mathrm{dx}}{\mathrm{dy}}},n=1,\mathrm{2,3}$

In pixel coordinate system, with manual or automatically mode determine the intersecting point coordinate of three parallel lines, on three parallel lines, choose three points except that intersection point then respectively, can directly calculate desired parameters;

3) through above-mentioned mathematical derivation and coordinate transform, obtain the angle of heel ψ, pitching angle theta, deflection of the relative car body of video camera _, video camera in car body overhead height h and the video camera photocentre apart from the lateral separation d of the car body longitudinal axis, can finish the video camera calibrating external parameters;

4) inner parameter of video camera uses the calibration tool case of University of Southern California's exploitation to demarcate, from the image of one group of demarcation thing different azimuth, extract the characteristic point of known geological information, then it is sent into optimizing process, just can obtain the principal point and the effective focal length of video camera.