CN102749061B

CN102749061B - Steel rail abrasion measuring method based on dynamic template

Info

Publication number: CN102749061B
Application number: CN201210261886.6A
Authority: CN
Inventors: 郑树彬; 柴晓冬; 安小雪; 李立明; 许晓伟; 刘新厂; 蒋啟榛
Original assignee: Shanghai University of Engineering Science
Current assignee: Shanghai University of Engineering Science
Priority date: 2012-07-26
Filing date: 2012-07-26
Publication date: 2014-12-24
Anticipated expiration: 2032-07-26
Also published as: CN102749061A

Abstract

The invention proposes a rail wear measurement method based on a dynamic template. The steps of the method include: respectively installing a CCD camera and a fan-shaped laser light source on the inside of two rails; calibrating each CCD camera and light plane parameters; calculating according to the rail contour space The model obtains the spatial coordinates of each pixel of the rail profile in the image; extracts the coordinates of the feature points of the rail waist and the lower end of the rail head; generates a standard template of the rail profile based on the feature points; compares the measured profile of the rail with the standard template to obtain the wear value. This method only needs to determine the two feature points of the measured rail to establish a measurement coordinate system according to the geometric relationship of the standard rail profile, and can quickly and accurately obtain the standard template, without the need for alignment analysis of the measured profile and the reference design profile, which breaks the Traditionally based on the difficult problem of static template matching, it greatly improves the accuracy of wear measurement; reduces the computational load of image analysis and processing and has good stability.

Description

Rail wear measurement method based on dynamic template

技术领域 technical field

本发明涉及轨道交通技术，尤其涉及一种基于动态模板的钢轨磨耗测量方法。The invention relates to rail transit technology, in particular to a method for measuring rail wear based on a dynamic template.

背景技术 Background technique

钢轨的磨耗一般主要发生在轨头部位，是决定钢轨使用寿命的主要因素。磨耗一方面加速了机车车轮的磨损，增大了轨距，并增加与机车车轮踏面的接触面积，使运行阻力增大，另一方面产生了严重的噪声。当磨损超过一定限度时，轨头断面与车轮踏面就会失去匹配，将严重影响高速铁路行车平稳性，对行车安全造成极大的危害。特别是对于高速铁路而言，当列车速度很高时，即使很小的磨损也可能造成列车脱轨。The wear and tear of the rail generally mainly occurs at the rail head, which is the main factor determining the service life of the rail. On the one hand, the abrasion accelerates the wear of the locomotive wheels, increases the gauge, and increases the contact area with the locomotive wheel tread, which increases the running resistance; on the other hand, it produces serious noise. When the wear exceeds a certain limit, the rail head section and the wheel tread will lose their matching, which will seriously affect the running stability of the high-speed railway and cause great harm to the driving safety. Especially for high-speed railways, when the speed of the train is high, even small wear and tear can cause the train to derail.

目前我国在磨耗检测方面研究最多的是基于机器视觉的非接触检测方法。该方法大多利用坐标变换将图像坐标映射到物方坐标进行图像校正，最后再与标准模板进行匹配，如采用ICP匹配算法，从而获取钢轨头部的磨耗值。不仅计算量大，模板匹配或特征点匹配困难，而且数据处理速度慢，误差大等缺点，使测量结果不能有效为钢轨的维护提供可靠的依据。至于现场磨耗检测，则主要依赖机械式接触测量。该法测量速度慢，工作面的选取对测量结果影响很大。使用一段时间后固定和活动侧头磨损，会使测量结果存在一定的误差。At present, the most researched in wear detection in our country is the non-contact detection method based on machine vision. Most of the methods use coordinate transformation to map the image coordinates to the object space coordinates for image correction, and finally match with the standard template, such as using the ICP matching algorithm, so as to obtain the wear value of the rail head. Not only the amount of calculation is large, template matching or feature point matching is difficult, but also the data processing speed is slow and the error is large, so that the measurement results cannot effectively provide a reliable basis for rail maintenance. As for on-site wear detection, it mainly relies on mechanical contact measurement. The measurement speed of this method is slow, and the selection of the working surface has a great influence on the measurement results. After a period of use, the fixed and movable side heads are worn out, which will cause certain errors in the measurement results.

发明内容 Contents of the invention

本发明的目的是提供一种基于动态模板的钢轨磨耗测量方法，以克服现有方法模板匹配或特征点匹配困难的问题。The purpose of the present invention is to provide a method for measuring rail wear based on a dynamic template, so as to overcome the difficulty of template matching or feature point matching in the existing method.

本发明为解决其技术问题所采用的技术方案是，The technical scheme that the present invention adopts for solving its technical problem is,

一种基于动态模板的钢轨磨耗测量方法，包括以下步骤：A method for measuring rail wear based on a dynamic template, comprising the following steps:

1）在两根钢轨内侧上方分别安装CCD摄像机和扇形激光光源；1) Install a CCD camera and a fan-shaped laser light source on the inside of the two rails;

2）标定每个CCD摄像机及光平面参数；2) Calibrate each CCD camera and light plane parameters;

3）根据钢轨轮廓空间计算模型获取图像中钢轨轮廓每个像素点的空间坐标；3) Obtain the spatial coordinates of each pixel of the rail profile in the image according to the rail profile spatial calculation model;

4）提取轨腰及轨头下端特征点坐标；4) Extract the coordinates of the feature points of the rail waist and the lower end of the rail head;

5）基于特征点生成钢轨轮廓标准模板；5) Generate rail profile standard template based on feature points;

6）对比钢轨测量轮廓和标准模板得到磨耗值。6) Compare the measured profile of the rail with the standard template to obtain the wear value.

步骤1）中每侧钢轨各设置一个CCD摄像机和一个扇形激光光源，均位于钢轨内侧上方，且扇形激光光源发出的光平面与钢轨的纵向垂直。In step 1), a CCD camera and a fan-shaped laser light source are installed on each side of the rail, both of which are located above the inner side of the rail, and the light plane emitted by the fan-shaped laser light source is perpendicular to the longitudinal direction of the rail.

步骤2）中标定每个CCD摄像机参数的具体过程如下：The specific process of calibrating each CCD camera parameter in step 2) is as follows:

将摄像机固定在一个平面上，拍摄三张以上位于不同位置的棋盘格标定板图像，通过标定板上的点与图像点进行匹配，计算出它们之间的映射矩阵：Fix the camera on a plane, take more than three images of the checkerboard calibration board at different positions, match the points on the calibration board with the image points, and calculate the mapping matrix between them:

${z z}_{c c} (\begin{matrix} u u \\ v v \\ 11 \end{matrix}) = = (\begin{matrix} {f f}_{x x} & 00 & {u u}_{00} & 00 \\ 00 & {f f}_{y the y} & {v v}_{00} & 00 \\ 00 & 00 & 11 & 00 \end{matrix}) (\begin{matrix} R R & T T \\ 00^{T T} & 11 \end{matrix}) (\begin{matrix} {x x}_{w w} \\ {y the y}_{w w} \\ {z z}_{w w} \\ 11 \end{matrix}) = = (\begin{matrix} {m m}_{1111} & {m m}_{1212} & {m m}_{1313} & {m m}_{1414} \\ {m m}_{21 twenty one} & {m m}_{22 twenty two} & {m m}_{23 twenty three} & {m m}_{24 twenty four} \\ {m m}_{3131} & {m m}_{3232} & {m m}_{3333} & {m m}_{3434} \end{matrix}) (\begin{matrix} {x x}_{w w} \\ {y the y}_{w w} \\ {z z}_{w w} \\ 11 \end{matrix}),,$

并通过该矩阵解出摄像机参数，其中z_c为棋盘格上某交点在摄像机坐标系中的分量，f_x，f_y，u₀，v₀为摄像机的内部参数；R为一个具有正交性的旋转矩阵，T为一个平移矩阵，它们是摄像机的外部参数。x_w，y_w，z_w，1为空间第i个点的坐标；(u，v，1)为第i个点的图像坐标；m_ij为投影矩阵M的第i行j列元素；分解消去z_c可以得到关于m_ij的线性方程：And solve the camera parameters through this matrix, where z _c is the component of an intersection point on the checkerboard in the camera coordinate system, f _x , f _y , u ₀ , v ₀ are the internal parameters of the camera; R is an orthogonal The rotation matrix, T is a translation matrix, which are the external parameters of the camera. x _w , y _w , z _w , 1 is the coordinate of the i-th point in space; (u, v, 1) is the image coordinate of the i-th point; m _ij is the i-th row and j-column element of the projection matrix M; decomposition Eliminating z _c can get the linear equation about m _ij :

$\{\begin{matrix} {x x}_{w w} {m m}_{1111} + + {y the y}_{w w} {m m}_{1212} + + {z z}_{w w} {m m}_{1313} + + {m m}_{1414} - - {ux ux}_{w w} - - {uy uy}_{w w} {m m}_{3232} - - {uz uz}_{w w} {m m}_{3333} = = {um um}_{3434} \\ {x x}_{w w} {m m}_{21 twenty one} + + {y the y}_{w w} {m m}_{22 twenty two} + + {z z}_{w w} {m m}_{23 twenty three} + + {m m}_{24 twenty four} - - v v {x x}_{w w} - - v v {y the y}_{w w} {m m}_{3232} - - {vz vz}_{w w} {m m}_{3232} = = {vm vm}_{3434} \end{matrix}$

定标块上有n个已知点，得到2n个关于M矩阵元素的线性方程矩阵：There are n known points on the calibration block, and 2n linear equation matrices about the elements of the M matrix are obtained:

$[\begin{matrix} {x x}_{w w 11} & {y the y}_{w w 11} & {z z}_{w w 11} & 11 & 00 & 00 & 00 & - - {u u}_{11} {x x}_{w w 11} & - - {u u}_{11} {y the y}_{w w 11} & - - {u u}_{11} {z z}_{w w 11} \\ 00 & 00 & 00 & 00 & {x x}_{w w 11} & {y the y}_{w w 11} & {z z}_{w w 11} & - - {v v}_{11} {x x}_{w w 11} & - - {v v}_{11} {y the y}_{w w 11} & - - {v v}_{11} {z z}_{w w 11} \\ . . . . . . & . . . . . . & . . . . . . \\ . . . . . . & . . . . . . & . . . . . . \\ {x x}_{wn wn} & {y the y}_{wn wn} & {z z}_{wn wn} & 11 & 00 & 00 & 00 & - - {u u}_{n no} {x x}_{wn wn} & - - {u u}_{n no} {y the y}_{wn wn} & - - {u u}_{n no} {z z}_{wn wn} \\ 00 & 00 & 00 & 00 & {x x}_{wn wn} & {y the y}_{wn wn} & {z z}_{wn wn} & - - {v v}_{n no} {x x}_{wn wn} & - - {v v}_{n no} {y the y}_{wn wn} & - - {v v}_{n no} {z z}_{wn wn} \end{matrix}] \times \times [\begin{matrix} {m m}_{1111} \\ {m m}_{1212} \\ {m m}_{1313} \\ {m m}_{1414} \\ {m m}_{21 twenty one} \\ {m m}_{22 twenty two} \\ {m m}_{23 twenty three} \\ {m m}_{24 twenty four} \\ {m m}_{3131} \\ {m m}_{3232} \\ {m m}_{3333} \end{matrix}] = = [\begin{matrix} {u u}_{11} {m m}_{3434} \\ {v v}_{11} {m m}_{3434} \\ . . . . . . \\ . . . . . . \\ . . . . . . \\ . . . . . . \\ . . . . . . \\ . . . . . . \\ {u u}_{n no} {m m}_{3434} \\ {v v}_{n no} {m m}_{3434} \end{matrix}]$

指定m₃₄＝1，得到关于M矩阵其他元素的2n个线性方程，未知元素的个数为11个，记为11维向量m，简写成：Km＝U，K为左边2n×11矩阵；m为未知的11维向量；U为右边的2n维向量；K、U为已知向量；用最小二乘法求出当2n>11时上述线性方程的解为：Specify m ₃₄ =1 to get 2n linear equations about other elements of the M matrix, the number of unknown elements is 11, which is recorded as an 11-dimensional vector m, abbreviated as: Km=U, K is the left 2n×11 matrix; m is an unknown 11-dimensional vector; U is a 2n-dimensional vector on the right; K and U are known vectors; use the least square method to find the solution of the above linear equation when 2n>11:

m＝K^TK^-1K^TUm＝K ^T K ^-1 K ^T U

m向量与m₃₄＝1构成了所求解得M矩阵；由上可见，由空间6个以上已知点与它们的图像点坐标，可以求出M矩阵。The m vector and m ₃₄ =1 constitute the obtained M matrix; it can be seen from the above that the M matrix can be obtained from more than 6 known points in space and their image point coordinates.

求出M矩阵后，可由关系分解算出摄像机的全部内外参数。After obtaining the M matrix, all the internal and external parameters of the camera can be calculated by the relationship decomposition.

步骤2）中标定光平面参数的具体过程如下：The specific process of calibrating the light plane parameters in step 2) is as follows:

定标时增加辅助摄像机C₂，与摄像机C₁形成双目定标系统，共同拍摄位于标定板上的光带图像，此时将世界坐标系原点建立在摄像机C₁的光心处，通过分别对C₁、C₂定标，可确定其内部参数A₁、A₂及外部参数B₁、B₂，则它们的投影矩阵分别为M₁=A₁B₁（由于世界坐标系建立在C₁光心处，故B₁=I，I为单位矩阵）=A₁，M₂=A₂B₂=A₂[R₁₂，T₁₂]（[R₁₂，T₁₂]为摄像机C₁、C₂之间的位置关系矩阵），CCD摄取光带形成RGB图像之后，对其进行提取分量、灰度化、差影运算、二值化、细化等图像处理，以抽取光条中轴上各点的像素坐标，投影具有以下形式：When calibrating, an auxiliary camera C ₂ is added to form a binocular calibration system with camera C ₁ , and jointly shoot the light band image on the calibration board. At this time, the origin of the world coordinate system is established at the optical center of camera C ₁ , and through the For calibration of C ₁ and C ₂ , its internal parameters A ₁ and A ₂ and external parameters B ₁ and B ₂ can be determined, then their projection matrices are respectively M ₁ =A ₁ B ₁ (because the world coordinate system is established in C ₁ optical center, so B ₁ =I, I is the identity matrix) = A ₁ , M ₂ =A ₂ B ₂ =A ₂ [R ₁₂ , T ₁₂ ] ([R ₁₂ , T ₁₂ ] is camera C ₁ , The position relationship matrix between C ₂ ), after the CCD captures the light strip to form an RGB image, it performs image processing such as extraction, grayscale, difference operation, binarization, and thinning to extract the light strip on the central axis The pixel coordinates of each point, the projection has the following form:

${Z Z}_{11} (\begin{matrix} {u u}_{11} \\ {v v}_{11} \\ 11 \end{matrix}) = = {M m}_{11} (\begin{matrix} {x x}_{w w} \\ {y the y}_{w w} \\ {z z}_{w w} \\ 11 \end{matrix}) = = (\begin{matrix} {m m}_{1111}^{11} & {m m}_{1212}^{11} & {m m}_{1313}^{11} & {m m}_{1414}^{11} \\ {m m}_{21 twenty one}^{11} & {m m}_{22 twenty two}^{11} & {m m}_{23 twenty three}^{11} & {m m}_{24 twenty four}^{11} \\ {m m}_{3131}^{11} & {m m}_{3232}^{11} & {m m}_{3333}^{11} & {m m}_{3434}^{11} \end{matrix}) (\begin{matrix} {x x}_{w w} \\ {y the y}_{w w} \\ {z z}_{w w} \\ 11 \end{matrix})$

${Z Z}_{22} (\begin{matrix} {u u}_{22} \\ {v v}_{22} \\ 11 \end{matrix}) = = {M m}_{22} (\begin{matrix} {x x}_{w w} \\ {y the y}_{w w} \\ {z z}_{w w} \\ 11 \end{matrix}) = = (\begin{matrix} {m m}_{1111}^{22} & {m m}_{1212}^{22} & {m m}_{1313}^{22} & {m m}_{1414}^{22} \\ {m m}_{21 twenty one}^{22} & {m m}_{22 twenty two}^{22} & {m m}_{23 twenty three}^{22} & {m m}_{24 twenty four}^{22} \\ {m m}_{3131}^{22} & {m m}_{3232}^{22} & {m m}_{3333}^{22} & {m m}_{3434}^{22} \end{matrix}) (\begin{matrix} {x x}_{w w} \\ {y the y}_{w w} \\ {z z}_{w w} \\ 11 \end{matrix})$

其中，Z₁、Z₂为标定板光带上点P在两个摄像机坐标中的分量，计算时可消去；(u₁,v₁)，(u₂,v₂)分别为点P在C₁、C₂中的像素坐标。联立以上两式得到：Among them, Z ₁ and Z ₂ are the components of the point P on the light strip of the calibration plate in the coordinates of the two cameras, which can be eliminated during calculation; (u ₁ , v ₁ ), (u ₂ , v ₂ ) are the points P in C _1. Pixel coordinates in C ₂ . Combine the above two formulas to get:

$\{\begin{matrix} (({u u}_{11} {m m}^{11}_{3131} - - {m m}^{11}_{1111})) {x x}_{w w} + + (({u u}_{11} {m m}^{11}_{3232} - - {m m}^{11}_{1212})) {y the y}_{w w} + + (({u u}_{11} {m m}^{11}_{3333} - - {m m}^{11}_{3333})) {z z}_{w w} = = {m m}^{11}_{1414} - - {u u}_{11} {m m}^{11}_{3434} \\ (({v v}_{11} {m m}^{11}_{3131} - - {m m}^{11}_{1111})) {x x}_{w w} + + (({v v}_{11} {m m}^{11}_{3232} - - {m m}^{11}_{22 twenty two})) {y the y}_{w w} + + (({v v}_{11} {m m}^{11}_{3333} - - {m m}^{11}_{23 twenty three})) {z z}_{w w} = = {m m}^{11}_{24 twenty four} - - {v v}_{11} {m m}^{11}_{3434} \\ (({u u}_{22} {m m}^{22}_{3131} - - {m m}^{22}_{1111})) {x x}_{w w} + + (({u u}_{22} {m m}^{22}_{3232} - - {m m}^{22}_{1212})) {y the y}_{w w} + + (({u u}_{22} {m m}^{22}_{3333} - - {m m}^{22}_{1313})) {z z}_{w w} = = {m m}^{22}_{1414} - - {u u}_{22} {m m}^{22}_{3434} \\ (({v v}_{22} {m m}^{22}_{3131} - - {m m}^{22}_{21 twenty one})) {x x}_{w w} + + (({v v}_{22} {m m}^{22}_{22 twenty two} - - {m m}^{22}_{22 twenty two})) {y the y}_{w w} + + (({v v}_{22} {m m}^{22}_{3333} - - {m m}^{22}_{23 twenty three})) {z z}_{w w} = = {m m}^{22}_{24 twenty four} - - {v v}_{22} {m m}^{22}_{3434} \end{matrix}$

由此，可求出点P的世界坐标。同理，不断移动标定板的空间位置，可以得到光带上m(m>3)个点的世界坐标(x_wi,y_wi,z_wi)(i＝1,2,3,...m)。Thus, the world coordinates of the point P can be obtained. Similarly, by constantly moving the spatial position of the calibration board, the world coordinates (x _wi , y _wi , z _wi ) (i=1,2,3,...m ).

空间光平面的方程可表示如下：The equation of the spatial light plane can be expressed as follows:

Ax_w+By_w+Cz_w+1=0Ax _w +By _w +Cz _w +1=0

其中，A、B、C为该平面法向量n的3个分量。Among them, A, B, C are the three components of the plane normal vector n.

由于光带上特征点的世界坐标亦满足光平面方程，则可用m个特征点构造一个超定方程组，其矩阵形式为：Since the world coordinates of the feature points on the light strip also satisfy the light plane equation, an overdetermined equation system can be constructed with m feature points, and its matrix form is:

$[\begin{matrix} {x x}_{w w 11} & {y the y}_{w w 11} & {z z}_{w w 11} \\ {x x}_{w w 22} & {y the y}_{w w 22} & {z z}_{w w 22} \\ . . & . . & . . \\ . . & . . & . . \\ . . & . . & . . \\ {x x}_{wm wm} & {y the y}_{wm wm} & {z z}_{wm wm} \end{matrix}] [\begin{matrix} A A \\ B B \\ C C \end{matrix}] = = [\begin{matrix} - - 11 \\ - - 11 \\ . . \\ . . \\ . . \\ - - 11 \end{matrix}]$

或简写为：or in short:

GS=LGS=L

其中，G为等式左边的系数矩阵，S=[A,B,C]^T，L=[1,1,…,1]^T，然后利用最小二乘法可得到S=(G^TG)^-1G^TL及系数A,B,C。Among them, G is the coefficient matrix on the left side of the equation, S=[A,B,C] ^T , L=[1,1,…,1] ^T , and then use the least square method to get S=(G ^T G) ^{- 1} G ^T L and coefficients A, B, C.

步骤3）中根据钢轨轮廓空间计算模型获取图像中钢轨轮廓每个像素点的空间坐标的具体过程如下：In step 3), the specific process of obtaining the spatial coordinates of each pixel of the rail profile in the image according to the rail profile spatial calculation model is as follows:

将世界坐标系建立在摄像机坐标系上，令两者完全重合，则两者之间不存在旋转与平移关系，此时Establish the world coordinate system on the camera coordinate system, so that the two are completely coincident, then there is no rotation and translation relationship between the two, at this time

$(\begin{matrix} R R & T T \\ 00^{T T} & 11 \end{matrix}) = = I I$

为单位矩阵并且有z_c=z_w，则is the identity matrix and has z _c =z _w , then

${z z}_{c c} (\begin{matrix} u u \\ v v \\ 11 \end{matrix}) = = (\begin{matrix} {f f}_{x x} & 00 & {u u}_{00} & 00 \\ 00 & {f f}_{y the y} & {v v}_{00} & 00 \\ 00 & 00 & 11 & 00 \end{matrix}) (\begin{matrix} {x x}_{w w} \\ {y the y}_{w w} \\ {z z}_{w w} \\ 11 \end{matrix})$

同时p点也在激光所投射的平面内，因此满足光平面方程：At the same time, point p is also in the plane projected by the laser, so it satisfies the light plane equation:

Ax_w+By_w+Cz_w+1=0Ax _w +By _w +Cz _w +1=0

式中，A,B,C为光平面系数。联立可得到：In the formula, A, B, C are light plane coefficients. Together you can get:

$(\begin{matrix} {f f}_{x x} & 00 & {u u}_{00} - - u u \\ 00 & {f f}_{y the y} & {v v}_{00} - - v v \\ a a & b b & c c \end{matrix}) (\begin{matrix} {x x}_{w w} \\ {y the y}_{w w} \\ {z z}_{w w} \end{matrix}) = = (\begin{matrix} 00 \\ 00 \\ - - 11 \end{matrix})$

可得钢轨断面轮廓线上任一点的世界坐标(x_w，y_w，z_w)。The world coordinates (x _w , y _w , z _w ) of any point on the contour line of the rail section can be obtained.

步骤4）中提取轨腰及轨头下端特征点坐标的具体过程如下，The specific process of extracting the coordinates of the feature points of the rail waist and the lower end of the rail head in step 4) is as follows,

（1）轨腰特征点提取：(1) Extraction of rail waist feature points:

在三维重建后的轨腰圆弧中任取一点X_i(x_wi，y_wi，z_wi)，以半径R作空间球面，记空间球面方程为：Take any point X _i (x _wi , y _wi , z _wi ) in the three-dimensionally reconstructed rail waist arc, use the radius R as the space sphere, and record the space sphere equation as:

X^TQX=0X ^T QX=0

其中x为球面上点的坐标，X=[x_w，y_w，z_w，1]^T，Q为4×4的对称矩阵： $Q = [\begin{matrix} 1 & 0 & 0 & - x_{wi} \\ 0 & 1 & 0 & - y_{wi} \\ 0 & 0 & 1 & - z_{wi} \\ - x_{wi} & - y_{wi} & - z_{wi} & l^{2} \end{matrix}],$ l²=x_wi ²+y_wi ²+z_wi ²-R² Where x is the coordinates of a point on the sphere, X=[x _w , y _w , z _w , 1] ^T , and Q is a 4×4 symmetric matrix: $Q = [\begin{matrix} 1 & 0 & 0 & - x_{wi} \\ 0 & 1 & 0 & - {the y}_{wi} \\ 0 & 0 & 1 & - z_{wi} \\ - x_{wi} & - {the y}_{wi} & - z_{wi} & l^{2} \end{matrix}],$ l ² =x _wi ² +y _wi ² +z _wi ² -R ²

由于钢轨轮廓线上的点在光平面内，令x_t=x_w，y_t＝y_w，则光平面方程可写成：Since the points on the rail contour line are in the light plane, let x _t = x _w , y _t = y _w , then the light plane equation can be written as:

X＝MtX=Mt

其中 $M = [\begin{matrix} - b / a & - c / a & - 1 / a \\ 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \end{matrix}],$ $t = [\begin{matrix} x_{t} \\ y_{t} \\ 1 \end{matrix}],$ 可得X^TQX=t^TM^TQMt=0，in $m = [\begin{matrix} - b / a & - c / a & - 1 / a \\ 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \end{matrix}],$ $t = [\begin{matrix} x_{t} \\ {the y}_{t} \\ 1 \end{matrix}],$ It can be obtained that X ^T QX=t ^T M ^T QMt=0,

令make

$C C = = {M m}^{T T} QM QM = = [\begin{matrix} {((b b / / a a))}^{22} + + 11 & bc bc / / {a a}^{22} & b b / / {a a}^{22} + + ((b b / / c c)) {x x}_{wi wi} - - {y the y}_{wi wi} \\ bc bc / / {a a}^{22} & {((c c / / a a))}^{22} + + 11 & c c / / {a a}^{22} + + ((c c / / a a)) {x x}_{wi wi} - - {z z}_{wi wi} \\ b b / / {a a}^{22} + + ((b b / / a a)) {x x}_{wi wi} - - {y the y}_{wi wi} & c c / / {a a}^{22} + + ((c c / / a a)) {x x}_{wi wi} - - {z z}_{wi wi} & 11 / / {a a}^{22} + + ((22 / / a a)) {x x}_{wi wi} + + {l l}^{22} \end{matrix}]$

即有t^TCt＝0，C为对称矩阵，因此t为二次曲线上的点。如果在轨腰同一圆弧中任取一对点作半径为R的空间球面，在这里R等于轨腰圆弧段的半径，则可得到两个交点：That is, t ^T Ct = 0, C is a symmetric matrix, so t is a point on the quadratic curve. If a pair of points in the same arc of the rail waist are randomly selected as a space sphere with radius R, where R is equal to the radius of the rail waist arc segment, two intersection points can be obtained:

$\{\begin{matrix} {t t}^{T T} {C C}_{i i} t t = = 00 \\ {t t}^{T T} {C C}_{j j} t t = = 00 \end{matrix}$

由检测原理可知，两个交点中距离摄像机光心（也就是距离世界坐标系原点）近的点即为所求圆弧段的圆心点，其在三维空间的坐标值可计算获得。在实际工程中，由于图像中每段圆弧轮廓有m对个点，可得到出m个圆心X₁，X₂，..．，X_m的坐标，令：It can be seen from the detection principle that the point of the two intersection points that is closest to the optical center of the camera (that is, the origin of the world coordinate system) is the center point of the arc segment to be sought, and its coordinate value in the three-dimensional space can be calculated. In actual engineering, since there are m pairs of points in each arc profile in the image, m circle centers X ₁ , X ₂ ,... , the coordinates of X _m , let:

d_k=(x_wo-x_wk)²+(y_wo-y_wk)²+(z_wo-z_wk)2d _k =(x _wo -x _wk ) ² +(y _wo -y _wk ) ² +(z _wo -z _wk )2

其中x_wo，y_wo，z_wo为圆心最优点X_o的坐标分量，x_wk，y_wk，z_wk为X_k(k＝1，2，..．，m)的坐标分量，通过下式可求出X_o的最优解：Among them x _wo , y _wo , z _wo are the coordinate components of the optimal point X _o of the center of the circle, x _wk , y _wk , z _wk are the coordinate components of X _k (k=1, 2,..., m), through the following formula The optimal solution of X _o can be obtained:

$\{\begin{matrix} {Σ Σ}_{k k = = 11}^{m m} {d d}_{k k} = = L L \\ \frac{&PartialD; &PartialD; L L}{{&PartialD; &PartialD; x x}_{wo the w}} = = \frac{&PartialD; &PartialD; L L}{&PartialD; &PartialD; {y the y}_{wo the w}} = = \frac{&PartialD; &PartialD; L L}{&PartialD; &PartialD; {z z}_{wo the w}} = = 00 \end{matrix}$

（2）轨头下端特征点提取：(2) Feature point extraction at the lower end of the rail head:

由于在检测原理上结构光和摄像机位于钢轨侧上方，实际图像轨头和轨腰存在明显的分割，因此能进行快速搜索定位。另一方面，由于图像经过细化处理大多会存在一个像素的偏差，因此实际搜索定位的得到的轨头下端点及其8邻点均有可能是实际的下端点，{X_b1，X_b2，...，X_b9}坐标可计算得到。求其与轨腰圆弧段圆心点X_o的距离{d_ob1，d_ob2，...，d_ob9，记理论距离与实际距离的误差为εi₌|d_obi-d_ob|，i＝1，2，..．，9，其中d_ob为理论距离。取ε_min=min{ε₁，ε₂，..．，ε₉}，记取得ε_min时所对应的X_bi为X_b，即为所求的轨头下端点。Since the structured light and the camera are located above the side of the rail in the detection principle, there is an obvious division between the rail head and the rail waist in the actual image, so fast search and positioning can be performed. On the other hand, due to the fact that most images have a deviation of one pixel after refinement processing, the lower endpoint of the track head and its 8 neighbors obtained by the actual search and positioning may be the actual lower endpoint, {X _b1 , X _b2 , ..., X _b9 } coordinates can be calculated. Find the distance between it and the center point X _o of the arc segment of the rail waist {d _ob1 , d _ob2 , ..., d _ob9 , and record the error between the theoretical distance and the actual distance as εi ₌ |d _obi -d _ob |, i=1 ,2,... , 9, where d _ob is the theoretical distance. Take ε _min =min{ε ₁ , ε ₂ ,... _. _{_} _{_} _{_}

步骤5）中基于特征点生成钢轨轮廓标准模板的具体过程如下：The specific process of generating the rail profile standard template based on the feature points in step 5) is as follows:

确立空间坐标系需要不在同一直线上的三个点，当轨腰圆弧段特征点和轨头下端点确定之后，在钢轨轮廓上任取不与X_o和X_b共线的一点X_r，取矢量以X_o点为原点建立笛卡尔坐标系，x’方向的矢量为则z’方向的矢量为 $\overset{&RightArrow;}{o^{'} z^{'}} = \overset{&RightArrow;}{o^{'} x^{'}} \times \overset{&RightArrow;}{X_{o} X_{r}},$ y’方向的矢量为一旦该坐标系建立，由标准钢轨的空间轮廓几何关系可知，整个钢轨的空间断面轮廓得以建立，因此，可动态的在每帧测量图像中生成一个钢轨轮廓的标准模板。To establish the spatial coordinate system, three points that are not on the same straight line are required. After the feature point of the rail waist arc segment and the lower end point of the rail head are determined, any point X _r that is not collinear with X _o and X _b is taken on the rail profile, and vector Establish a Cartesian coordinate system with X _o as the origin, and the vector in the x' direction is Then the vector in the z' direction is $\overset{&Right Arrow;}{o^{'} z^{'}} = \overset{&Right Arrow;}{o^{'} x^{'}} \times \overset{&Right Arrow;}{x_{o} x_{r}},$ The vector in the y' direction is Once the coordinate system is established, it can be known from the spatial profile geometric relationship of the standard rail that the spatial section profile of the entire rail is established. Therefore, a standard template of the rail profile can be dynamically generated in each frame of measurement image.

步骤6）中对比钢轨测量轮廓和标准模板得到磨耗值的具体过程如下：In step 6), the specific process of comparing the measured profile of the rail with the standard template to obtain the wear value is as follows:

将拍摄到的测量图像进行处理得到钢轨轮廓的测量光带，计算得到建立位于摄像机光心处世界坐标系下的钢轨轮廓空间三维坐标。建立新的世界坐标，令其原点位于钢轨底部的中心，x″轴与钢轨底边重合，y″轴与钢轨断面中心线重合，z″垂直于x"y"平面，由于通过特征点建立的坐标系o’x’y’z’与o"x"y"z"存在明确的旋转和平移关系，因此可将钢轨轮廓上的空间坐标映射到坐标系o″x″y″x″下，从而计算出磨耗值。The captured measurement images are processed to obtain the measurement light band of the rail profile, and the three-dimensional coordinates of the rail profile space in the world coordinate system located at the optical center of the camera are calculated and established. Establish a new world coordinate, so that its origin is located at the center of the bottom of the rail, the x″ axis coincides with the bottom edge of the rail, the y″ axis coincides with the center line of the rail section, and z″ is perpendicular to the x”y” plane. There is a clear rotation and translation relationship between the coordinate system o'x'y'z' and o"x"y"z", so the spatial coordinates on the rail profile can be mapped to the coordinate system o″x″y″x″, The wear value is thus calculated.

由于采用了以上的技术方案，本发明与现有技术相比，具有如下优点和积极效果：Owing to adopting above technical scheme, the present invention has following advantage and positive effect compared with prior art:

1.不需要将测量轮廓和基准设计轮廓进行对齐分析，打破了传统的基于静态模板匹配难的问题，极大的提高了磨耗测量的精确性；1. There is no need to align and analyze the measurement profile and the reference design profile, which breaks the traditional problem of difficult matching based on static templates, and greatly improves the accuracy of wear measurement;

2.降低了图像分析处理的运算量并具有良好的稳定性。2. It reduces the computational load of image analysis and processing and has good stability.

当然，实施本发明内容的任何一个具体实施例，并不一定同时达到以上全部的技术效果。Of course, implementing any specific embodiment of the content of the present invention does not necessarily achieve all the above technical effects at the same time.

附图说明 Description of drawings

图1是本发明提出的钢轨磨耗测量方法的流程图；Fig. 1 is the flow chart of the rail wear measurement method that the present invention proposes;

图2是该方法的磨耗测量系统原理图；Fig. 2 is the schematic diagram of the wear measurement system of the method;

图3是该方法的视觉测量数学模型；Fig. 3 is the visual measurement mathematical model of this method;

图4是轨头下端点识别示意图；Fig. 4 is a schematic diagram of identifying the lower end point of the rail head;

图5是轨腰圆弧中心示意图；Fig. 5 is a schematic diagram of the center of the arc of the rail waist;

图6是一个实施例中的标准钢轨轮廓图像；Figure 6 is a profile image of a standard rail in one embodiment;

图7a是测量到的钢轨轮廓与标准轮廓的三维空间轮廓曲线比较图；Figure 7a is a comparison diagram of the three-dimensional space profile curve between the measured rail profile and the standard profile;

图7b是图7a坐标转换后的平面轮廓曲线图。Fig. 7b is a graph of the plane profile after coordinate transformation in Fig. 7a.

具体实施方式 Detailed ways

为了使本发明实现的技术手段、创作特征、达成目的与功效易于明白了解，下面结合图示与具体实施例，进一步阐述本发明。In order to make the technical means, creative features, goals and effects achieved by the present invention easy to understand, the present invention will be further elaborated below in conjunction with illustrations and specific embodiments.

如图1所示，本发明提出的基于动态模板的钢轨磨耗测量方法包括以下步骤：As shown in Figure 1, the rail wear measurement method based on the dynamic formwork that the present invention proposes comprises the following steps:

1）在两根钢轨内侧上方分别安装CCD摄像机和扇形激光光源，扇形激光光源发出的光平面垂直于钢轨纵向，具体安装方式如图2所示；1) Install a CCD camera and a fan-shaped laser light source on the inner side of the two rails. The light plane emitted by the fan-shaped laser light source is perpendicular to the longitudinal direction of the rail. The specific installation method is shown in Figure 2;

其原理是：The principle is:

首先对CCD摄像机和光平面参数进行标定，其中摄像机标定过程为：Firstly, the CCD camera and light plane parameters are calibrated, and the camera calibration process is as follows:

将摄像机固定在一个平面上，拍摄三张以上位于不同位置的棋盘格标定板图像，通过标定板上的点与图像点进行匹配，计算出它们之间的映射矩阵，并通过该矩阵解出摄像机参数，Fix the camera on a plane, take more than three images of the checkerboard calibration board at different positions, match the points on the calibration board with the image points, calculate the mapping matrix between them, and use this matrix to solve the camera parameter,

${z z}_{c c} (\begin{matrix} u u \\ v v \\ 11 \end{matrix}) = = (\begin{matrix} {f f}_{x x} & 00 & {u u}_{00} & 00 \\ 00 & {f f}_{y the y} & {v v}_{00} & 00 \\ 00 & 00 & 11 & 00 \end{matrix}) (\begin{matrix} R R & T T \\ 00^{T T} & 11 \end{matrix}) (\begin{matrix} {x x}_{w w} \\ {y the y}_{w w} \\ {z z}_{w w} \\ 11 \end{matrix}) = = (\begin{matrix} {m m}_{1111} & {m m}_{1212} & {m m}_{1313} & {m m}_{1414} \\ {m m}_{21 twenty one} & {m m}_{22 twenty two} & {m m}_{23 twenty three} & {m m}_{24 twenty four} \\ {m m}_{3131} & {m m}_{3232} & {m m}_{3333} & {m m}_{3434} \end{matrix}) (\begin{matrix} {x x}_{w w} \\ {y the y}_{w w} \\ {z z}_{w w} \\ 11 \end{matrix}) - - - - - - ((11))$

其中z_c为棋盘格上某交点在摄像机坐标系中的分量，f_x，f_y，u₀，v₀为摄像机的内部参数；R为一个具有正交性的旋转矩阵，T为一个平移矩阵，它们是摄像机的外部参数。x_w，y_w，z_w，1为空间第i个点的坐标；(u，v，1)为第i个点的图像坐标；m_ij为投影矩阵M的第i行j列元素；对式(1)进行分解消去z_c可以得到关于m_ij的线性方程：Where z _c is the component of an intersection point on the checkerboard in the camera coordinate system, f _x , f _y , u ₀ , v ₀ are the internal parameters of the camera; R is an orthogonal rotation matrix, and T is a translation matrix , which are the extrinsic parameters of the camera. x _w , y _w , z _w , 1 is the coordinate of the i-th point in space; (u, v, 1) is the image coordinate of the i-th point; m _ij is the i-th row and j-column element of the projection matrix M; The linear equation about m _ij can be obtained by decomposing and eliminating z _c in formula (1):

$\{\begin{matrix} {x x}_{w w} {m m}_{1111} + + {y the y}_{w w} {m m}_{1212} + + {z z}_{w w} {m m}_{1313} + + {m m}_{1414} - - {ux ux}_{w w} - - {uy uy}_{w w} {m m}_{3232} - - {uz uz}_{w w} {m m}_{3333} = = {um um}_{3434} \\ {x x}_{w w} {m m}_{21 twenty one} + + {y the y}_{w w} {m m}_{22 twenty two} + + {z z}_{w w} {m m}_{23 twenty three} + + {m m}_{24 twenty four} - - v v {x x}_{w w} - - v v {y the y}_{w w} {m m}_{3232} - - {vz vz}_{w w} {m m}_{3232} = = {vm vm}_{3434} \end{matrix} - - - - - - ((22))$

$[\begin{matrix} {x x}_{w w 11} & {y the y}_{w w 11} & {z z}_{w w 11} & 11 & 00 & 00 & 00 & - - {u u}_{11} {x x}_{w w 11} & - - {u u}_{11} {y the y}_{w w 11} & - - {u u}_{11} {z z}_{w w 11} \\ 00 & 00 & 00 & 00 & {x x}_{w w 11} & {y the y}_{w w 11} & {z z}_{w w 11} & - - {v v}_{11} {x x}_{w w 11} & - - {v v}_{11} {y the y}_{w w 11} & - - {v v}_{11} {z z}_{w w 11} \\ . . . . . . & . . . . . . & . . . . . . \\ . . . . . . & . . . . . . & . . . . . . \\ {x x}_{wn wn} & {y the y}_{wn wn} & {z z}_{wn wn} & 11 & 00 & 00 & 00 & - - {u u}_{n no} {x x}_{wn wn} & - - {u u}_{n no} {y the y}_{wn wn} & - - {u u}_{n no} {z z}_{wn wn} \\ 00 & 00 & 00 & 00 & {x x}_{wn wn} & {y the y}_{wn wn} & {z z}_{wn wn} & - - {v v}_{n no} {x x}_{wn wn} & - - {v v}_{n no} {y the y}_{wn wn} & - - {v v}_{n no} {z z}_{wn wn} \end{matrix}] \times \times [\begin{matrix} {m m}_{1111} \\ {m m}_{1212} \\ {m m}_{1313} \\ {m m}_{1414} \\ {m m}_{21 twenty one} \\ {m m}_{22 twenty two} \\ {m m}_{23 twenty three} \\ {m m}_{24 twenty four} \\ {m m}_{3131} \\ {m m}_{3232} \\ {m m}_{3333} \end{matrix}] = = [\begin{matrix} {u u}_{11} {m m}_{3434} \\ {v v}_{11} {m m}_{3434} \\ . . . . . . \\ . . . . . . \\ . . . . . . \\ . . . . . . \\ . . . . . . \\ . . . . . . \\ {u u}_{n no} {m m}_{3434} \\ {v v}_{n no} {m m}_{3434} \end{matrix}] - - - - - - ((33))$

在式(2)中指定m₃₄＝1，得到关于M矩阵其他元素的2n个线性方程，未知元素的个数为11个，记为11维向量m，将式(3)简写成：Designate m ₃₄ =1 in formula (2), and get 2n linear equations about other elements of the M matrix, the number of unknown elements is 11, which is recorded as an 11-dimensional vector m, and formula (3) is abbreviated as:

Km＝U (4)Km＝U (4)

其中，K为左边2n×11矩阵，m为未知的11维向量，U为右边的2n维向量，K、U为已知向量。用最小二乘法求出当2n>11时上述线性方程的解为：Among them, K is a 2n×11 matrix on the left, m is an unknown 11-dimensional vector, U is a 2n-dimensional vector on the right, and K and U are known vectors. The solution to the above linear equation when 2n>11 is found by the least square method is:

m=K^TK^-1K^TU (5)m=K ^T K ^-1 K ^T U (5)

光平面标定过程为：The light plane calibration process is:

定标时增加辅助摄像机C₂，与摄像机C₁形成双目定标系统，共同拍摄位于标定板上的光带图像。此时将世界坐标系原点建立在摄像机C₁的光心处，通过分别对C₁、C₂定标，可确定其内部参数A₁、A₂及外部参数B₁、B₂。则它们的投影矩阵分别为M₁=A₁B₁（由于世界坐标系建立在C₁光心处，故B₁=I，I为单位矩阵）=A₁，M₂=A₂B₂=A₂[R₁₂，T₁₂]（[R₁₂，T₁₂]为摄像机C₁、C₂之间的位置关系矩阵）。CCD摄取光带形成RGB图像之后，对其进行提取分量、灰度化、差影运算、二值化、细化等图像处理，以抽取光条中轴上各点的像素坐标。投影具有以下形式：When calibrating, an auxiliary camera C ₂ is added to form a binocular calibration system with camera C ₁ to jointly capture images of light bands on the calibration board. At this time, the origin of the world coordinate system is established at the optical center of camera C ₁ , and its internal parameters A ₁ _, A ₂ _and external parameters B 1 , B 2 can be determined by respectively calibrating C ₁ , C ₂ . Then their projection matrices are respectively M ₁ =A ₁ B ₁ (Since the world coordinate system is established at the optical center of C ₁ , so B ₁ =I, I is the unit matrix) =A ₁ , M ₂ =A ₂ B ₂ = A ₂ [R ₁₂ , T ₁₂ ] ([R ₁₂ , T ₁₂ ] is the position relationship matrix between cameras C ₁ and C ₂ ). After the CCD captures the light strip to form an RGB image, it performs image processing such as component extraction, gray scale, difference operation, binarization, and thinning to extract the pixel coordinates of each point on the central axis of the light strip. Projections have the following form:

${Z Z}_{11} (\begin{matrix} {u u}_{11} \\ {v v}_{11} \\ 11 \end{matrix}) = = {M m}_{11} (\begin{matrix} {x x}_{w w} \\ {y the y}_{w w} \\ {z z}_{w w} \\ 11 \end{matrix}) = = (\begin{matrix} {m m}_{1111}^{11} & {m m}_{1212}^{11} & {m m}_{1313}^{11} & {m m}_{1414}^{11} \\ {m m}_{21 twenty one}^{11} & {m m}_{22 twenty two}^{11} & {m m}_{23 twenty three}^{11} & {m m}_{24 twenty four}^{11} \\ {m m}_{3131}^{11} & {m m}_{3232}^{11} & {m m}_{3333}^{11} & {m m}_{3434}^{11} \end{matrix}) (\begin{matrix} {x x}_{w w} \\ {y the y}_{w w} \\ {z z}_{w w} \\ 11 \end{matrix}) - - - - - - ((66))$

${Z Z}_{22} (\begin{matrix} {u u}_{22} \\ {v v}_{22} \\ 11 \end{matrix}) = = {M m}_{22} (\begin{matrix} {x x}_{w w} \\ {y the y}_{w w} \\ {z z}_{w w} \\ 11 \end{matrix}) = = (\begin{matrix} {m m}_{1111}^{22} & {m m}_{1212}^{22} & {m m}_{1313}^{22} & {m m}_{1414}^{22} \\ {m m}_{21 twenty one}^{22} & {m m}_{22 twenty two}^{22} & {m m}_{23 twenty three}^{22} & {m m}_{24 twenty four}^{22} \\ {m m}_{3131}^{22} & {m m}_{3232}^{22} & {m m}_{3333}^{22} & {m m}_{3434}^{22} \end{matrix}) (\begin{matrix} {x x}_{w w} \\ {y the y}_{w w} \\ {z z}_{w w} \\ 11 \end{matrix}) - - - - - - ((77))$

其中，Z₁、Z₂为标定板光带上任一点P在两个摄像机坐标中的分量，计算时可消去；(u₁,v₁)，(u₂,v₂)分别为点P在C₁、C₂中的像素坐标。联立式(6)和式(7)得到：Among them, Z ₁ and Z ₂ are the components of any point P on the light strip of the calibration plate in the coordinates of the two cameras, which can be eliminated during calculation; (u ₁ , v ₁ ), (u ₂ , v ₂ ) are the points P at C _1. Pixel coordinates in C ₂ . Simultaneous formula (6) and formula (7) get:

$\{\begin{matrix} (({u u}_{11} {m m}^{11}_{3131} - - {m m}^{11}_{1111})) {x x}_{w w} + + (({u u}_{11} {m m}^{11}_{3232} - - {m m}^{11}_{1212})) {y the y}_{w w} + + (({u u}_{11} {m m}^{11}_{3333} - - {m m}^{11}_{3333})) {z z}_{w w} = = {m m}^{11}_{1414} - - {u u}_{11} {m m}^{11}_{3434} \\ (({v v}_{11} {m m}^{11}_{3131} - - {m m}^{11}_{1111})) {x x}_{w w} + + (({v v}_{11} {m m}^{11}_{3232} - - {m m}^{11}_{22 twenty two})) {y the y}_{w w} + + (({v v}_{11} {m m}^{11}_{3333} - - {m m}^{11}_{23 twenty three})) {z z}_{w w} = = {m m}^{11}_{24 twenty four} - - {v v}_{11} {m m}^{11}_{3434} \\ (({u u}_{22} {m m}^{22}_{3131} - - {m m}^{22}_{1111})) {x x}_{w w} + + (({u u}_{22} {m m}^{22}_{3232} - - {m m}^{22}_{1212})) {y the y}_{w w} + + (({u u}_{22} {m m}^{22}_{3333} - - {m m}^{22}_{1313})) {z z}_{w w} = = {m m}^{22}_{1414} - - {u u}_{22} {m m}^{22}_{3434} \\ (({v v}_{22} {m m}^{22}_{3131} - - {m m}^{22}_{21 twenty one})) {x x}_{w w} + + (({v v}_{22} {m m}^{22}_{22 twenty two} - - {m m}^{22}_{22 twenty two})) {y the y}_{w w} + + (({v v}_{22} {m m}^{22}_{3333} - - {m m}^{22}_{23 twenty three})) {z z}_{w w} = = {m m}^{22}_{24 twenty four} - - {v v}_{22} {m m}^{22}_{3434} \end{matrix} - - - - - - ((88))$

Ax_w+By_w+Cz_w+1=0 (9)Ax _w +By _w +Cz _w +1=0 (9)

$[\begin{matrix} {x x}_{w w 11} & {y the y}_{w w 11} & {z z}_{w w 11} \\ {x x}_{w w 22} & {y the y}_{w w 22} & {z z}_{w w 22} \\ . . & . . & . . \\ . . & . . & . . \\ . . & . . & . . \\ {x x}_{wm wm} & {y the y}_{wm wm} & {z z}_{wm wm} \end{matrix}] [\begin{matrix} A A \\ B B \\ C C \end{matrix}] = = [\begin{matrix} - - 11 \\ - - 11 \\ . . \\ . . \\ . . \\ - - 11 \end{matrix}] - - - - - - ((1010))$

或简写为：or in short:

GS=L (11)GS=L (11)

以下说明如何根据钢轨轮廓空间计算模型获取图像中钢轨轮廓每个像素点的空间坐标，如图3所示。The following describes how to obtain the spatial coordinates of each pixel of the rail profile in the image according to the rail profile spatial calculation model, as shown in Figure 3.

令O_wX_wY_wZ_w为世界坐标系，O_cX_cY_cZ_c为摄像机坐标系，O_uX_uY_u为图像坐标系。在本系统中，将世界坐标系建立在摄像机坐标系上，令两者完全重合，则两者之间不存在旋转与平移关系，此时Let O _w X _w Y _w Z _w be the world coordinate system, O _c X _c Y _c Z _c be the camera coordinate system, and O _u X _u Y _u be the image coordinate system. In this system, the world coordinate system is established on the camera coordinate system, so that the two are completely coincident, so there is no rotation and translation relationship between the two, at this time

$(\begin{matrix} R R & T T \\ 00^{T T} & 11 \end{matrix}) = = I I$

${z z}_{c c} (\begin{matrix} u u \\ v v \\ 11 \end{matrix}) = = (\begin{matrix} {f f}_{x x} & 00 & {u u}_{00} & 00 \\ 00 & {f f}_{y the y} & {v v}_{00} & 00 \\ 00 & 00 & 11 & 00 \end{matrix}) (\begin{matrix} {x x}_{w w} \\ {y the y}_{w w} \\ {z z}_{w w} \\ 11 \end{matrix}) - - - - - - ((1212))$

同时该点也在激光所投射的平面内，因此满足空间光平面方程，联立式(12)和式(9)可得到：At the same time, the point is also in the plane projected by the laser, so it satisfies the spatial light plane equation. Simultaneous formula (12) and formula (9) can be obtained:

$(\begin{matrix} {f f}_{x x} & 00 & {u u}_{00} - - u u \\ 00 & {f f}_{y the y} & {v v}_{00} - - v v \\ a a & b b & c c \end{matrix}) (\begin{matrix} {x x}_{w w} \\ {y the y}_{w w} \\ {z z}_{w w} \end{matrix}) = = (\begin{matrix} 00 \\ 00 \\ - - 11 \end{matrix}) - - - - - - ((1313))$

从而得到钢轨断面轮廓线上任一点的世界坐标(x_w，y_w，z_w)。Thus, the world coordinates (x _w , y _w , z _w ) of any point on the contour line of the rail section can be obtained.

以下说明提取轨腰及轨头下端特征点坐标的方法。The following describes the method of extracting the coordinates of the feature points of the rail waist and the lower end of the rail head.

轨腰特征点提取Rail Waist Feature Point Extraction

X^TQX=0 (14)X ^T QX=0 (14)

其中x为球面上点的坐标，X=[x_w，y_w，z_w，1]^T，Q为4×4的对称矩阵：Where x is the coordinates of a point on the sphere, X=[x _w , y _w , z _w , 1] ^T , and Q is a 4×4 symmetric matrix:

$Q = [\begin{matrix} 1 & 0 & 0 & - x_{wi} \\ 0 & 1 & 0 & - y_{wi} \\ 0 & 0 & 1 & - z_{wi} \\ - x_{wi} & - y_{wi} & - z_{wi} & l^{2} \end{matrix}],$ l²=x_wi ²+y_wi ²+z_wi ²-R²。 $Q = [\begin{matrix} 1 & 0 & 0 & - x_{wi} \\ 0 & 1 & 0 & - {the y}_{wi} \\ 0 & 0 & 1 & - z_{wi} \\ - x_{wi} & - {the y}_{wi} & - z_{wi} & l^{2} \end{matrix}],$ l ² =x _wi ² +y _wi ² +z _wi ² -R ² .

由于钢轨轮廓线上的点在光平面内，令x_t=x_w，y_t=y_w，则光平面方程可写成：Since the points on the rail contour line are in the light plane, let x _t = x _w , y _t = y _w , then the light plane equation can be written as:

X=Mt (15)X=Mt (15)

其中 $t = [\begin{matrix} x_{t} \\ y_{t} \\ 1 \end{matrix}] .$ 由式(14)和式(15)可得X^TQ＝X^Tt^TM＝0，in $t = [\begin{matrix} x_{t} \\ {the y}_{t} \\ 1 \end{matrix}] .$ From formula (14) and formula (15), it can be obtained that X ^T Q = X ^T t ^T M = 0,

令 $C = M^{T} QM = [\begin{matrix} {(b / a)}^{2} + 1 & bc / a^{2} & b / a^{2} + (b / c) x_{wi} - y_{wi} \\ bc / a^{2} & {(c / a)}^{2} + 1 & c / a^{2} + (c / a) x_{wi} - z_{wi} \\ b / a^{2} + (b / a) x_{wi} - y_{wi} & c / a^{2} + (c / a) x_{wi} - z_{wi} & 1 / a^{2} + (2 / a) x_{wi} + l^{2} \end{matrix}],$ make $C = m^{T} QM = [\begin{matrix} {(b / a)}^{2} + 1 & bc / a^{2} & b / a^{2} + (b / c) x_{wi} - {the y}_{wi} \\ bc / a^{2} & {(c / a)}^{2} + 1 & c / a^{2} + (c / a) x_{wi} - z_{wi} \\ b / a^{2} + (b / a) x_{wi} - {the y}_{wi} & c / a^{2} + (c / a) x_{wi} - z_{wi} & 1 / a^{2} + (2 / a) x_{wi} + l^{2} \end{matrix}],$

即有t^TCt=0，C为对称矩阵，因此t为二次曲线上的点。如果在轨腰同一圆弧中任取一对点作半径为R的空间球面，在这里R等于轨腰圆弧段的半径，则可得到两个交点，如式(16)所示：That is, t ^T Ct = 0, C is a symmetric matrix, so t is a point on the quadratic curve. If a pair of points in the same arc of the rail waist are randomly selected as a space sphere with radius R, where R is equal to the radius of the rail waist arc segment, two intersection points can be obtained, as shown in formula (16):

$\{\begin{matrix} {t t}^{T T} {C C}_{i i} t t = = 00 \\ {t t}^{T T} {C C}_{j j} t t = = 00 \end{matrix} - - - - - - ((1616))$

由检测原理可知，两个交点中距离摄像机光心（也就是距离世界坐标系原点）近的点即为所求圆弧段的圆心点，其在三维空间的坐标值可由式(15)可计算获得。在实际工程中，由于图像中每段圆弧轮廓有m对个点，可得到出m个圆心X₁，X₂，..．，X_m的坐标，令：It can be seen from the detection principle that the point closest to the optical center of the camera (that is, the origin of the world coordinate system) among the two intersection points is the center point of the arc segment to be obtained, and its coordinate value in three-dimensional space can be calculated by formula (15) get. In actual engineering, since there are m pairs of points in each arc profile in the image, m circle centers X ₁ , X ₂ ,... , the coordinates of X _m , let:

d_k=(x_wo-x_wk)²+(y_wo-y_wk)²+(z_wo-z_wk)² d _k =(x _wo -x _wk ) ² +(y _wo -y _wk ) ² +(z _wo -z _wk ) ²

其中x_wo，y_wo，z_wo为圆心最优点X_o的坐标分量，x_wk，y_wk，z_wk为X_k(k＝1，2，..．，m)的坐标分量，通过式(17)可求出X_o的最优解：Among them, x _wo , y _wo , z _wo are the coordinate components of the optimal point X _o of the center of the circle, x _wk , y _wk , z _wk are the coordinate components of X _k (k=1, 2,..., m), through the formula ( 17) The optimal solution of X _o can be obtained:

$\{\begin{matrix} {Σ Σ}_{k k = = 11}^{m m} {d d}_{k k} = = L L \\ \frac{&PartialD; &PartialD; L L}{{&PartialD; &PartialD; x x}_{wo the w}} = = \frac{&PartialD; &PartialD; L L}{&PartialD; &PartialD; {y the y}_{wo the w}} = = \frac{&PartialD; &PartialD; L L}{&PartialD; &PartialD; {z z}_{wo the w}} = = 00 \end{matrix} - - - - - - ((1717))$

轨头下端特征点提取Extraction of feature points at the lower end of the rail head

由于在检测原理上结构光和摄像机位于钢轨侧上方，实际图像轨头和轨腰存在明显的分割，因此能进行快速搜索定位。另一方面，由于图像经过细化处理大多会存在一个像素的偏差，因此实际搜索定位的得到的轨头下端点及其8邻点均有可能是实际的下端点，通过式(13)求其{X_b1，X_b2，.．．，X_b9)坐标，如图4所示。求其与轨腰圆弧段圆心点X_o的距离{d_ob1，d_ob2，...，d_ob9}，记理论距离与实际距离的误差为ε_i＝|d_obi-d_ob|，i＝1，2，..．，9，其中d_ob为理论距离。取记取得ε_min时所对应的X_bi为X_b，即为所求的轨头下端点。Since the structured light and the camera are located above the side of the rail in the detection principle, there is an obvious division between the rail head and the rail waist in the actual image, so fast search and positioning can be performed. On the other hand, due to the fact that most images have a deviation of one pixel after the thinning process, the lower endpoint of the track head and its eight neighbors obtained by the actual search and positioning may be the actual lower endpoint. {X _b1 , X _b2 , . . . ． , X _b9 ) coordinates, as shown in Figure 4. Find the distance between it and the center point X _o of the arc segment of the rail waist {d _ob1 , d _ob2 ,..., d _ob9 }, and record the error between the theoretical distance and the actual distance as ε _i ＝|d _obi -d _ob |, i =1,2,... , 9, where d _ob is the theoretical distance. Pick Note that X _bi corresponding to ε _min is X _b , which is the lower end point of the track head.

以下说明基于特征点生成钢轨轮廓标准模板的方法。The method for generating a rail profile standard template based on feature points is described below.

由于确立空间坐标系需要不在同一直线上的三个点，当轨腰圆弧段特征点和轨头下端点确定之后，在钢轨轮廓上任取不与X_o和X_b共线的一点X_r，取矢量以X_o点为原点建立笛卡尔坐标系，x’方向的矢量为则z’方向的矢量为 $\overset{&RightArrow;}{o^{'} z^{'}} = \overset{&RightArrow;}{o^{'} x^{'}} \times \overset{&RightArrow;}{X_{o} X_{r}},$ y’方向的矢量为如图5所示。一旦该坐标系建立，由标准钢轨的空间轮廓几何关系可知，整个钢轨的空间断面轮廓得以建立，因此，可动态的在每帧测量图像中生成一个钢轨轮廓的标准模板。Since the establishment of the spatial coordinate system requires three points that are not on the same straight line, after the feature point of the rail waist arc segment and the lower end point of the rail head are determined, a point X _r that is not collinear with X _o and X _b is randomly selected on the rail profile, take vector Establish a Cartesian coordinate system with X _o as the origin, and the vector in the x' direction is Then the vector in the z' direction is $\overset{&Right Arrow;}{o^{'} z^{'}} = \overset{&Right Arrow;}{o^{'} x^{'}} \times \overset{&Right Arrow;}{x_{o} x_{r}},$ The vector in the y' direction is As shown in Figure 5. Once the coordinate system is established, it can be known from the spatial profile geometric relationship of the standard rail that the spatial section profile of the entire rail is established. Therefore, a standard template of the rail profile can be dynamically generated in each frame of measurement image.

以下说明如何对比钢轨测量轮廓和标准模板得到磨耗值。The following shows how to compare the measured profile of the rail with the standard template to obtain the wear value.

将拍摄到的测量图像进行处理得到钢轨轮廓的测量光带，根据式(13)计算得到建立位于摄像机光心处世界坐标系下的钢轨轮廓空间三维坐标。建立新的世界坐标，令其原点位于钢轨底部的中心，x″轴与钢轨底边重合，y″轴与钢轨断面中心线重合，z″垂直于x"y"平面，由于通过特征点建立的坐标系o’x’y’z’与o″x″y″z″存在明确的旋转和平移关系，因此可将钢轨轮廓上的空间坐标映射到坐标系o″x″y″z″下，从而计算出磨耗值。Process the captured measurement image to obtain the measurement light band of the rail profile, and calculate the three-dimensional coordinates of the rail profile space in the world coordinate system at the optical center of the camera according to formula (13). Establish a new world coordinate, so that its origin is located at the center of the bottom of the rail, the x″ axis coincides with the bottom edge of the rail, the y″ axis coincides with the center line of the rail section, and z″ is perpendicular to the x”y” plane. The coordinate system o'x'y'z' has a clear rotation and translation relationship with o″x″y″z″, so the spatial coordinates on the rail profile can be mapped to the coordinate system o″x″y″z″, Thus the wear value is calculated.

实施例：Example:

本实施例采用标准60轨为检测对象，相机采用德国AVT-FC125 1934接口的CCD工业相机，分辨率为1280×960像素，在实际运用中可启动开窗功能，在不降低图像分辨率同时提高图像处理和数据传输能力。激光器输出波长为635nm的红色平面结构光，功率为40mW。在实验室内先进行相机参数和光平面方程参数的定标，确定了相机和光平面的空间几何关系。对60标准钢轨断面轮廓进行拍摄，如图6所示，经过三维重建后得到它的空间曲线，通过特征点的获取计算出相应位置的理论轮廓空间坐标值，表1列出了轨头轮廓参数的测量值和动态生成的模板理论值。从误差看，x分量的最大误差为0.0509mm，y分量的最大误差为0.1846mm，z分量的最大误差为0.1531mm。由于检测系统理论上要求光平面必须完全与钢轨断面重合，实际检测系统难以保证该条件，因此存在一定的误差。误差还涉及到相机参数和光平面参数的定标误差以及图像处理非亚像素误差等。以上整体误差小于0.16mm，能满足磨耗的测量要求。This embodiment adopts the standard 60 tracks as the detection object, and the camera adopts a CCD industrial camera with a German AVT-FC125 1934 interface, and the resolution is 1280×960 pixels. Image processing and data transfer capabilities. The laser outputs red planar structured light with a wavelength of 635nm and a power of 40mW. In the laboratory, the camera parameters and light plane equation parameters are calibrated first, and the spatial geometric relationship between the camera and the light plane is determined. The profile of the 60 standard rail section was photographed, as shown in Figure 6, its space curve was obtained after three-dimensional reconstruction, and the theoretical profile space coordinate value of the corresponding position was calculated through the acquisition of feature points. Table 1 lists the profile parameters of the rail head The measured value and the theoretical value of the dynamically generated template. From the perspective of error, the maximum error of the x component is 0.0509mm, the maximum error of the y component is 0.1846mm, and the maximum error of the z component is 0.1531mm. Because the detection system theoretically requires that the optical plane must completely coincide with the rail section, the actual detection system is difficult to guarantee this condition, so there are certain errors. Errors also involve calibration errors of camera parameters and light plane parameters, as well as non-sub-pixel errors in image processing. The above overall error is less than 0.16mm, which can meet the measurement requirements of wear.

表1钢轨轨头测量点与理论值的比较Table 1 Comparison of rail head measurement points and theoretical values

将完成定标的检测系统安装实验小型轨道车上，小型轨道车完全满足铁道运行安全标准，可运行于标准轨距为1435mm的线路上，最高运行速度45km／h。实验中对同一钢轨位置进行测量，图7a和图7b为测量得到的钢轨轮廓与标准轮廓的曲线比较图，表2为重复测量10次所得到的磨耗测量值。测量结果重复性高，标准差在0.07mm以内，具有良好的稳定性。The calibrated detection system will be installed on the experimental small rail car. The small rail car fully meets the safety standards of railway operation, and can run on a line with a standard gauge of 1435mm, with a maximum operating speed of 45km/h. The same rail position was measured in the experiment. Fig. 7a and Fig. 7b are curve comparison diagrams between the measured rail profile and the standard profile. Table 2 shows the wear measurement values obtained by repeating the measurement 10 times. The measurement results have high repeatability, the standard deviation is within 0.07mm, and it has good stability.

表2磨耗测量结果Table 2 Abrasion measurement results

本发明提出基于实际图像进行钢轨轨腰和轨头下端特征点提取，根据特征点动态生成世界坐标系下的钢轨轮廓模板，进而进行对比计算获得磨耗值的测量方法。该方法只需确定测量钢轨两个特征点即能根据标准钢轨轮廓的几何关系建立测量坐标系，且能快速、精确的得到标准模板，不需要将测量轮廓和基准设计轮廓进行对齐分析，打破了传统的基于静态模板匹配难的问题，极大的提高了磨耗测量的精确性；降低了图像分析处理的运算量并具有良好的稳定性。The invention proposes a method for extracting feature points of the rail waist and the lower end of the rail head based on actual images, dynamically generating a rail profile template in the world coordinate system according to the feature points, and then performing comparison and calculation to obtain a measurement method for wear values. This method only needs to determine the two feature points of the measured rail to establish a measurement coordinate system according to the geometric relationship of the standard rail profile, and can quickly and accurately obtain the standard template, without the need for alignment analysis of the measured profile and the reference design profile, which breaks the Traditionally based on the difficult problem of static template matching, it greatly improves the accuracy of wear measurement; reduces the computational load of image analysis and processing and has good stability.

以上显示和描述了本发明的基本原理、主要特征和本发明的优点。本行业的技术人员应该了解，本发明不受上述实施例的限制，上述实施例和说明书中描述的只是说明本发明的原理，在不脱离本发明精神和范围的前提下本发明还会有各种变化和改进，这些变化和改进都落入要求保护的本发明范围内。本发明要求保护范围由所附的权利要求书及其等同物界定。The basic principles, main features and advantages of the present invention have been shown and described above. Those skilled in the industry should understand that the present invention is not limited by the above-mentioned embodiments, and that described in the above-mentioned embodiments and the description only illustrates the principles of the present invention, and the present invention also has various aspects without departing from the spirit and scope of the present invention. Variations and improvements all fall within the scope of the claimed invention. The protection scope of the present invention is defined by the appended claims and their equivalents.

Claims

1., based on a measurement of rail wear based method for dynamic template, it is characterized in that, comprise the following steps:

1) at two one steel rail inside fronts, ccd video camera and fan laser light source are installed respectively;

2) each ccd video camera and light-plane parameters is demarcated;

3) volume coordinate of each pixel of rail profile in image is obtained according to rail profile space computing model;

4) web of the rail and rail head lower end unique point coordinate is extracted;

5) feature based dot generation rail profile standard form;

6) contrast rail measuring wheel exterior feature and standard form obtain wearing valve;

Step 1) in every side rail a ccd video camera and a fan laser light source are set, be all positioned at rail inside front, and the optical plane that sends of fan laser light source and rail is longitudinal vertical;

Step 2) in demarcate the detailed process of each ccd video camera parameter as follows,

Video camera is fixed in one plane, takes the gridiron pattern scaling board image that more than three are positioned at diverse location, mated with picture point by the point on scaling board, calculate the mapping matrix between them:

And solve camera parameters by this matrix; Wherein z _cfor the component of certain intersection point in camera coordinate system on gridiron pattern, f _x, f _y, u ₀, v ₀for the inner parameter of video camera; R is a rotation matrix with orthogonality, and T is a translation matrix, and they are external parameters of video camera; (x _w, y _w, z _w, 1) and be the coordinate of i-th point in space; (u, v, 1) is the image coordinate of i-th point; m _ijfor the i-th row j column element of projection matrix M; Decompose cancellation z _cobtain about m _ijlinear equation:

Calibration block there is n known point, obtains 2n the linear equation matrix about Metzler matrix element:

Specify m ₃₄=1, obtain 2n the 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 into: Km=U, K are 2n × 11, left side matrixes; M is 11 unknown dimensional vectors; U is the 2n dimensional vector on the right; K, U are known vector; Obtaining the solution of above-mentioned linear equation as 2n>11 by least square method is:

m＝(K ^TK) ^-1K ^TU，

M vector and m ₃₄=1 constitute required by solve Metzler matrix; By more than 6, space known point and their picture point coordinate, obtain Metzler matrix;

After obtaining Metzler matrix, calculated whole inside and outside parameter of video camera by relation;

Step 2) in demarcate the detailed process of light-plane parameters as follows:

Auxiliary camera C is increased during calibration ₂, with video camera C ₁form binocular scaling system, jointly take the light belt image be positioned on scaling board, now world coordinate system initial point is based upon video camera C ₁photocentre place, by respectively to C ₁, C ₂calibration, determines its inner parameter A ₁, A ₂and external parameter B ₁, B ₂, their projection matrix is respectively M ₁=A ₁b ₁=A ₁, M ₂=A ₂b ₂=A ₂[R ₁₂, T ₁₂], after CCD absorbs light belt formation RGB image, it is carried out to the image procossing such as extraction component, gray processing, the computing of difference shadow, binaryzation, refinement,

To extract the pixel coordinate of each point on striation axis, projection has following form:

Wherein, Z ₁, Z ₂for scaling board light belt being put the component of P in two camera coordinates; (u ₁, v ₁), (u ₂, v ₂) be respectively a P at C ₁, C ₂in pixel coordinate; It is more than simultaneous that two formulas obtain:

Thus, the world coordinates of a P is obtained; The locus of continuous mobile scaling board, obtains the world coordinates (x of m on light belt (m > 3) individual point _wi, y _wi, z _wi) (i=1,2,3 ... m);

The Representation Equation of spatial light plane is as follows:

Ax _w+By _w+Cz _w+1＝0，

Wherein, A, B, C are 3 components of this planar process vector n;

Construct an over-determined systems by m unique point, its matrix form is:

Or be abbreviated as GS=L, wherein, G is the matrix of coefficients on the equation left side, S=[A, B, C] ^t, L=[1,1 ..., 1] ^t, then utilize least square method to obtain S=(G ^tg) ^-1gTL and coefficient A, B, C;

Step 3) in obtain the detailed process of the volume coordinate of each pixel of rail profile in image according to rail profile space computing model as follows:

World coordinate system is based upon camera coordinates fasten, both orders overlap completely, then there is not rotation and translation relation between the two, now,

For unit matrix, and there is z _c=z _w, then

P point is also in the plane that laser projects simultaneously, meets optic plane equations:

Ax _w+By _w+Cz _w+1＝0，

In formula, A, B, C are optical plane coefficient; Simultaneous obtains:

Obtain the world coordinates (x of any point on rail profile outline line _w, y _w, z _w);

Step 4) in extract the detailed process of the web of the rail and rail head lower end unique point coordinate as follows,

(1) web of the rail feature point extraction:

Appoint in web of the rail circular arc after three-dimensional reconstruction and get 1 X _i(x _wi, y _wi, z _wi), make space sphere with radius R, note space spherical equation is:

X ^TQX＝0，

Wherein X is the coordinate that sphere is put, X=[x _w, y _w, z _w, 1] ^t, Q is the symmetric matrix of 4 × 4:

l ₂＝x _wi ²+y _wi ²+z _wi ²-R ²；

Make x _t=x _w, y _t=y _w, optic plane equations is write as:

X＝Mt，

Wherein,

Obtain X ^tqX=t ^tm ^tqMt=0,

Order:

Namely t is had ^tct=0, C are symmetric matrix, and t is the point on quafric curve; Appoint in the same circular arc of the web of the rail and get the space sphere that as radius be R at a pair, here R equals the radius of web of the rail arc section, obtains two intersection points:

The near point of two intersection point middle distance video camera photocentres is the centre point of required arc section, and it can calculate acquisition at three-dimensional coordinate figure; In image, every section of arc profile has m to individual point, obtains out m center of circle X ₁, X ₂..., X _mcoordinate, order:

d _k＝(x _wo-x _wk) ²+(y _wo-y _wk) ²+(z _wo-z _wk) ²

Wherein x _wo, y _wo, z _wofor center of circle optimum point X _ocoordinate components, x _wk, y _wk, z _wkfor X _k(k=1,2 ..., coordinate components m), obtains X by following formula _ooptimum solution:

(2) rail head lower end feature point extraction:

Ask rail head lower end unique point { X _b1, X _b2..., X _b9and web of the rail arc section centre point X _odistance { d _ob1, d _ob2..., d _ob9, the error of note theoretical and actual range is e _i=| d _obi-d _ob|, i=1,2 ..., 9, wherein d _obfor theoretical; Get e _min=min{e ₁, e ₂..., e ₉, keep to obtain e in mind _mintime corresponding X _bifor X _b, be required rail head lower extreme point;

Step 5) middle feature based dot generation rail profile standard form, its detailed process is as follows:

After web of the rail arc section unique point and rail head lower extreme point are determined, rail profile take up an official post get not with X _oand X _b1 X of conllinear _r, get vector with X _oput as initial point sets up cartesian coordinate system, the vector in x ' direction is the vector in z ' direction is the vector in y ' direction is set up the space section profile of rail, in every frame measurement image, generate the standard form of a rail profile;

Step 6) in the wide and standard form of contrast rail measuring wheel obtain wearing valve, its detailed process is as follows:

Carry out the measurement image photographed to process the measurement light belt obtaining rail profile, calculate the rail profile 3 d space coordinate set up and be positioned at video camera photocentre and conduct oneself in society under boundary's coordinate system; Set up new world coordinates, make its initial point be positioned at the center of rail foot, x " axle and rail base coincident; y " axle overlaps with rail profile center line, " plane, under the volume coordinate on rail profile being mapped to coordinate system o " x " y " z ", calculates wearing valve to z " perpendicular to x " y.