Multi-view DLT three-dimensional positioning method for spatial points

Zuo-xi ZHAO; Rong FENG; Yu-chang ZHU; Ting TAN

doi:10.3788/OPE.20202801.0212

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Multi-view DLT three-dimensional positioning method for spatial points

Information Sciences | 更新时间：2020-08-13

- Multi-view DLT three-dimensional positioning method for spatial points
- Optics and Precision Engineering Vol. 28, Issue 1, Pages: 212-222(2020)
- 作者机构：
  
  华南农业大学工程学院，广东广州 510642
- 作者简介：
- 基金信息：
- DOI：10.3788/OPE.20202801.0212
  CLC： TP394.1
- Received：21 May 2019，
  
  Accepted：14 June 2019，
  
  Published：25 January 2020
- 稿件说明：
移动端阅览
Zuo-xi ZHAO, Rong FENG, Yu-chang ZHU, et al. Multi-view DLT three-dimensional positioning method for spatial points[J]. Optics and precision engineering, 2020, 28(1): 212-222.
DOI：

Zuo-xi ZHAO, Rong FENG, Yu-chang ZHU, et al. Multi-view DLT three-dimensional positioning method for spatial points[J]. Optics and precision engineering, 2020, 28(1): 212-222. DOI： 10.3788/OPE.20202801.0212.

摘要

物理点的三维定位是计算机视觉实现特征提取、模式识别、测绘、运动分析的基础，为了减少遮挡的影响及增大视场面积，可以通过多视图实现点的三维定位，但目前使用专门仪器设备及专门软件实现，定位的点数、二次开发功能都有一定限制。本论文提出一种基于直接线性变换(Direct Linear Transformation，DLT)的物体上点的世界坐标系下的三维定位方法，适用于单台相机移动获取的多视图实现的静态结构体点的定位，也适合于多台相机同时拍摄获取的机器上点的三维动态定位。采用DLT方法进行各相机(或不同位置下的相机)进行标定获取内外参数，即布置6个以上不共面且坐标已知的控制点，根据空间三维坐标与图像二维坐标的线性变换关系列出方程组，通过最小二乘法对相机内外参数进行线性估计；再利用这些内外参数实现点的三维定位，即依据空间几何线-线交会原理利用最小二乘法求解实现空间点的世界坐标测量。论文论证了本方法的原理，提出了方法的步骤，并以水田平地机为试验平台，测量平地铲上待测点的世界坐标来验证。试验结果表明：该方法测得的坐标在

方向的平均绝对误差为4.19 mm，3.97 mm，3.69 mm，空间相对距离误差为0.81%，满足一般测量精度要求。进一步提高精度可以考虑在标定步骤中校正相机失真。基于一台或多台相机得到的多视图，该方法能够实现任意多个物理点的世界坐标测量，测量结果不受相机位置影响。

Abstract

3D positioning of physical body points plays an important role in machine vision applications involving feature extractions

pattern recognition

geometrical measurement and motion analysis. To cover a wide detection and mitigate the influence of occlusion some multiple view technique for positioning is adopted

a technique that is generally fulfilled using expensive instruments and specialized software and thus its applications are restricted in terms of number of points that can be positioned simultaneously

ability for user programming and affordability. With both complete algorithm and procedure

this paper proposed a DLT(Direct Linear Transformation)-based method for 3D positioning of object point in the world coordinate frame via multiple view geometry

applicable to multiple view provided by either a single camera moving into different positions for still scene positioning

or by multiple cameras for a dynamic positioning application. This method consisted of 2 main steps

i.e. a DLT-based camera calibration and a 3D coordinates reconstruction (positioning) with the camera parameters obtained in calibration. In the calibration step

a minimum of 6 control points

not co-planar but with known world coordinates

were set up and linear equations were formulated modeling relationship between world frame coordinates of these control points and their relevant image points' position in the camera coordinate frame

and equations then were solved via least squares method for best linear estimation of the camera parameters in the form of a series of L intermediary parameters. In the positioning step

the concept of finding intersection point of multiple spatial ray-each ray emanating formed the corresponding camera's optical center and the image point corresponding to the same physical point-was used to formulate equations for the 3D positioning

which than were solved also via the linear least square method with the obtained L parameters. Still scene physical point positioning tests of 10 control points and 20 test points were conducted on a field leveler machine platform

where the scene was captured by one camera in 3 different positions and true reference positions of the test points provided by a total station. Results show that the average absolute error of the coordinates measured in the

and

directions is 4.19 mm

3.97 mm

3.69 mm

and the spatial relative distance error is 0.81%

thus satisfying the needs of general geometrical measurement. The method proposed can measure static and dynamic 3D world coordinates for multiple physical points

though higher via a more complicated DLT-based calibration procedure for the additional cameras' distortion parameters.

关键词

Keywords

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