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

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 X, Y and Z 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. © 2020, Science Press. All right reserved.