WO2022222428A1 - 基于无人机多视角影像的既有铁路轨道线高精度三维重建方法 - Google Patents

基于无人机多视角影像的既有铁路轨道线高精度三维重建方法 Download PDF

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WO2022222428A1
WO2022222428A1 PCT/CN2021/129311 CN2021129311W WO2022222428A1 WO 2022222428 A1 WO2022222428 A1 WO 2022222428A1 CN 2021129311 W CN2021129311 W CN 2021129311W WO 2022222428 A1 WO2022222428 A1 WO 2022222428A1
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rail
image
straight line
coordinates
dimensional
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PCT/CN2021/129311
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French (fr)
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王广帅
邓继伟
高文峰
赵海
张冠军
王凯
张英杰
聂虎啸
张文腾
岳亮
葛玉辉
高帅
赵罗明
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中国铁路设计集团有限公司
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Priority to US18/063,273 priority Critical patent/US20230112991A1/en

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    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06T—IMAGE DATA PROCESSING OR GENERATION, IN GENERAL
    • G06T7/00—Image analysis
    • G06T7/70—Determining position or orientation of objects or cameras
    • G06T7/73—Determining position or orientation of objects or cameras using feature-based methods
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01C—MEASURING DISTANCES, LEVELS OR BEARINGS; SURVEYING; NAVIGATION; GYROSCOPIC INSTRUMENTS; PHOTOGRAMMETRY OR VIDEOGRAMMETRY
    • G01C11/00—Photogrammetry or videogrammetry, e.g. stereogrammetry; Photographic surveying
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01C—MEASURING DISTANCES, LEVELS OR BEARINGS; SURVEYING; NAVIGATION; GYROSCOPIC INSTRUMENTS; PHOTOGRAMMETRY OR VIDEOGRAMMETRY
    • G01C11/00—Photogrammetry or videogrammetry, e.g. stereogrammetry; Photographic surveying
    • G01C11/04—Interpretation of pictures
    • G01C11/06—Interpretation of pictures by comparison of two or more pictures of the same area
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01C—MEASURING DISTANCES, LEVELS OR BEARINGS; SURVEYING; NAVIGATION; GYROSCOPIC INSTRUMENTS; PHOTOGRAMMETRY OR VIDEOGRAMMETRY
    • G01C11/00—Photogrammetry or videogrammetry, e.g. stereogrammetry; Photographic surveying
    • G01C11/04—Interpretation of pictures
    • G01C11/30—Interpretation of pictures by triangulation
    • G01C11/34—Aerial triangulation
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06T—IMAGE DATA PROCESSING OR GENERATION, IN GENERAL
    • G06T11/00—2D [Two Dimensional] image generation
    • G06T11/003—Reconstruction from projections, e.g. tomography
    • G06T11/006—Inverse problem, transformation from projection-space into object-space, e.g. transform methods, back-projection, algebraic methods
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06T—IMAGE DATA PROCESSING OR GENERATION, IN GENERAL
    • G06T7/00—Image analysis
    • G06T7/70—Determining position or orientation of objects or cameras
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06T—IMAGE DATA PROCESSING OR GENERATION, IN GENERAL
    • G06T2207/00—Indexing scheme for image analysis or image enhancement
    • G06T2207/10—Image acquisition modality
    • G06T2207/10032—Satellite or aerial image; Remote sensing
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06T—IMAGE DATA PROCESSING OR GENERATION, IN GENERAL
    • G06T2207/00—Indexing scheme for image analysis or image enhancement
    • G06T2207/30—Subject of image; Context of image processing
    • G06T2207/30172—Centreline of tubular or elongated structure
    • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
    • Y02T—CLIMATE CHANGE MITIGATION TECHNOLOGIES RELATED TO TRANSPORTATION
    • Y02T10/00—Road transport of goods or passengers
    • Y02T10/10—Internal combustion engine [ICE] based vehicles
    • Y02T10/40—Engine management systems

Definitions

  • the invention relates to the technical field of surveying and mapping of existing railway lines, in particular to a high-precision three-dimensional reconstruction method of existing railway track lines based on multi-view images of unmanned aerial vehicles.
  • UAV aerial survey has become an indispensable means of obtaining surveying and mapping image data. Compared with traditional aerial photography, UAV aerial survey has the advantages of low cost, flexibility and high spatial resolution of images, and it plays an important role in engineering survey and construction.
  • the survey tasks of the existing railway lines are gradually increasing.
  • the surveying and mapping tasks of existing railway lines include topographic surveying, plane surveying and mapping, leveling surveying, cross-section surveying and mapping, and station surveying and mapping, etc.
  • One of the core steps is to obtain the accurate plane and elevation coordinates of the line centerline, that is, to obtain the high-precision three-dimensional coordinates of the line. .
  • the present invention proposes a high-precision three-dimensional reconstruction method of existing railway track lines based on UAV multi-view images, which can obtain a high-precision track line plane without manual online operation. Elevation geographic coordinates provide high-precision basic data for subsequent line reconstruction and operation and maintenance.
  • the purpose of the present invention is to provide a high-precision three-dimensional reconstruction method of existing railway track lines based on multi-view images of unmanned aerial vehicles.
  • the line objects can be directly calculated by using image information.
  • Square coordinates plane and elevation accuracy of about 2cm
  • no need for field personnel to work online which can effectively improve the safety of railway operation line surveying and mapping. Therefore, this method has important engineering application value and application prospect.
  • a high-precision three-dimensional reconstruction method of an existing railway track line based on a multi-view image of an unmanned aerial vehicle of the present invention includes S1 , obtaining initial data, and the initial data includes: the original image of the multi-view UAV , the external orientation elements of the image, the internal parameters of the camera, and the initial coordinates of the center line of the top surface of the railway rail; S2, using the external orientation elements of the image and the internal parameters of the camera, the initial coordinates of the center line of the top surface of the rail are back-projected to the original image, and the straight line segment of the image is adjusted.
  • S3 use the nonlinear least squares method to optimize the image track top center line observation value, obtain the object coordinate parameters of the straight line segment of the track top surface, and use the object coordinate parameters to connect the adjacent
  • the straight line segments are connected in sequence to obtain the complete three-dimensional coordinates of the rail top centerline;
  • S4 according to the obtained three-dimensional coordinates of the rail top centerline, divide the rail straight/curved line segments, calculate the three-dimensional centerline coordinates of each segment in turn, and finally obtain the high-precision three-dimensional coordinates of the rail centerline .
  • the method when back-projecting the initial coordinates of the rail top midline to the original image, includes the following method: according to a preset length threshold, segment the input initial rail top midline to obtain a plurality of rail tops The straight line segment of the surface center line; according to the collinear condition equation, using the precise external orientation elements of the image and the internal parameters of the camera, the segmented straight line segment of the rail top is back-projected to the original image of the UAV with multiple viewing angles, and each rail top straight line is obtained. The rough position of the segment on the image.
  • the method of optimizing the observation value of the image rail top midline by using the nonlinear least squares method to obtain the object coordinate parameters of the straight line segment of the rail top surface is as follows: Calculate the angle between the projection planes of the two images as the intersection angle, and take the object-side straight line segment formed by the intersection of the projections of the two image lines with the largest intersection angle as the initial value of the least squares adjustment of the straight line segment; it will be used as the initial value
  • the Euclidean distance between the back-projected line on the image and the observation value of the corresponding image line is used as the cost, and the cost equation is listed; according to the cost equation, calculate the overall least squares optimization of any object square rail top line segment Cost function; perform Taylor series expansion on the overall cost function, and omit higher-order terms to obtain the linearized error equation; use the linearized error equation to solve the top surface of the track according to the least squares adjustment criterion Object coordinate parameters of the line segment.
  • any object-square rail top straight line segment Li if it has image line observations on multiple images, several cost equations can be listed, and the straight line Li is the least two
  • the overall cost function for multiplication optimization is of the form:
  • C represents the overall back-projection cost of the least squares optimization of the straight line Li
  • dist(*) is the Euclidean distance function from the observation value of the image line to the back-projection line of the top line of the track
  • proj(*) represents the back-projection function based on perspective imaging
  • T k is the inner and outer azimuth elements of the k - th image where Li can be observed
  • lik represents the observation value of the image line segment corresponding to Li on the image.
  • the adjacent straight line segments are connected in sequence by using the object coordinate parameters to obtain the complete three-dimensional coordinates of the rail top center line; including the distance image line on the obtained rail top straight line
  • the closest point of the projection ray of the end point is taken as the point with the same name of the end point on the top line of the track, and the coordinates of the point with the same name of the end point of all image lines on the line of the track top line are calculated, and the average value is taken as the end point of the line top line; according to the start and end of each segment
  • the coordinates determine the corresponding connection order, calculate the average of the end points of the adjacent rail top straight line segments that are close to each other as the rail node coordinates, realize the edge connection of the adjacent straight line segments, and obtain the complete rail top surface centerline.
  • the three-dimensional centerline coordinates of each segment are sequentially calculated, and when the high-precision three-dimensional coordinates of the track centerline are finally obtained, including if it is a straight line segment, each node P G1 on the straight line segment , calculate the point P G2 closest to P G1 on G 2 , and calculate the midpoint of P G1 and P G2 as the node of the three-dimensional midline.
  • the three-dimensional centerline of the straight line segment can be obtained.
  • the elevation value of the three-dimensional midline node of the curve segment takes the elevation Z P of the corresponding inner rail point, and the three-dimensional midline node coordinates corresponding to the point P N are (X S , Y S , Z P ).
  • the method for high-precision 3D reconstruction of existing railway track lines based on UAV multi-view images disclosed in the present application has at least the following advantages:
  • the present invention utilizes the internal geometric relationship of the multi-view image area network to reconstruct the track directly based on the result of the three-dimensional orientation of the image, avoiding the errors introduced by the orthophoto and the three-dimensional model making process, and the present invention can achieve a higher calculation of the center line of the top surface of the rail.
  • Accuracy plane elevation accuracy can reach 2cm), which can fully meet the accuracy requirements of existing line surveying and mapping;
  • the present invention designs a track straight/curved segment judgment method based on a rectangular slice space, which can accurately classify track points on straight/curved segments, thereby ensuring the accuracy of the three-dimensional coordinate calculation result of the track center line;
  • FIG. 1 is a flowchart of a method for high-precision 3D reconstruction of existing railway track lines based on UAV multi-view images provided by the present invention.
  • FIG. 2 is a schematic diagram of the least squares optimization of the centerline of the top surface of the rail in the high-precision three-dimensional reconstruction method of the existing railway track line based on the multi-view image of the UAV according to the present invention.
  • FIG. 3 is a schematic diagram of the track straightness/curve judgment of the high-precision three-dimensional reconstruction method of the existing railway track line based on the multi-view image of the UAV according to the present invention.
  • a method for high-precision three-dimensional reconstruction of an existing railway track line based on a multi-view image of an unmanned aerial vehicle includes the following steps:
  • Step 1 obtaining initial data, the initial data includes: the original image of the multi-view UAV, the external orientation elements of the image, the internal parameters of the camera (the results after the three-dimensional orientation) and the initial coordinates of the center line of the top surface of the railway rail;
  • Step 2 the centerline of the top surface of the rail is obtained from the drone image.
  • the initial coordinates of the centerline of the rail top surface are back-projected to the original image, and the position of the straight line segment of the image is fine-tuned through human-computer interaction to obtain accurate image rail top centerline observations.
  • the specific method is as follows:
  • Step 2.1 Automatic segmentation of the centerline of the top surface of the rail.
  • the preset length threshold usually set to 10-15m
  • Step 2.2 Prediction of the back projection of the midline of the top surface of the rail. Based on the collinear condition equation, using the precise external azimuth elements of the image and the internal parameters of the camera, the rail top straight segment segmented in step 2.2 is back-projected onto the UAV image, and the rough position of each rail top straight segment on the image is obtained. ;
  • Step 2.3 is based on the man-machine interactive image track top line precision measurement. According to the rough position of each track top line segment obtained in step 2.2, the end point position of the image line segment is finely adjusted by means of human-computer interaction to ensure that each image track line segment is accurately located on the midline of the track top surface.
  • Step 3 Calculate the centerline of the top surface of the rail based on the nonlinear least squares method. Taking the straight line segment of the image track top obtained in step 2 as the observation value, the object coordinate parameters of the straight line segment of the track top surface are optimized by the nonlinear least square method, and the adjacent straight line segments are sequentially connected to form a complete center line of the track top.
  • the specific method is as follows:
  • Step 3.1 Calculation of initial value of straight line segment adjustment. For each straight line segment at the top of the track, calculate the angle between the two image projection planes (the plane formed by the photography center and the image track line) as the intersection angle. As the initial value for the least squares adjustment of the line segment.
  • Step 3.2 Least squares optimization of the midline of the top surface of the rail. Specific steps are as follows:
  • step 3.2.1 the straight line segment of the track top obtained in step 3.1 is used as the initial value, and the Euclidean distance between the back-projected line on the image and the observation value of the corresponding image line is used as the cost, and the cost equation is listed.
  • the cost value d q of point q can be calculated, and the cost value of the track top image line is (d p +d q )/2.
  • L O is the observed value of the image line
  • L P is the back-projection line of the corresponding object line on the image
  • the cost value is (d 1 +d 2 )/2.
  • Equation (3) C represents the overall back-projection cost of the least squares optimization of the straight line Li
  • dist(*) is the Euclidean distance function from the observation value of the image line to the back-projection line of the top line of the track
  • proj(*) represents the perspective imaging-based Back-projection function
  • T k is the inner and outer azimuth elements of the k - th image where Li can be observed
  • lik represents the observed value of the image line segment corresponding to Li on the image.
  • step 3.2.2 Taylor series expansion is performed on the terms of formula (3), and the higher-order terms are omitted.
  • the error equation after linearization is of the form:
  • VL A L lb L , PL (4)
  • VL is the residual distance of the back-projection distance of the rail top straight line
  • l [ ⁇ X s , ⁇ Y s , ⁇ Z s , ⁇ u, ⁇ v]
  • T is the correction number vector of the rail top straight line parameters
  • PL is the objective function pair
  • b L is a constant vector
  • P L is a unit weight matrix.
  • Step 3.3 Calculate the end point of the straight line segment on the top surface of the rail.
  • the specific method is as follows: Calculate the point on the track top line obtained in step 3.2 that is closest to the projected ray of the end point of the image line, as the point with the same name of the end point on the track top line. Calculate the coordinates of the points with the same name on the top line of all image lines, and take the average value as the end point of the top line.
  • Step 3.4 Fusion of the straight line segment on the top surface of the rail For the straight line segment of the rail top obtained in step 3.3, the corresponding connection sequence is determined according to the start and end coordinates of each segment. The average value of the coordinates of the end points of the adjacent straight line segments of the rail top that are close to each other is calculated as the rail node coordinates, so as to realize the edge processing of the adjacent straight line segments and obtain the complete center line of the top surface of the rail.
  • Step 4 According to the obtained three-dimensional coordinates of the center line of the rail top, divide the straight/curved line segments of the rail, calculate the three-dimensional center line coordinates of each segment in turn, and finally obtain the high-precision three-dimensional coordinates of the track center line.
  • the specific method is as follows:
  • Step 4.1 Rail straight/curved line segment division.
  • the specific method is as follows:
  • Step 4.1.1 Calculate the azimuth angle of the centerline of the top surface of the rail. For the midline of the rail top surface obtained in step 3, the azimuth angle of each section is calculated with the node as the dividing point, and the minimum value ⁇ min and the maximum value ⁇ max of the azimuth angle are counted;
  • Step 4.1.2 Determine the straight/curved section of the rail. Taking the ⁇ min obtained in step 4.1.1 as the starting point and the preset threshold ⁇ as the search width, a rectangular slice space is formed, and the number N of rail nodes falling into the rectangle is counted. If N>N min , the rail nodes in the rectangular space are all straight points; otherwise, the rail nodes in the rectangular space are determined to be curved points. As shown in Figure 3 , the horizontal axis represents the straight line segment of the rail, and the vertical axis represents the azimuth angle corresponding to the straight line segment, then the points in the S1 and S3 regions are straight line points, and the S2 region is the curve segment point. Move the rectangular slice up a distance of ⁇ /2, and continue to judge straight/curved points according to the above method. Until the minimum value of the rectangular slice space reaches the maximum value of the azimuth angle, this step ends;
  • Step 4.2 Calculation of the coordinates of the three-dimensional midline nodes of the orbit.
  • Step 4.1 Divide the rail nodes into several straight line segments and curve segments, and calculate the three-dimensional centerline coordinates of each segment in turn for the rail points of each segment. Assuming that the two rails of the track are G 1 and G 2 respectively, the specific method for calculating the three-dimensional centerline is as follows:
  • Step 4.2(b) The elevation value of the three-dimensional midline node of the curve segment takes the elevation Z P of the corresponding inner track point, so that the three-dimensional midline node coordinates corresponding to the point P N can be obtained as (X S , Y S , Z P ).
  • the three-dimensional centerline coordinates of the entire track can be obtained by processing the straight and curved segments of the track according to the above (a) and (b) methods. Combining the three-dimensional coordinates of the midline of the top surface of the rail obtained in step 3, the three-dimensional coordinates of the completed track can be obtained.

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Abstract

一种基于无人机多视角影像的既有铁路轨道线高精度三维重建方法，包括获取初始数据，无人机影像钢轨顶面中线获取，基于非线性最小二乘方法的钢轨顶面中线计算及轨道中线三维坐标计算；基于计算机视觉和摄影测量中的多视几何原理，利用影像信息直接计算得到线路物方坐标，无需外业人员上线作业，能够有效提高铁路运营线测绘工作的安全性。因此，具有重要的工程应用价值和应用前景。

Description

基于无人机多视角影像的既有铁路轨道线高精度三维重建方法 技术领域
本发明涉及铁路既有线路测绘技术领域，尤其涉及基于无人机多视角影像的既有铁路轨道线高精度三维重建方法。
背景技术
无人机航测已成为一种不可或缺的测绘影像数据获取手段。相较于传统航摄，无人机航测具有成本低、机动灵活、影像空间分辨率高的优势，其在工程勘察建设中发挥着重要的作用。随着我国铁路大规模提速改造工程的推进，铁路既有线的勘测任务逐渐增多。通常铁路既有线的测绘任务包括地形测绘、平面测绘、水准测量、横断面测绘和站场测绘等，其中核心步骤之一是获取线路中线精确的平面和高程坐标，即获取线路的高精度三维坐标。
目前，既有铁路三维中线的获取主要有三种方式：(1)全站仪、GPS-RTK测量。这种方法可以满足既有线测绘的精度要求，但是效率较低，且需要人工上线作业，安全风险高；(2)传统大飞机航摄测绘。此方法只需人工内业在航摄立体像对上采集轨道点，即可得到铁路中线坐标，避免了人工上线作业，但其缺点是测量精度较低(5～10cm)，尤其是高程方向上的精度往往无法满足实际需求；(3)轨道车载激光雷达测绘。这种方法可以直接得到高精度的轨道点坐标数据，其缺点也是需要上线测量，需要与运营单位进行大量的沟通协调工作。总体来看，现有的三种方法各有特点，但均无法同时兼顾不上线与高精度这两个要求。
针对铁路既有线测绘上线难问题，本发明提出了一种基于无人机多视角影像的既有铁路轨道线高精度三维重建方法，在无需人工上线作业的前提下，可获得高精度轨道线平面高程地理坐标，为后续线路改造和运营维护提供高精度的基础数据。
发明内容
因此，本发明的目的在于提供一种基于无人机多视角影像的既有铁路轨道线高精度三维重建方法，基于计算机视觉和摄影测量中的多视几何原理，利用影像信息直接计算得到线路物方坐标(平面和高程精度约2cm)，无需外业人员上线作业，能够有效提高铁路运营线测绘工作的安全性。因此，本方法具有重要的工程应用价值和应用前景。
为了实现上述目的，本发明的一种基于无人机多视角影像的既有铁路轨道线高精度三维重建方法，包括S1，获取初始数据，所述初始数据包括：无人机多视角的原始影像、影像外方位元素、相机内参数及铁路钢轨顶面中线初始坐标；S2，利用影像的外方位元素和相机内参数，将钢轨顶面中线初始坐标反投影至 所述原始影像，调整影像直线段位置，得到精确的影像轨顶中线观测值；S3，利用非线性最小二乘法优化影像轨顶中线观测值，得到轨道顶面直线段的物方坐标参数，利用所述物方坐标参数将相邻直线段顺次连接，得到完整的轨顶中线三维坐标；S4，根据得到的轨顶中线三维坐标，划分钢轨直/曲线线段，依次计算各段三维中线坐标，最终得到高精度的轨道中线三维坐标。
优选的，在S2中，将钢轨顶面中线初始坐标反投影至所述原始影像时，包括如下方法：根据预设长度阈值，对输入的初始铁路轨顶中线进行分段，得到多条钢轨顶面中线直线段；根据共线条件方程，利用精确的影像外方位元素和相机内参数，将分段后的轨顶直线段反投影至无人机多视角的原始影像上，得到各轨顶直线段在影像上的粗略位置。
在上述任意一项实施例中优选的，在S2中，调整影像直线段位置时，采用精调影像直线段端点位置，实现每条影像轨道线段准确位于轨道顶面中线上。
在上述任意一项实施例中优选的，在S3中，利用非线性最小二乘法优化影像轨顶中线观测值，得到轨道顶面直线段的物方坐标参数方法如下：对各钢轨顶面中线直线段，计算两两影像投影平面之间的夹角作为交会角，以交会角最大的两张影像线投影相交形成的物方直线段作为直线段最小二乘平差的初始值；将作为初始值的轨顶直线段，在影像上的反投影直线与相应影像线观测值间的欧式距离作为代价，列出代价方程；根据代价方程计算任意一条物方轨顶直线段的最小二乘优化的整体代价函数；对所述整体代价函数进行泰勒级数展开，并略去高阶项，得到线性化之后的误差方程；利用线性化之后的误差方程，按照最小二乘平差准则，求解轨道顶面直线段的物方坐标参数。
在上述任意一项实施例中优选的，对于任意物方轨顶直线段L i，若其在多张影像上具有影像线观测值，则可列出若干个代价方程，则直线L i最小二乘优化的整体代价函数形式如下：
Figure PCTCN2021129311-appb-000001
其中：C表示直线L i最小二乘优化的整体反投影代价，dist(*)为影像线观测值到轨顶线反投影直线的欧式距离函数，proj(*)表示基于透视成像的反投影函数，T k为能观测到L i的第k张影像的内外方位元素，l ik表示L i在该影像上对应的影像直线段观测值。
在上述任意一项实施例中优选的，在S3中，利用所述物方坐标参数将相邻直线段顺次连接，得到完整的轨顶中线三维坐标；包括得到的轨顶直线上距离影像线端点投影光线最近的点，作为该端点在轨顶直线上的同名点，计算所有影像线端点在轨顶直线上的同名点坐标，取其平均值作为轨顶直线的端点；依据各段的起止坐标确定相应的连接顺序，计算相邻轨顶直线段相互靠近的端点坐标平均值作为钢轨节点坐标，实现相邻直线段接边，得到完整的钢轨顶面中线。
在上述任意一项实施例中优选的，在S4中，根据得到的轨顶中线三维坐标，划分钢轨直/曲线线段时， 包括以下方法：对得到的钢轨顶面中线，以钢轨节点作为分界点，计算各段的方位角，并统计方位角最小值和最大值；以预设的阈值δ作为搜索宽度，形成长方形的切片空间，统计落入该长方形内的钢轨节点数目N；若N大于预设阈值，则该长方形空间内的钢轨节点均为直线点；否则该长方形空间内的钢轨节点为曲线点；以最小值作为起点，将长方形切片向上移动距离δ/2，继续判断直/曲线点；直至长方形切片空间达到方位角最大值。
在上述任意一项实施例中优选的，在S4中，依次计算各段三维中线坐标，最终得到高精度的轨道中线三维坐标时，包括若为直线段，对该直线段上每个节点P G1，计算G 2上与P G1最近的点P G2，计算P G1和P G2的中点，作为三维中线的节点。遍历钢轨G 1上所有节点进行上述操作，可得到直线段的三维中线。
在上述任意一项实施例中优选的，在S4中，依次计算各段三维中线坐标，最终得到高精度的轨道中线三维坐标时，包括若为曲线段，对每一个内轨节点P N(X P,Y P,Z P)，首先计算二维平面上其前后两直线段法方向的方位角α 1和α 2，则将平面点P T(X P,Y P)沿(α 1+α 2)/2方向朝轨道内侧偏移距离d＝(1.435+θ)/2，其中θ为铁轨顶面宽度值，得到坐标(X S,Y S)，计算方法如下：
Figure PCTCN2021129311-appb-000002
曲线段三维中线节点的高程值取相应内轨点的高程Z P，得到点P N对应的三维中线节点坐标为(X S,Y S,Z P)。
本申请公开的基于无人机多视角影像的既有铁路轨道线高精度三维重建方法，相比于现有技术，至少具有以下优点：
1、本发明利用多视角影像区域网内部几何关系，直接基于影像空三定向结果重建轨道，避免了正射影像和三维模型制作过程引入的误差，本发明可以达到较高的钢轨顶面中线计算精度(平面高程精度均可达到2cm)，完全可以满足既有线测绘的精度要求；
2本发明设计了基于长方形切片空间的轨道直/曲线段判断方法，可以准确对轨道点进行直/曲段点分类，从而保证轨道中线三维坐标计算结果的准确性；
3相比于现有既有线测量方法(GPS/RTK测量、大飞机航摄、车载激光雷达)，本方法同时兼顾了线下测量与高精度两个优势，有效提高了作业效率与安全性，具有较强的实用和推广价值。
附图说明
图1为本发明提供的基于无人机多视角影像的既有铁路轨道线高精度三维重建方法的流程图。
图2为本发明基于无人机多视角影像的既有铁路轨道线高精度三维重建方法的钢轨顶面中线最小二乘优化示意图。
图3为本发明基于无人机多视角影像的既有铁路轨道线高精度三维重建方法的轨道直/曲线判断示意图。
具体实施方式
以下通过附图和具体实施方式对本发明作进一步的详细说明。
如图1所示，本发明一方面实施例提供的一种基于无人机多视角影像的既有铁路轨道线高精度三维重建方法，包括以下步骤：
步骤1，获取初始数据，所述初始数据包括：无人机多视角的原始影像、影像外方位元素、相机内参数(空三定向后的成果)及铁路钢轨顶面中线初始坐标；
步骤2，无人机影像钢轨顶面中线获取。利用影像的外方位元素和相机内参数，将钢轨顶面中线初始坐标反投影至原始影像，通过人机交互的方式进行影像直线段位置精调，得到精确的影像轨顶中线观测值。具体方法如下：
步骤2.1钢轨顶面中线自动分段。根据预设长度阈值(一般设为10～15m)，对输入的初始铁路轨顶中线进行分段，得到多条钢轨顶面中线直线段；
步骤2.2钢轨顶面中线反投影预测。基于共线条件方程，利用精确的影像外方位元素和相机内参数，将步骤2.2分段后的轨顶直线段反投影至无人机影像上，得到各轨顶直线段在影像上的粗略位置；
步骤2.3基于人机交互式的影像轨顶直线精测。根据步骤2.2得到的各轨顶直线段的粗略位置，通过人机交互的方式精调影像直线段端点位置，保证每条影像轨道线段准确位于轨道顶面中线上。
步骤3，基于非线性最小二乘方法的钢轨顶面中线计算。以步骤2得到的影像轨顶直线段作为观测值，通过非线性最小二乘方法优化轨道顶面直线段的物方坐标参数，并将相邻直线段顺次连接形成完整的轨顶中线。具体方法如下：
步骤3.1直线段平差初始值计算。对各轨顶直线段，计算两两影像投影平面(摄影中心与影像轨道线形成的平面)之间的夹角作为交会角，以交会角最大的两张影像线投影相交形成的物方直线段作为直线段最小二乘平差的初始值。本发明采用点向式来描述物方直线，若直线段L上某点坐标为[X,Y,Z] T，直线单位方向向量为
Figure PCTCN2021129311-appb-000003
则该直线物方参数为L＝[X,Y,Z,u,v] T。
步骤3.2钢轨顶面中线最小二乘优化。具体步骤如下：
步骤3.2.1以步骤3.1得到的轨顶直线段作为初始值，将其在影像上的反投影直线与相应影像线观测值间的欧式距离作为代价，列出代价方程。代价值的计算方法如下：若直线参数为l＝[X,Y,Z,u,v,w] T，投影中心坐标为[X S,Y S,Z S] T，a i、b i和c i(i＝1,2,3)为摄影测量旋转矩阵中的元素值，f为焦距，x 0和y 0为像主点坐标。轨顶影像线l的两端点分别为p＝[x p,y p] T和q＝[x q,y q] T，则p点代价值计算公式如下：
Figure PCTCN2021129311-appb-000004
公式(1)中，各变量符号定义如下：
Figure PCTCN2021129311-appb-000005
同理，可计算得到q点的代价值d q，则该条轨顶影像线的代价值为(d p+d q)/2。如图2所示，L O为影像线观测值，L P为相应物方线在影像上的反投影线，则代价值为(d 1+d 2)/2。对于物方轨顶直线段L i，若其在多张影像上具有影像线观测值，则可列出若干个公式(1)和(2)所述代价方程，则直线L i最小二乘优化的整体代价函数形式如下：
Figure PCTCN2021129311-appb-000006
式(3)中C表示直线L i最小二乘优化的整体反投影代价，dist(*)为影像线观测值到轨顶线反投影直线的欧式距离函数，proj(*)表示基于透视成像的反投影函数，T k为能观测到L i的第k张影像的内外方位元素，l ik表示L i在该影像上对应的影像直线段观测值。
步骤3.2.2对公式(3)各项进行泰勒级数展开，并略去高阶项。线性化之后的误差方程形式如下：
V L＝A Ll-b L，P L       (4)
式(4)中，V L为轨顶直线反投影距离残差，l＝[ΔX s,ΔY s,ΔZ s,Δu,Δv] T为轨顶直线参数改正数向量，P L为目标函数对直线参数向量的一阶偏导数矩阵，b L为常数向量，P L为单位权矩阵。按照最小二乘平差准则，精确求解轨顶直线参数。
步骤3.3钢轨顶面直线段端点计算。具体方法如下：计算步骤3.2得到的轨顶直线上距离影像线端点投影光线最近的点，作为该端点在轨顶直线上的同名点。计算所有影像线端点在轨顶直线上的同名点坐标，取其平均值作为轨顶直线的端点。
步骤3.4钢轨顶面直线段融合。对于步骤3.3得到的轨顶直线段，依据各段的起止坐标确定相应的连接顺序。计算相邻轨顶直线段相互靠近的端点坐标平均值作为钢轨节点坐标，以实现相邻直线段的接边处理，得到完整的钢轨顶面中线。
步骤4，根据得到的轨顶中线三维坐标，划分钢轨直/曲线线段，依次计算各段三维中线坐标，最终得到高精度的轨道中线三维坐标。具体方法如下：
步骤4.1钢轨直/曲线线段划分。具体方法如下：
步骤4.1.1钢轨顶面中线方位角计算。对步骤3得到的钢轨顶面中线，以节点作为分界点，计算各段的方位角，并统计方位角最小值β min和最大值β max；
步骤4.1.2判断钢轨直/曲线段。以步骤4.1.1得到的β min作为起点，以预设的阈值δ作为搜索宽度，形成长方形的切片空间，统计落入该长方形内的钢轨节点数目N。若N>N min，则该长方形空间内的钢轨节点均为直线点；反之，判定该长方形空间内的钢轨节点为曲线点。如附图3所示，横轴表示钢轨直线段，纵轴表示直线段对应的方位角，则S 1和S 3区域内的点为直线点，S 2区域内为曲线段点。将长方形切片向上 移动距离δ/2，按照上述方法继续判断直/曲线点。直至长方形切片空间的最小值达到方位角最大值，此步骤结束；
步骤4.2轨道三维中线节点坐标计算。步骤4.1将钢轨节点划分为了若干直线段和曲线段，对各段钢轨点，依次计算各段三维中线坐标。假设轨道的两钢轨分别为G 1和G 2，则三维中线计算的具体方法如下：
(a)若为直线段，对该直线段上每个节点P G1，计算G 2上与P G1最近的点P G2，计算P G1和P G2的中点，作为三维中线的节点。遍历G 1上所有节点进行上述操作，可得到直线段的三维中线；
(b)若为曲线段，对每一个内轨节点P N(X P,Y P,Z P)，首先计算二维平面上其前后两直线段法方向的方位角α 1和α 2，则将平面点P T(X P,Y P)沿(α 1+α 2)/2方向朝轨道内侧偏移距离d＝(1.435+θ)/2，其中θ为铁轨顶面宽度值，得到坐标(X S,Y S)，计算方法如下：
Figure PCTCN2021129311-appb-000007
步骤4.2(b)曲线段三维中线节点的高程值取相应内轨点的高程Z P，由此可以得到点P N对应的三维中线节点坐标为(X S,Y S,Z P)。
对轨道的直线和曲线段按照上述(a)和(b)方法进行处理，即可得到整条轨道的三维中线坐标。联合步骤3得到的钢轨顶面中线三维坐标，即可得到完成的轨道三维坐标。
显然，上述实施例仅是为清楚地说明所作的举例，而并非对实施方式的限定。对于所属领域的普通技术人员来说，在上述说明的基础上还可以做出其它不同形式的变化或变动。这里无需也无法对所有的实施方式予以穷举。而由此所引伸出的显而易见的变化或变动仍处于本发明创造的保护范围之中。

Claims (9)

  1. 一种基于无人机多视角影像的既有铁路轨道线高精度三维重建方法，其特征在于：包括
    S1，获取初始数据，所述初始数据包括：无人机多视角的原始影像、影像外方位元素、相机内参数及铁路钢轨顶面中线初始坐标；
    S2，利用影像的外方位元素和相机内参数，将钢轨顶面中线初始坐标反投影至所述原始影像，调整影像直线段位置，得到精确的影像轨顶中线观测值；
    S3，利用非线性最小二乘法优化影像轨顶中线观测值，得到轨道顶面直线段的物方坐标参数，利用所述物方坐标参数将相邻直线段顺次连接，得到完整的轨顶中线三维坐标；
    S4，根据得到的轨顶中线三维坐标，划分钢轨直/曲线线段，依次计算各段三维中线坐标，最终得到高精度的轨道中线三维坐标。
  2. 根据权利要求1所述的基于无人机多视角影像的既有铁路轨道线高精度三维重建方法，其特征在于：在S2中，将钢轨顶面中线初始坐标反投影至所述原始影像时，包括如下方法：
    根据预设长度阈值，对输入的初始铁路轨顶中线进行分段，得到多条钢轨顶面中线直线段；
    根据共线条件方程，利用精确的影像外方位元素和相机内参数，将分段后的轨顶直线段反投影至无人机多视角的原始影像上，得到各轨顶直线段在影像上的粗略位置。
  3. 根据权利要求2所述的基于无人机多视角影像的既有铁路轨道线高精度三维重建方法，其特征在于：在S2中，调整影像直线段位置时，采用精调影像直线段端点位置，实现每条影像轨道线段准确位于轨道顶面中线上。
  4. 根据权利要求2所述的基于无人机多视角影像的既有铁路轨道线高精度三维重建方法，其特征在于：在S3中，利用非线性最小二乘法优化影像轨顶中线观测值，得到轨道顶面直线段的物方坐标参数方法如下：对各钢轨顶面中线直线段，计算两两影像投影平面之间的夹角作为交会角，以交会角最大的两张影像线投影相交形成的物方直线段作为直线段最小二乘平差的初始值；
    将作为初始值的轨顶直线段，在影像上的反投影直线与相应影像线观测值间的欧式距离作为代价，列出代价方程；
    根据代价方程计算任意一条物方轨顶直线段的最小二乘优化的整体代价函数；
    对所述整体代价函数进行泰勒级数展开，并略去高阶项，得到线性化之后的误差方程；
    利用线性化之后的误差方程，按照最小二乘平差准则，求解轨道顶面直线段的物方坐标参数。
  5. 根据权利要求4所述的基于无人机多视角影像的既有铁路轨道线高精度三维重建方法，其特征在于：对于任意物方轨顶直线段L i，若其在多张影像上具有影像线观测值，则可列出若干个代价方程，则直线L i最小二乘优化的整体代价函数形式如下：
    Figure PCTCN2021129311-appb-100001
    其中：C表示直线L i最小二乘优化的整体反投影代价，dist(*)为影像线观测值到轨顶线反投影直线的 欧式距离函数，proj(*)表示基于透视成像的反投影函数，T k为能观测到L i的第k张影像的内外方位元素，l ik表示L i在该影像上对应的影像直线段观测值。
  6. 根据权利要求2所述的基于无人机多视角影像的既有铁路轨道线高精度三维重建方法，其特征在于：在S3中，利用所述物方坐标参数将相邻直线段顺次连接，得到完整的轨顶中线三维坐标；包括
    得到的轨顶直线上距离影像线端点投影光线最近的点，作为该端点在轨顶直线上的同名点，计算所有影像线端点在轨顶直线上的同名点坐标，取其平均值作为轨顶直线的端点；
    依据各段的起止坐标确定相应的连接顺序，计算相邻轨顶直线段相互靠近的端点坐标平均值作为钢轨节点坐标，实现相邻直线段接边，得到完整的钢轨顶面中线。
  7. 根据权利要求6所述的基于无人机多视角影像的既有铁路轨道线高精度三维重建方法，其特征在于：在S4中，根据得到的轨顶中线三维坐标，划分钢轨直/曲线线段时，包括以下方法：
    对得到的钢轨顶面中线，以钢轨节点作为分界点，计算各段的方位角，并统计方位角最小值和最大值；
    以预设的阈值δ作为搜索宽度，形成长方形的切片空间，统计落入该长方形内的钢轨节点数目N；
    若N大于预设阈值，则该长方形空间内的钢轨节点均为直线点；否则该长方形空间内的钢轨节点为曲线点；
    以最小值作为起点，将长方形切片向上移动距离δ/2，继续判断直/曲线点；直至长方形切片空间达到方位角最大值。
  8. 根据权利要求1所述的基于无人机多视角影像的既有铁路轨道线高精度三维重建方法，其特征在于：在S4中，依次计算各段三维中线坐标，最终得到高精度的轨道中线三维坐标时，包括
    若为直线段，对该直线段上每个节点P G1，计算G 2上与P G1最近的点P G2，计算P G1和P G2的中点，作为三维中线的节点。遍历钢轨G 1上所有节点进行上述操作，可得到直线段的三维中线。
  9. 根据权利要求1所述的基于无人机多视角影像的既有铁路轨道线高精度三维重建方法，其特征在于：在S4中，依次计算各段三维中线坐标，最终得到高精度的轨道中线三维坐标时，包括
    若为曲线段，对每一个内轨节点P N(X P,Y P,Z P)，首先计算二维平面上其前后两直线段法方向的方位角α 1和α 2，则将平面点P T(X P,Y P)沿(α 1+α 2)/2方向朝轨道内侧偏移距离d＝(1.435+θ)/2，其中θ为铁轨顶面宽度值，得到坐标(X S,Y S)，计算方法如下：
    Figure PCTCN2021129311-appb-100002
    曲线段三维中线节点的高程值取相应内轨点的高程Z P，得到点P N对应的三维中线节点坐标为(X S,Y S,Z P)。
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