CN102679896A - Track gauge measuring method based on machine vision - Google Patents

Abstract

The invention provides a rail gauge measuring method based on machine vision. The method comprises: step 1, disposing two groups of binocular type back CCD (Charge Coupled Device) cameras on a bracket above a steel rail; step 2, measuring and calculating parameters of each CCD camera; step 3, measuring and calculating the geometrical relationships of all CCD cameras; step 4, selecting corresponding point positions shot by the CCD cameras; step 5, selecting a rail gauge measuring point position; step 6, mapping the rail gauge measuring point position to a world coordinate; and step 7, measuring the distance between the measuring points in the world coordinate, i.e. the rail gauge. With the rail gauge measuring method provided by the invention, the distance between two rails is calculated by using two groups of back binocular type view imaging systems in cooperation of the coordinates in the world coordinate; and the precision and the accuracy are improved.

Description

Gauge assay method based on machine vision

Technical field

The present invention relates to the rail safety field, be specifically related to a kind of gauge assay method based on machine vision.

Background technology

The gauge irregularity can cause wheel to slide down or block rail; In time gauge does not expand the degree that wheel is slided down as yet to; Because the bigger wheel tread of gradient will make rail suffer the horizontal thrust of extra increase, if therefore the heavy grade section of wheel tread gets into the tread inner arc and also should avoid with interior.Gauge changes acutely in the short distance, shows to have serious direction irregularity, also can influence train safe certainly, so the gauge parameter is a requisite monitoring project in the track monitoring.

For a long time, the monitoring of irregularity parameters such as gauge is all adopted the method for hand dipping.Yet begin research in the world at the end of the seventies to the automatic measurement system of rail gauge; Particularly developed countries such as Japan, Germany are beginning to utilize the computer vision measurement technology to carry out the rail monitoring around the eighties; But be limited by the restriction of computer hardware and computer image processing technology, do not have fine this type of solution problem.China begins the research of this project in the nineties, wherein the 4th generation track checking car adopted photoelectric sensing and servo control mechanism to measure, its major defect is because on-the-spot vibrations, servo control mechanism damages easily.

Development along with computer image processing technology; The automatic monitoring system that is made up of several parts of line source, image capturing system and data handling system is developed out; How utilizing machine vision technique to reach and improve the track monitoring accuracy, is the direction of joint research in the industry.

Summary of the invention

To above-mentioned defective, the purpose of this invention is to provide a kind of gauge measuring method, the coarse technical matters of data that records with the gauge measuring method that solves prior art based on machine vision.

For realizing above-mentioned purpose, the present invention has adopted following technical scheme:

A kind of gauge assay method based on machine vision comprises:

Step 1, be provided with two groups of binocular formulas back to ccd video camera on gauge is measured kickstand, be positioned at the rail top;

Step 2, calculate the parameter of each ccd video camera;

Geometric relationship between step 3, the whole ccd video cameras of measuring and calculating;

Step 4, choose the corresponding point position that ccd video camera is taken;

Step 5, choose gauge measurement point position;

Step 6, with gauge measurement point location map to world coordinates;

Step 7, the spacing of in world coordinates, calculating the gauge measurement point are gauge.

According to the described gauge assay method of preferred embodiment of the present invention, said every group of ccd video camera comprises two ccd video cameras with public view field.

According to the described gauge assay method of preferred embodiment of the present invention, in said step 1, also be included on the support, be positioned at the fan-shaped light source of rail installed inside, make fan-shaped light source be radiated on the rail.

According to the described gauge assay method of preferred embodiment of the present invention, the parameter of each ccd video camera of measuring and calculating comprises in said step 2:

Template is fixed on the plane; Video camera matees through point and picture point on the template at the plural template image of different azimuth photographs, calculates the mapping matrix between image and the template; And can linearity solve intrinsic parameters of the camera through this matrix

$Z_{\mathrm{oi}}\left[\begin{array}{c}{u}_i\\ v_i\\ 1\end{array}\right]=\left[\begin{array}{cccc}{m}_{11}& m_{12}& m_{13}& m_{14}\\ m_{21}& m_{22}& m_{23}& m_{24}\\ m_{31}& m_{32}& m_{33}& m_{34}\end{array}\right]\left[\begin{array}{c}{X}_{\mathrm{wi}}\\ Y_{\mathrm{wi}}\\ Z_{\mathrm{wi}}\\ 1\end{array}\right]$

Wherein, (X _Wi, Y _Wi, Z _Wi, 1) do Space iThe coordinate of point; (u _i, v _i, 1) and be i IndividualThe image coordinate of point; m _IjBe of projection matrix M iRow j column element; Decompose cancellation Z _OiCan obtain about m _IjLinear equation:

$\left\{\begin{array}{c}{X}_{\mathrm{wi}}{m}_{11}+Y_{\mathrm{wi}}{m}_{12}+Z_{\mathrm{wi}}{m}_{13}+m_{14}-u_i{X}_{\mathrm{wi}}-u_i{Y}_{\mathrm{wi}}{m}_{32}-u_i{Z}_{\mathrm{wi}}{m}_{33}=u_i{m}_{34}\\ X_{\mathrm{wi}}{m}_{21}+Y_{\mathrm{wi}}{m}_{22}+Z_{\mathrm{wi}}{m}_{23}+m_{24}-v_i{X}_{\mathrm{wi}}-v_i{Y}_{\mathrm{wi}}{m}_{32}-v_i{Z}_{\mathrm{wi}}{m}_{33}=v_i{m}_{34}\end{array}\right.$

On the calibration piece n is arranged IndividualKnown point, the volume coordinate of said known point

(X _Wi, Y _Wi, Z _Wi) (i=1 ..., n) with their picture point coordinate

(u _i, v _i) (i=1 ..., n), obtain 2n IndividualLinear equation matrix about the Metzler matrix element:

$\left[\begin{array}{cccccccccc}{X}_{\mathrm{wi}}& Y_{\mathrm{wi}}& Z_{\mathrm{wi}}& 1& 0& 0& 0& -u_1{X}_{w1}& -u_1{Y}_{w1}& -u_1{Z}_{w1}\\ 0& 0& 0& 0& X_{\mathrm{wi}}& Y_{\mathrm{wi}}& Z_{\mathrm{wi}}& -v_1{X}_{w1}& -v_1{Y}_{w1}& -v_1{Z}_{w1}\\ & & & & ...& ...& ...& & & \\ & & & & ...& ...& ...& & & \\ X_{\mathrm{wi}}& Y_{\mathrm{wi}}& Z_{\mathrm{wi}}& 1& 0& 0& 0& -u_1{X}_{\mathrm{wi}}& -u_1{Y}_{\mathrm{wi}}& -u_1{Z}_{\mathrm{wi}}\\ 0& 0& 0& 0& X_{\mathrm{wi}}& Y_{\mathrm{wi}}& Z_{\mathrm{wi}}& -v_1{X}_{\mathrm{wi}}& -v_1{Y}_{\mathrm{wi}}& -v_1{Z}_{\mathrm{wi}}\end{array}\right]$

$\×\left[\begin{array}{c}{m}_{11}\\ m_{12}\\ m_{13}\\ m_{14}\\ m_{21}\\ m_{22}\\ m_{23}\\ m_{24}\\ m_{31}\\ m_{32}\\ m_{33}\end{array}\right]=\left[\begin{array}{c}{u}_1{m}_{34}\\ v_1{m}_{34}\\ ...\\ ...\\ ...\\ ...\\ ...\\ ...\\ ...\\ u_n{m}_{34}\\ v_n{m}_{34}\end{array}\right]$

Specify m ₃₄=1, obtain 2n about other elements of Metzler matrix IndividualLinear equation, the number of unknown element is 11, is designated as 11 dimensional vector m, writes a Chinese character in simplified form: Km=U, K are left side 2n * 11 matrixes; M is 11 unknown dimensional vectors; U is the 2n dimensional vector on the right; K, U are known vector; With least square method obtain when the 2n＞11 above-mentioned linear equation separate for:

m＝(K ^TK) ^-1K ^TU

M vector and m ₃₄=1 constituted the institute find the solution the M battle array; Therefore, by 6 above known points in space and their picture point coordinate, can obtain Metzler matrix;

After obtaining Metzler matrix, can divide the whole inside and outside parameter that calculate video camera by relation;

$z_c\left[\begin{array}{c}u\\ v\\ 1\end{array}\right]=\left[\begin{array}{ccc}\frac{1}{\mathrm{dx}}& 0& c_x\\ 0& \frac{1}{\mathrm{dy}}& c_y\\ 0& 0& 1\end{array}\right]\left[\begin{array}{cccc}f& 0& 0& 0\\ 0& f& 0& 0\\ 0& 0& 1& 0\end{array}\right]\left[\begin{array}{cc}R& t\\ 0^T& 1\end{array}\right]\left[\begin{array}{c}{x}_w\\ y_w\\ z_w\\ 1\end{array}\right]$

$=\left[\begin{array}{cccc}\frac{f}{\mathrm{dx}}& 0& c_x& 0\\ 0& \frac{f}{\mathrm{dy}}& c_y& 0\\ 0& 0& 1& 0\end{array}\right]\left[\begin{array}{cc}R& t\\ 0^T& 1\end{array}\right]\left[\begin{array}{c}{x}_w\\ y_w\\ z_w\\ 1\end{array}\right]$

$=\left[\begin{array}{cccc}{f}_x& 0& c_x& 0\\ 0& f_y& c_y& 0\\ 0& 0& 1& 0\end{array}\right]\left[\begin{array}{cc}R& t\\ 0^T& 1\end{array}\right]\left[\begin{array}{c}{x}_w\\ y_w\\ z_w\\ 1\end{array}\right]$

$=M_1{M}_2{X}_w={\mathrm{MX}}_w$

Wherein,

is defined as the equivalent focal length of x and y direction respectively with

.

According to the described gauge assay method of preferred embodiment of the present invention, the geometric relationship in said step 2 between the whole ccd video cameras of measuring and calculating comprises: the coordinate system unification that two cameras are obtained is in same world coordinate system.Observe surrounding environment simultaneously with two video cameras, utilize formula M _C1=[RT] M _C2The transformation relation of two coordinate systems of expression;

With [R ₁t ₁] and [R ₂t ₂] represent the external parameter of each video camera respectively, with [R ₁t ₁] relative position between expression C1 video camera and the world coordinates, [R ₂t ₂] relative position between expression C2 video camera and the generation world coordinates;

Use $\left\{\begin{array}{c}{M}_{c1}=R_1{M}_{w1}+t_1\\ {\mathrm{<figure-callout\; id="2"\; label="M\; c"\; filenames="HDA0000108634390000033.png"\; state="\{\{state\}\}">M</figure-callout>}}_c=R_2{\mathrm{<figure-callout\; id="2"\; label="M\; w"\; filenames="HDA0000108634390000033.png"\; state="\{\{state\}\}">M</figure-callout>}}_w+{\mathrm{<figure-callout\; id="2"\; label="t"\; filenames="HDA0000108634390000033.png"\; state="\{\{state\}\}">t</figure-callout>}}_2\end{array}\right.$ Expression is to the inhomogeneous coordinate of any 1 P under world coordinate system, C1 coordinate system and C2 coordinate system;

Binocular camera is calibrated respectively, obtained R ₁, t ₁With R ₂, t ₂, the relative position R and the T of calculating binocular camera;

Design calibration template; A gridiron pattern with hi-Fix is respectively adopted in the template both sides, and two gridiron patterns are positioned on the same plane, and four video cameras are taken the template image more than 2 width of cloth in different angles; Point and picture point through on the template are mated; Calculate the mapping matrix between image and the template, can solve the inner parameter of 4 video cameras, formula $\left\{\begin{array}{c}{R}_{}\end{array}\right.$ $\left\{\begin{array}{c}{}_{\mathrm{1,2}}=R_1{R}_2^{-1},{\mathrm{<figure-callout\; id="2"\; label="T"\; filenames="HDA0000108634390000033.png"\; state="\{\{state\}\}">T</figure-callout>}}_{\mathrm{1,2}}=t_1-R_1{R}_2^{-1}{t}_2\\ R_{\mathrm{3,4}}=R_3{R}_4^{-1},R_{\mathrm{3,4}}=t_3-R_4^{-1}{t}_4\\ R_{\mathrm{1,3}}=R_1{R}_3^{-1},T_{\mathrm{1,3}}=t_1-R_1{R}_3^{-1}{t}_3+t_{\mathrm{Lr}}\end{array}\right.$ Expression.

According to the described gauge assay method of preferred embodiment of the present invention, also comprise in said step 6:

The corresponding point matching point of representing same point P with p1 and p2;

Represent that with M1 and M2 C1 and the C2 video camera projection matrix separately calibrated are respectively:

$Z_{c1}\left[\begin{array}{c}{u}_1\\ v_1\\ 1\end{array}\right]=\left[\begin{array}{cccc}{m}_{11}^1& m_{12}^1& m_{13}^1& m_{14}^1\\ m_{21}^1& m_{22}^1& m_{23}^1& m_{24}^1\\ m_{31}^1& m_{32}^1& m_{33}^1& m_{34}^1\end{array}\right]\left[\begin{array}{c}X\\ Y\\ Z\\ 1\end{array}\right]$

$Z_{c2}\left[\begin{array}{c}{u}_2\\ v_2\\ 1\end{array}\right]=\left[\begin{array}{cccc}{m}_{11}^2& m_{12}^2& m_{13}^2& m_{14}^2\\ m_{21}^2& m_{22}^2& m_{23}^2& m_{24}^2\\ m_{31}^2& m_{32}^2& m_{33}^2& m_{34}^2\end{array}\right]\left[\begin{array}{c}X\\ Y\\ Z\\ 1\end{array}\right]$

(u wherein ₁, v ₁, 1) and (u ₂, v ₂, 1) and the homogeneous coordinates that are respectively p1 and p2 point in image separately; (X, Y, Z, 1) is the homogeneous coordinates of P point under world coordinate system; $m_{\mathrm{Ij}}^k(k=\mathrm{1,2};i=1,\&CenterDot;\&CenterDot;\&CenterDot;,3;j=1,\&CenterDot;\&CenterDot;\&CenterDot;,4)$ The M that is respectively _k iRow j column element;

Cancellation Z _C1Or Z _C2, obtain about X, Y, four linear equations of Z:

$\left\{\begin{array}{c}(u_1{m}_{31}^1-m_{11}^1)X+(u_1{m}_{32}^1-m_{12}^1)Y+(u_1{m}_{33}^1-m_{13}^1)Z=m_{14}^1-u_1{m}_{34}^1\\ (v_1{m}_{31}^1-m_{21}^1)X+(v_1{m}_{32}^1-m_{22}^1)Y+(v_1{m}_{33}^1-m_{23}^1)Z=m_{24}^1-v_1{m}_{34}^1\end{array}\right.$ With

$\left\{\begin{array}{c}(u_2{m}_{31}^2-m_{11}^2)X+(u_1{m}_{32}^2-m_{12}^2)Y+(u_1{m}_{33}^2-m_{13}^2)Z=m_{14}^2-u_1{m}_{34}^2\\ (v_2{m}_{31}^2-m_{21}^2)X+(v_2{m}_{32}^2-m_{22}^2)Y+(v_2{m}_{33}^2-m_{23}^2)Z=m_{24}^2-v_2{m}_{34}^2\end{array}\right.$

Simultaneous obtain the coordinate that P orders (X, Y, Z); After obtaining the inside and outside parameter matrix of video camera; And after obtaining the relative position relation of 2 cameras,, from image, find left and right sides rail gauge measurement point respectively through measuring the image of left and right sides rail; Obtain the coordinate of gauge point under world coordinate system through three-dimensional reconstruction, thereby calculate gauge through the distance between two points formula to pixel in the image.

According to the described gauge assay method of preferred embodiment of the present invention, said step 7 also comprises: utilize stereoscopic vision to realize the some three-dimensional reconstruction; Use P _l, P _rThe expression gauge is measured match point, some P _l(x _W1, y _W1, z _W1) be positioned at world coordinate system X _W1In, some P _r(x _W2, y _W2, z _W2) be positioned at world coordinate system X _W2In:

World coordinate system X _W1True origin be selected on the scaling board through type $\left\{\begin{array}{c}{X}_{w1}=X_w+t_1\\ {\mathrm{<figure-callout\; id="2"\; label="X\; w"\; filenames="HDA0000108634390000033.png"\; state="\{\{state\}\}">X</figure-callout>}}_w=X_w+{\mathrm{<figure-callout\; id="2"\; label="t"\; filenames="HDA0000108634390000033.png"\; state="\{\{state\}\}">t</figure-callout>}}_2\end{array}\right.$ Set up world coordinate system X _W1With X _W2Conversion, set up starting point P _lWith a P _rGeometric relationship under same coordinate system is according to space distance between two points formula $l=\sqrt{{(x_1-x_2)}^2+{(y_1-y_2)}^2+{(z_1-z_2)}^2}$ Try to achieve a P _lWith a P _rDistance.

Owing to adopted above technical characterictic, make the present invention than prior art, have following advantage and good effect:

The first, gauge measuring method provided by the invention is utilized the binocular vision imaging system of two groups of opposite types, cooperates the coordinate in the world coordinates, calculates the spacing between two rails, can improve precision and accuracy.

Certainly, any one specific embodiment of embodiment of the present invention content might not reach above whole technique effect simultaneously.

Description of drawings

Fig. 1 is a method flow diagram of the present invention;

Fig. 2 is the structural representation of binocular scaling system

Fig. 3 is the scaling board synoptic diagram;

Fig. 4 is a world coordinates calibration template synoptic diagram;

Fig. 5 is three and rebuilds the coordinate synoptic diagram;

Fig. 6 is gauge measuring principle figure;

Fig. 7 is rail square coordinates computed figure.

Embodiment

Below in conjunction with accompanying drawing several preferred embodiments of the present invention is described in detail, but the present invention is not restricted to these embodiment.The present invention contain any on marrow of the present invention and scope, make substitute, modification, equivalent method and scheme.Understand for the public is had completely the present invention, in the following preferred embodiment of the present invention, specified concrete details, and do not had the description of these details also can understand the present invention fully for a person skilled in the art.In addition, for fear of essence of the present invention is caused unnecessary obscuring, do not specify well-known method, process, flow process, element and circuit etc.

As shown in Figure 1, the present invention provides a kind of scaling method based on machine vision, and it comprises:

S101: two groups of binocular formulas are set measure on the kickstand at gauge back to ccd video camera, be positioned at the rail top, also on support, be positioned at the fan-shaped light source of rail installed inside, concrete mounting means is as shown in Figure 2.

S102: the parameter of calculating each ccd video camera;

S103: calculate the geometric relationship between whole ccd video cameras;

S104: choose the corresponding point position that ccd video camera is taken;

S105: choose gauge measurement point position;

S106: gauge measurement point location map is arrived world coordinates;

S107: the spacing of in world coordinates, calculating the gauge measurement point is a gauge.

Its principle is: select angle point on the scaling board as shown in Figure 3; Obtain the pixel coordinate of each intersection point; Because scaling board is that laser engraving forms, the volume coordinate of each angle point on it is known, carries out monocular (single ccd video camera) and demarcates the inside and outside parameter that obtains video camera.

Can obtain the relativeness matrix of 2 ccd video cameras through the transformation matrix of correspondence, also can obtain any 2 relative position relation matrix of 4 ccd video cameras.

Want to realize that converting the pixel coordinate of a point in the image to the actual physical coordinate can pass through the spatial point three-dimensional reconstruction, the former point selection of volume coordinate is based upon on the scaling board,

Because 4 video cameras have constituted two groups of biocular systems, these two groups of biocular systems do not have public view field, at this moment can obtain the position relational matrix of our interested 2 video cameras through the transformation relation matrix computations, like 1,3 video cameras.

Rebuild us through the space and can obtain 1 the volume coordinate on each limit, the position relational matrix of the both sides biocular systems of setting up with us again, we just set up the spatial relation of 2 points in both sides, thereby obtain the gauge that we are concerned about.

The camera interior and exterior parameter method is calculated in following simple declaration:

$Z_{\mathrm{oi}}\left[\begin{array}{c}{u}_i\\ v_i\\ 1\end{array}\right]=\left[\begin{array}{cccc}{m}_{11}& m_{12}& m_{13}& m_{14}\\ m_{21}& m_{22}& m_{23}& m_{24}\\ m_{31}& m_{32}& m_{33}& m_{34}\end{array}\right]\left[\begin{array}{c}{X}_{\mathrm{wi}}\\ Y_{\mathrm{wi}}\\ Z_{\mathrm{wi}}\\ 1\end{array}\right]---\left(1\right)$

Wherein, (X _Wi, Y _Wi, Z _Wi, 1) and be the coordinate of i the point in space; (u _i, v _i, 1) and be the image coordinate of i point; m _iThe capable j column element of i for projection matrix M.Breakdown (1) obtains three equations:

$\left\{\begin{array}{c}{Z}_{\mathrm{ci}}{u}_i=m_{11}{X}_{\mathrm{wi}}+m_{12}{Y}_{\mathrm{wi}}+m_{13}{Z}_{\mathrm{wi}}+m_{14}\\ Z_{\mathrm{ci}}{v}_i=m_{21}{X}_{\mathrm{wi}}+m_{22}{Y}_{\mathrm{wi}}+m_{23}{Z}_{\mathrm{wi}}+m_{24}\\ Z_{\mathrm{ci}}=m_{31}{X}_{\mathrm{wi}}+m_{32}{Y}_{\mathrm{wi}}+m_{33}{Z}_{\mathrm{wi}}+m_{34}\end{array}\right.---\left(2\right)$

First formula in the formula (2) is removed the 3rd formula, and second formula is removed the 3rd formula cancellation Z respectively _CiAfter can obtain following two about m _IjLinear equation:

$\left\{\begin{array}{c}{X}_{\mathrm{wi}}{m}_{11}+Y_{\mathrm{wi}}{m}_{12}+Z_{\mathrm{wi}}{m}_{13}+m_{14}-u_i{X}_{\mathrm{wi}}-u_i{Y}_{\mathrm{wi}}{m}_{32}-u_i{Z}_{\mathrm{wi}}{m}_{33}=u_i{m}_{34}\\ X_{\mathrm{wi}}{m}_{21}+Y_{\mathrm{wi}}{m}_{22}+Z_{\mathrm{wi}}{m}_{23}+m_{24}-v_i{X}_{\mathrm{wi}}-v_i{Y}_{\mathrm{wi}}{m}_{32}-v_i{Z}_{\mathrm{wi}}{m}_{33}=v_i{m}_{34}\end{array}\right.---\left(3\right)$

Following formula representes if calibrate on the piece n known point arranged, and the volume coordinate (X of known its door _Wi, Y _Wi, Z _Wi) (i=1 ..., n) with their picture point coordinate (u _i, v _i) (i=1 ..., n), 2n the linear equation about the Metzler matrix element arranged then, write out these equations with matrix;

$\left[\begin{array}{cccccccccc}{X}_{\mathrm{wi}}& Y_{\mathrm{wi}}& Z_{\mathrm{wi}}& 1& 0& 0& 0& -u_1{X}_{w1}& -u_1{Y}_{w1}& -u_1{Z}_{w1}\\ 0& 0& 0& 0& X_{\mathrm{wi}}& Y_{\mathrm{wi}}& Z_{\mathrm{wi}}& -v_1{X}_{w1}& -v_1{Y}_{w1}& -v_1{Z}_{w1}\\ & & & & ...& ...& ...& & & \\ & & & & ...& ...& ...& & & \\ X_{\mathrm{wi}}& Y_{\mathrm{wi}}& Z_{\mathrm{wi}}& 1& 0& 0& 0& -u_1{X}_{\mathrm{wi}}& -u_1{Y}_{\mathrm{wi}}& -u_1{Z}_{\mathrm{wi}}\\ 0& 0& 0& 0& X_{\mathrm{wi}}& Y_{\mathrm{wi}}& Z_{\mathrm{wi}}& -v_1{X}_{\mathrm{wi}}& -v_1{Y}_{\mathrm{wi}}& -v_1{Z}_{\mathrm{wi}}\end{array}\right]$

$\&times;\left[\begin{array}{c}{m}_{11}\\ m_{12}\\ m_{13}\\ m_{14}\\ m_{21}\\ m_{22}\\ m_{23}\\ m_{24}\\ m_{31}\\ m_{32}\\ m_{33}\end{array}\right]=\left[\begin{array}{c}{u}_1{m}_{34}\\ v_1{m}_{34}\\ ...\\ ...\\ ...\\ ...\\ ...\\ ...\\ ...\\ u_n{m}_{34}\\ v_n{m}_{34}\end{array}\right]---\left(4\right)$

Metzler matrix multiply by arbitrarily, and non-vanishing constant does not influence (X _w, Y _w, Z _wWith (therefore u, relation v), can specify m in formula (4) ₃₄=1, thus 2n obtained about other elements of Metzler matrix IndividualLinear equation, 11 of the numbers of these unknown elements are designated as 11 dimensional vector m, and formula (4) is write a Chinese character in simplified form;

Km＝U (5)

In the formula, K is formula (4) left side 2n * 11 matrixes; M is 11 unknown dimensional vectors; U is the 2n dimensional vector on formula (4) the right; K, U are known vector.When 2n＞11, use least square method obtain above-mentioned linear equation separate for:

m＝(K ^TK) ^-1K ^TU (6)

M vector and m ₃₄=1 constituted the institute find the solution Metzler matrix.Therefore, by 6 above known points in space and their picture point coordinate, can obtain Metzler matrix.Owing on the calibration plate that we adopt the dozens of known point is arranged, makes the number of equation substantially exceed the number of unknown number, thereby find the solution to reduce the influence that the language difference causes with least square method

After obtaining Metzler matrix, can divide the whole inside and outside parameter that calculate video camera.

$z_c\left[\begin{array}{c}u\\ v\\ 1\end{array}\right]=\left[\begin{array}{ccc}\frac{1}{\mathrm{dx}}& 0& c_x\\ 0& \frac{1}{\mathrm{dy}}& c_y\\ 0& 0& 1\end{array}\right]\left[\begin{array}{cccc}f& 0& 0& 0\\ 0& f& 0& 0\\ 0& 0& 1& 0\end{array}\right]\left[\begin{array}{cc}R& t\\ 0^T& 1\end{array}\right]\left[\begin{array}{c}{x}_w\\ y_w\\ z_w\\ 1\end{array}\right]$

$=\left[\begin{array}{cccc}\frac{f}{\mathrm{dx}}& 0& c_x& 0\\ 0& \frac{f}{\mathrm{dy}}& c_y& 0\\ 0& 0& 1& 0\end{array}\right]\left[\begin{array}{cc}R& t\\ 0^T& 1\end{array}\right]\left[\begin{array}{c}{x}_w\\ y_w\\ z_w\\ 1\end{array}\right]$

$=\left[\begin{array}{cccc}{f}_x& 0& c_x& 0\\ 0& f_y& c_y& 0\\ 0& 0& 1& 0\end{array}\right]\left[\begin{array}{cc}R& t\\ 0^T& 1\end{array}\right]\left[\begin{array}{c}{x}_w\\ y_w\\ z_w\\ 1\end{array}\right]$

$=M_1{M}_2{X}_w={\mathrm{MX}}_w---\left(7\right)$

Wherein, With The equivalent focal length M that is defined as x and y direction respectively is 3 * 4 matrixes, is called projection matrix; M ₁Fully by f _x, f _y, c _x, c _yDecision because these four parameters are only relevant with the video camera inner structure, therefore claims that these parameters are intrinsic parameters of the camera.That is: $\left[\begin{array}{cccc}{f}_x& 0& c_x& 0\\ 0& f_y& c_y& 0\\ 0& 0& 1& 0\end{array}\right]$ Be video camera confidential reference items matrix.M ₂By the orientation decision of video camera, be called the outside matrix of video camera fully, also claim outer ginseng matrix with respect to world coordinate system.Quadrature rotation matrix R is the combination of the cosine of the relative world coordinate system change in coordinate axis direction of optical axis, and reality only contains three independent variables: the θ angle of pitch (pitch), and ψ crab angle (yaw), φ optical axis roll angle (roll) or torsion angle (twist) are added translational movement t _x, t _y, t _z, altogether six parameter determining the locus of camera optical axis in world coordinate system, so these six parameters are called the video camera external parameter, that is: $\left[\begin{array}{cc}R& t\\ 0^T& 1\end{array}\right]$ Constitute the outer ginseng matrix of video camera.

Below the method for the position relation between 2 cameras and a plurality of camera is calculated in explanation

Will accomplish calibration for binocular vision system, at first will accomplish one camera calibration, and the coordinate system unification that must two cameras be obtained is in same world coordinate system.Observe surrounding environment simultaneously with two video cameras, utilize the transformation relation of two coordinate systems of formula (8) expression.

M _c1＝[R?T]M _c2 (8)

Because two cameras are taken pictures to same template, draw corresponding external parameter and use [R respectively ₁t ₁] and [R ₂t ₂] expression, then [R ₁t ₁] relative position between expression C1 video camera and the world coordinates, [R ₂t ₂] relative position between expression C2 video camera and the world coordinates.To any 1 P, be respectively like its inhomogeneous coordinate under world coordinate system, C1 coordinate system and C2 coordinate system:

$\left\{\begin{array}{c}{M}_{c1}=R_1{M}_{w1}+t_1\\ M_{c2}=R_2{\mathrm{<figure-callout\; id="2"\; label="M\; w"\; filenames="HDA0000108634390000033.png"\; state="\{\{state\}\}">M</figure-callout>}}_w+t_2\end{array}\right.---\left(9\right)$

Because template is identical, M _W1=M _W2, then formula (9) becomes:

$\mathrm{Mc}1=R_1{R}_2^{-1}{M}_{o2}-R_1{R}_2^{-1}{\mathrm{<figure-callout\; id="2"\; label="t"\; filenames="HDA0000108634390000033.png"\; state="\{\{state\}\}">t</figure-callout>}}_2+t_1---\left(10\right)$

Wherein rotation matrix R and translation matrix T can be expressed as respectively:

$\left\{\begin{array}{c}R=R_1{R}_2^{-1}\\ T=t_1-R{t}_2\end{array}\right.---\left(11\right)$

Formula (11) expression if binocular camera is calibrated respectively, obtains R ₁, t ₁With R ₂, t ₂, then the relative position R of twin camera and T can be calculated by formula (11)

The outer ginseng matrix of the left and right sides camera that obtains through each calibration utilizes formula (11), calculates the total rotation matrix R and the translation matrix T of binocular calibration,

World coordinates calibration template as shown in Figure 4; A gridiron pattern with hi-Fix is respectively adopted in the template both sides; Two gridiron patterns are positioned on the same plane, and four video cameras are taken the template image more than 2 width of cloth in different angles, mate through point and picture point on the template; Calculate the mapping matrix between image and the template, can solve the inner parameter of 4 video cameras.

Method with the single camera calibration obtains 4 video cameras inside and outside parameter separately respectively, and outer parameter is used R _i, t _i(i=1,2,3,4) expression.Since the binocular vision system of left and right sides rail back to towards, so the calibration template image that the camera of left and right sides rail photographed is the parts of images at template two ends, do not have common visual field.Make world coordinate system be fixed on the template, then the volume coordinate relative position of all angle points on the template is the relations that only have translation.For any 2 P on the template that can be photographed in the binocular vision system of the left and right sides _lAnd P _r, the available formula of its relation in the camera coordinates system (12) expression, wherein X _Wl, X _WrExpression P _lAnd P _rWorld coordinates, t _LrBe X _Wl, X _WrBetween translation relation, X _Ci(i=1,2,3,4) are video camera C _iThe coordinate of coordinate system.Can try to achieve the geometric relationship between the video camera by formula (12), represent by formula (13).

$\left\{\begin{array}{c}{X}_{c1}=R_1{X}_{\mathrm{wl}}+t_1\\ {\mathrm{<figure-callout\; id="2"\; label="X\; c"\; filenames="HDA0000108634390000033.png"\; state="\{\{state\}\}">X</figure-callout>}}_c=R_2{X}_{\mathrm{wl}}+t_2\\ X_{c3}=R_3{X}_{\mathrm{wr}}+t_3\\ X_{c4}=R_4{X}_{\mathrm{wr}}+t_4\\ X_{\mathrm{wl}}=X_{\mathrm{wr}}+t_{\mathrm{lr}}\end{array}\right.---\left(12\right)$

$\left\{\begin{array}{c}{\mathrm{<figure-callout\; id="2"\; label="R"\; filenames="HDA0000108634390000033.png"\; state="\{\{state\}\}">R</figure-callout>}}_{\mathrm{1,2}}=R_1{R}_2^{-1},{\mathrm{<figure-callout\; id="2"\; label="T"\; filenames="HDA0000108634390000033.png"\; state="\{\{state\}\}">T</figure-callout>}}_{\mathrm{1,2}}=t_1-R_1{R}_2^{-1}{t}_2\\ R_{\mathrm{3,4}}=R_3{R}_4^{-1},R_{\mathrm{3,4}}=t_3-R_4^{-1}{t}_4\\ R_{\mathrm{1,3}}=R_1{R}_3^{-1},T_{\mathrm{1,3}}=t_1-R_1{R}_3^{-1}{t}_3+t_{\mathrm{lr}}\end{array}\right.---\left(13\right)$

The spatial point three-dimensional rebuilding method is following:

In this problem,, mainly carry out the spatial point three-dimensional reconstruction in order to find the world coordinates of the match point that gauge measures.

As shown in Figure 5, spatial point is counted as the primitive of space three-dimensional object, and the coordinate (being called the three-dimensional reconstruction based on point) that obtains three-dimensional point with the stereoscopic vision method is the most basic, also is the simplest.Picture point p1 and the p2 of arbitrfary point, space P on two video camera C1 and C2 is the point that detects respectively in the image, and promptly p1 and p2 are the corresponding point (match point) of space same point P.Suppose that C1 and C2 video camera calibrate, their projection matrixes separately are respectively M ₁With M ₂So, have

$Z_{c1}\left[\begin{array}{c}{u}_1\\ v_1\\ 1\end{array}\right]=\left[\begin{array}{cccc}{m}_{11}^1& m_{12}^1& m_{13}^1& m_{14}^1\\ m_{21}^1& m_{22}^1& m_{23}^1& m_{24}^1\\ m_{31}^1& m_{32}^1& m_{33}^1& m_{34}^1\end{array}\right]\left[\begin{array}{c}X\\ Y\\ Z\\ 1\end{array}\right]...........\left(14\right)$

$Z_{c2}\left[\begin{array}{c}{u}_2\\ {\mathrm{<figure-callout\; id="2"\; label="v"\; filenames="HDA0000108634390000033.png"\; state="\{\{state\}\}">v</figure-callout>}}_2\\ 1\end{array}\right]=\left[\begin{array}{cccc}{m}_{11}^2& m_{12}^2& m_{13}^2& m_{14}^2\\ m_{21}^2& m_{22}^2& m_{23}^2& m_{24}^2\\ m_{31}^2& m_{32}^2& m_{33}^2& m_{34}^2\end{array}\right]\left[\begin{array}{c}X\\ Y\\ Z\\ 1\end{array}\right].......\left(15\right)$

(u wherein ₁, v ₁, 1) and (u ₂, v ₂, 1) and the homogeneous coordinates that are respectively p1 and p2 point in image separately; (X, Y, Z, 1) is the homogeneous coordinates of P point under world coordinate system; $m_{\mathrm{Ij}}^k(k=\mathrm{1,2};i=1,\&CenterDot;\&CenterDot;\&CenterDot;,3;j=1,\&CenterDot;\&CenterDot;\&CenterDot;,4)$ The M that is respectively _k iRow j column element.By formula (2) and formula (3), cancellation Z _C1Or Z _C2, obtain about X, Y, four linear equations of Z:

$\left\{\begin{array}{c}(u_1{m}_{31}^1-m_{11}^1)X+(u_1{m}_{32}^1-m_{12}^1)Y+(u_1{m}_{33}^1-m_{13}^1)Z=m_{14}^1-u_1{m}_{34}^1\\ (v_1{m}_{31}^1-m_{21}^1)X+(v_1{m}_{32}^1-m_{22}^1)Y+(v_1{m}_{33}^1-m_{23}^1)Z=m_{24}^1-v_1{m}_{34}^1\end{array}\right.---\left(16\right)$

$\left\{\begin{array}{c}(u_2{m}_{31}^2-m_{11}^2)X+(u_1{m}_{32}^2-m_{12}^2)Y+(u_1{m}_{33}^2-m_{13}^2)Z=m_{14}^2-u_1{m}_{34}^2\\ (v_2{m}_{31}^2-m_{21}^2)X+(v_2{m}_{32}^2-m_{22}^2)Y+(v_2{m}_{33}^2-m_{23}^2)Z=m_{24}^2-v_2{m}_{34}^2\end{array}\right.---\left(17\right)$

Know that by cartesian geometry three-dimensional plane equation is a linear equation, the simultaneous equations of two plane equations are space line equation (this straight line is the intersection on two planes), and the geometric meaning of formula (16) or formula (17) was O ₁p ₁(formula O ₂p ₂) straight line.P is O ₁p ₁With O ₂p ₂Intersection point, so through type (16) and formula (17) but simultaneous obtain the coordinate that P orders (X, Y, Z).

After obtaining the inside and outside parameter matrix of video camera; And after obtaining the relative position relation of 2 cameras; Through measuring the image of left and right sides rail; From image, find left and right sides rail gauge measurement point respectively, obtain the coordinate of gauge point under world coordinate system through three-dimensional reconstruction, thereby calculate gauge through the distance between two points formula to pixel in the image.

The gauge measuring principle below is described:

As shown in Figure 6, adopt cross formula binocular stereo vision system acquisition left and right sides rail profile and gauge measurement match point image, utilize stereoscopic vision to realize a some three-dimensional reconstruction.If gauge is measured match point image (" ten " word point of crossing), and is expressed as P respectively _l, P _r, as shown in Figure 7, the some P _l(x _W1, y _W1, z _W1) be positioned at world coordinate system X _W1In, some P _r(x _W2, y _W2, z _W2), be positioned at world coordinate system X _W2In.World coordinate system X _W1True origin be selected on the scaling board, concrete chosen position is specified in the CCD calibration process, then P _lPoint is at world coordinate system X _W1In particular location (x _W1, y _W1, z _W1) can obtain by the spatial point reconstruction, in like manner at world coordinate system X _W2In can obtain P _rCoordinate (the x of point _W2, y _W2, z _W2).Two worlds coordinate system X _W1, X _W2Concern that we can try to achieve when camera calibration, when demarcating left side camera CCD1, CCD2, choose a known point on the scaling board as world coordinate system X _W1Initial point, in like manner when demarcating right side video camera CCD3, CCD4, also choose on the scaling board a bit as world coordinate system X _W2Initial point, like the O among Fig. 7 ₁, O ₂The point.Because be in same demarcation, to demarcate the initial point of coordinate system separately simultaneously, two coordinate systems are with respect to reference frame X _w(y z) has only translation relation, and does not have rotation relationship for O, x, and therefore three coordinate system relations can be expressed as:

$\left\{\begin{array}{c}{X}_{w1}=X_w+t_1\\ {\mathrm{<figure-callout\; id="2"\; label="X\; w"\; filenames="HDA0000108634390000033.png"\; state="\{\{state\}\}">X</figure-callout>}}_w=X_w+t_2\end{array}\right.---\left(18\right)$

Through type (18) has been set up world coordinate system X _W1With X _W2Transformational relation, can set up starting point P _lWith a P _rGeometric relationship under same coordinate system then can be tried to achieve a P according to space distance between two points formula (19) _lWith a P _rDistance, i.e. gauge.

$l=\sqrt{{(x_1-x_2)}^2+{(y_1-y_2)}^2+{(z_1-z_2)}^2}---\left(19\right)$

The preferred embodiment of the present invention just is used for helping to set forth the present invention.Preferred embodiment does not have all details of detailed descriptionthe, does not limit this invention yet and is merely described embodiment.Obviously, according to the content of this instructions, can do a lot of modifications and variation.These embodiment are chosen and specifically described to this instructions, is in order to explain principle of the present invention and practical application better, thereby person skilled can be utilized the present invention well under making.The present invention only receives the restriction of claims and four corner and equivalent.

Claims (7)

1. the gauge assay method based on machine vision is characterized in that, comprising:

Step 1, be provided with two groups of binocular formulas back to ccd video camera on gauge is measured kickstand, be positioned at the rail top;

Step 2, calculate the parameter of each ccd video camera;

Geometric relationship between step 3, the whole ccd video cameras of measuring and calculating;

Step 4, choose the corresponding point position that ccd video camera is taken;

Step 5, choose gauge measurement point position;

Step 6, with gauge measurement point location map to world coordinates;

Step 7, the spacing of in world coordinates, calculating the gauge measurement point are gauge.

2. gauge assay method as claimed in claim 1 is characterized in that, said every group of ccd video camera comprises two ccd video cameras with public view field.

3. rail square assay method as claimed in claim 1 is characterized in that, in said step 1, also is included on the support, is positioned at the fan-shaped light source of rail installed inside, makes fan-shaped light source be radiated on the rail.

4. gauge assay method as claimed in claim 1 is characterized in that, the parameter of each ccd video camera of measuring and calculating comprises in said step 2:

Template is fixed on the plane; Video camera matees through point and picture point on the template at the plural template image of different azimuth photographs, calculates the mapping matrix between image and the template; And can linearity solve intrinsic parameters of the camera through this matrix

$Z_{\mathrm{oi}}\left[\begin{array}{c}{u}_i\\ v_i\\ 1\end{array}\right]=\left[\begin{array}{cccc}{m}_{11}& m_{12}& m_{13}& m_{14}\\ m_{21}& m_{22}& m_{23}& m_{24}\\ m_{31}& m_{32}& m_{33}& m_{34}\end{array}\right]\left[\begin{array}{c}{X}_{\mathrm{wi}}\\ Y_{\mathrm{wi}}\\ Z_{\mathrm{wi}}\\ 1\end{array}\right]$

Wherein, (X _Wi, Y _Wi, Z _Wi, 1) Space iThe coordinate of point; (u _i, v _i, 1) and be i IndividualThe image coordinate of point; m _IjBe of projection matrix M iRow j column element; Decompose cancellation Z _OiCan obtain about m _IjLinear equation:

$\left\{\begin{array}{c}{X}_{\mathrm{wi}}{m}_{11}+Y_{\mathrm{wi}}{m}_{12}+Z_{\mathrm{wi}}{m}_{13}+m_{14}-u_i{X}_{\mathrm{wi}}-u_i{Y}_{\mathrm{wi}}{m}_{32}-u_i{Z}_{\mathrm{wi}}{m}_{33}=u_i{m}_{34}\\ X_{\mathrm{wi}}{m}_{21}+Y_{\mathrm{wi}}{m}_{22}+Z_{\mathrm{wi}}{m}_{23}+m_{24}-v_i{X}_{\mathrm{wi}}-v_i{Y}_{\mathrm{wi}}{m}_{32}-v_i{Z}_{\mathrm{wi}}{m}_{33}=v_i{m}_{34}\end{array}\right.$

On the calibration piece n is arranged IndividualKnown point, the volume coordinate of said known point

(X _Wi, Y _Wi, Z _Wi) (i=1 ..., n) with their visual point coordinate

(u _i, v _i) (i=1 ..., n), obtain 2n IndividualLinear equation matrix about the Metzler matrix element:

$\left[\begin{array}{cccccccccc}{X}_{\mathrm{wi}}& Y_{\mathrm{wi}}& Z_{\mathrm{wi}}& 1& 0& 0& 0& -u_1{X}_{w1}& -u_1{Y}_{w1}& -u_1{Z}_{w1}\\ 0& 0& 0& 0& X_{\mathrm{wi}}& Y_{\mathrm{wi}}& Z_{\mathrm{wi}}& -v_1{X}_{w1}& -v_1{Y}_{w1}& -v_1{Z}_{w1}\\ & & & & ...& ...& ...& & & \\ & & & & ...& ...& ...& & & \\ X_{\mathrm{wi}}& Y_{\mathrm{wi}}& Z_{\mathrm{wi}}& 1& 0& 0& 0& -u_1{X}_{\mathrm{wi}}& -u_1{Y}_{\mathrm{wi}}& -u_1{Z}_{\mathrm{wi}}\\ 0& 0& 0& 0& X_{\mathrm{wi}}& Y_{\mathrm{wi}}& Z_{\mathrm{wi}}& -v_1{X}_{\mathrm{wi}}& -v_1{Y}_{\mathrm{wi}}& -v_1{Z}_{\mathrm{wi}}\end{array}\right]$

$\&times;\left[\begin{array}{c}{m}_{11}\\ m_{12}\\ m_{13}\\ m_{14}\\ m_{21}\\ m_{22}\\ m_{23}\\ m_{24}\\ m_{31}\\ m_{32}\\ m_{33}\end{array}\right]=\left[\begin{array}{c}{u}_1{m}_{34}\\ v_1{m}_{34}\\ ...\\ ...\\ ...\\ ...\\ ...\\ ...\\ ...\\ u_n{m}_{34}\\ v_n{m}_{34}\end{array}\right]$

Specify m ₃₄=1, obtain 2n linear equation about other elements of Metzler matrix, the number of unknown element is 11, is designated as 11 dimensional vector m, writes a Chinese character in simplified form: Km=U, K are left side 2n * 11 matrixes; M is 11 unknown dimensional vectors; U is the 2n dimensional vector on the right; K, U are known vector; With least square method obtain when the 2n＞11 above-mentioned linear equation separate for:

m＝(K ^TK) ^-1K ^TU

M vector and m ₃₄=1 constituted the institute find the solution Metzler matrix; Therefore, by 6 above known points in space and their picture point coordinate, can obtain Metzler matrix;

After obtaining Metzler matrix, can divide the whole inside and outside parameter that calculate video camera by relation;

$z_c\left[\begin{array}{c}u\\ v\\ 1\end{array}\right]=\left[\begin{array}{ccc}\frac{1}{\mathrm{dx}}& 0& c_x\\ 0& \frac{1}{\mathrm{dy}}& c_y\\ 0& 0& 1\end{array}\right]\left[\begin{array}{cccc}f& 0& 0& 0\\ 0& f& 0& 0\\ 0& 0& 1& 0\end{array}\right]\left[\begin{array}{cc}R& t\\ 0^T& 1\end{array}\right]\left[\begin{array}{c}{x}_w\\ y_w\\ z_w\\ 1\end{array}\right]$

$=\left[\begin{array}{cccc}\frac{f}{\mathrm{dx}}& 0& c_x& 0\\ 0& \frac{f}{\mathrm{dy}}& c_y& 0\\ 0& 0& 1& 0\end{array}\right]\left[\begin{array}{cc}R& t\\ 0^T& 1\end{array}\right]\left[\begin{array}{c}{x}_w\\ y_w\\ z_w\\ 1\end{array}\right]$

$=\left[\begin{array}{cccc}{f}_x& 0& c_x& 0\\ 0& f_y& c_y& 0\\ 0& 0& 1& 0\end{array}\right]\left[\begin{array}{cc}R& t\\ 0^T& 1\end{array}\right]\left[\begin{array}{c}{x}_w\\ y_w\\ z_w\\ 1\end{array}\right]$

$=M_1{M}_2{X}_w={\mathrm{MX}}_w$

Wherein,

is defined as the equivalent focal length of x and y direction respectively with

.

5. Like rightRequire 1 described gauge assay method, it is characterized in that, the geometric relationship of measuring and calculating between whole ccd video cameras comprises in said step 2: the coordinate system unification that two cameras are obtained is in same world coordinate system.Observe surrounding environment simultaneously with two video cameras, utilize formula M _C1=[RT] M _C2The transformation relation of two coordinate systems of expression;

With [R ₁t ₁] and [R ₂t ₂] represent the external parameter of each video camera respectively, with [R ₁t ₁] relative position between expression C1 video camera and the world coordinates, [R ₂t ₂] relative position between expression C2 video camera and the world coordinates;

Use $\left\{\begin{array}{c}{M}_{c1}=R_1{M}_{w1}+t_1\\ M_{c2}=R_2{M}_{w2}+t_2\end{array}\right.$ Expression is to the inhomogeneous coordinate of any 1 P under world coordinate system, C1 coordinate system and C2 coordinate system;

Binocular camera is calibrated respectively, obtained R ₁, t ₁With R ₂, t ₂, the relative position R and the T of calculating binocular camera;

Design calibration template; A gridiron pattern with hi-Fix is respectively adopted in the template both sides, and two gridiron patterns are positioned on the same plane, and four video cameras are taken the template image more than 2 width of cloth in different angles; Point and picture point through on the template are mated; Calculate the mapping matrix between image and the template, can solve the inner parameter of 4 video cameras, formula $\left\{\begin{array}{c}{R}_{\mathrm{1,2}}=R_1{R}_2^{-1},T_{\mathrm{1,2}}=t_1-R_1{R}_2^{-1}{t}_2\\ R_{\mathrm{3,4}}=R_3{R}_4^{-1},R_{\mathrm{3,4}}=t_3-R_4^{-1}{t}_4\\ R_{\mathrm{1,3}}=R_1{R}_3^{-1},T_{\mathrm{1,3}}=t_1-R_1{R}_3^{-1}{t}_3+t_{\mathrm{Lr}}\end{array}\right.$ Expression.

6. Like rightRequire 1 described gauge assay method, it is characterized in that, also comprise in said step 6:

The corresponding point matching point of representing same point P with p1 and p2;

Represent that with M1 and M2 C1 and the C2 video camera projection matrix separately calibrated are respectively:

$Z_{c1}\left[\begin{array}{c}{u}_1\\ v_1\\ 1\end{array}\right]=\left[\begin{array}{cccc}{m}_{11}^1& m_{12}^1& m_{13}^1& m_{14}^1\\ m_{21}^1& m_{22}^1& m_{23}^1& m_{24}^1\\ m_{31}^1& m_{32}^1& m_{33}^1& m_{34}^1\end{array}\right]\left[\begin{array}{c}X\\ Y\\ Z\\ 1\end{array}\right]$

$Z_{c2}\left[\begin{array}{c}{u}_2\\ v_2\\ 1\end{array}\right]=\left[\begin{array}{cccc}{m}_{11}^2& m_{12}^2& m_{13}^2& m_{14}^2\\ m_{21}^2& m_{22}^2& m_{23}^2& m_{24}^2\\ m_{31}^2& m_{32}^2& m_{33}^2& m_{34}^2\end{array}\right]\left[\begin{array}{c}X\\ Y\\ Z\\ 1\end{array}\right]$

(u wherein ₁, v ₁, 1) and (u ₂, v ₂, 1) and the homogeneous coordinates that are respectively p1 and p2 point in image separately; (X, Y, Z, 1) is the homogeneous coordinates of P point under world coordinate system; $m_{\mathrm{Ij}}^k(k=\mathrm{1,2};i=1,\&CenterDot;\&CenterDot;\&CenterDot;,3;j=1,\&CenterDot;\&CenterDot;\&CenterDot;,4)$ The M that is respectively _k iRow j column element;

Cancellation Z _C1Or Z _C2, obtain about X, Y, four linear equations of Z:

$\left\{\begin{array}{c}(u_1{m}_{31}^1-m_{11}^1)X+(u_1{m}_{32}^1-m_{12}^1)Y+(u_1{m}_{33}^1-m_{13}^1)Z=m_{14}^1-u_1{m}_{34}^1\\ (v_1{m}_{31}^1-m_{21}^1)X+(v_1{m}_{32}^1-m_{22}^1)Y+(v_1{m}_{33}^1-m_{23}^1)Z=m_{24}^1-v_1{m}_{34}^1\end{array}\right.$ With

$\left\{\begin{array}{c}(u_2{m}_{31}^2-m_{11}^2)X+(u_1{m}_{32}^2-m_{12}^2)Y+(u_1{m}_{33}^2-m_{13}^2)Z=m_{14}^2-u_1{m}_{34}^2\\ (v_2{m}_{31}^2-m_{21}^2)X+(v_2{m}_{32}^2-m_{22}^2)Y+(v_2{m}_{33}^2-m_{23}^2)Z=m_{24}^2-v_2{m}_{34}^2\end{array}\right.$

Simultaneous obtain the coordinate that P orders (X, Y, Z); After obtaining the inside and outside parameter matrix of video camera; And after obtaining the relative position relation of 2 cameras,, from image, find left and right sides rail gauge measurement point respectively through measuring the image of left and right sides rail; Obtain the coordinate of gauge point under world coordinate system through three-dimensional reconstruction, thereby calculate gauge through the distance between two points formula to pixel in the image.

7. Like rightRequire 1 described gauge assay method, it is characterized in that said step 7 also comprises: utilize stereoscopic vision to realize the some three-dimensional reconstruction; Use P _l, P _rThe expression gauge is measured match point, some P _l(x _W1, y _W1, z _W1) be positioned at world coordinate system X _W1In, some P _r(x _W2, y _W2, z _W2) be positioned at world coordinate system X _W2In;

World coordinate system X _W1True origin be selected on the scaling board through type $\left\{\begin{array}{c}{X}_{w1}=X_w+t_1\\ X_{w2}=X_w+t_2\end{array}\right.$ Set up world coordinate system X _W1With X _W2Conversion, set up starting point P _lWith a P _rGeometric relationship under same coordinate system is according to space distance between two points formula $l=\sqrt{{(x_1-x_2)}^2+{(y_1-y_2)}^2+{(z_1-z_2)}^2}$ Try to achieve a P _lWith a P _rDistance.

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