An Accurate Linear Method for 3D Line Reconstruction for Binocular or Multiple View Stereo Vision

For the problem of 3D line reconstruction in binocular or multiple view stereo vision, when there are no corresponding points on the line, the method called Direction-then-Point (DtP) can be used, and if there are two pairs of corresponding points on the line, the method called Two Points 3D coordinates (TPS) can be used. However, when there is only one pair of corresponding points on the line, can we get the better accuracy than DtP for 3D line reconstruction? In this paper, a linear and more accurate method called Point-then-Direction (PtD) is proposed. First, we used the intersection method to obtain the 3D point's coordinate from its corresponding image points. Then, we used this point as a position on the line to calculate the direction of the line by minimizing the image angle residual. PtD is also suitable for multiple camera systems. The simulation results demonstrate that PtD increases the accuracy of both the direction and the position of the 3D line compared to DtP. At the same time, PtD achieves a better result in direction of the 3D line than TPS, but has a lower accuracy in the position of 3D lines than TPS.