The optimal triangulation method is not really optimal

Abstract

AbstractTriangulation refers to the problem of finding a 3D point from its 2D projections on multiple images taken at different camera poses. For solving this problem, it is a common practice to use the so‐called optimal triangulation method. But, the method can be optimal only if we assume no uncertainty in the camera parameters. In this paper, an extensive comparison between various existing methods for the calibrated cameras is performed, in which different poses are considered. Furthermore, uncertainty sensitivity analysis is conducted for extrinsic parameters of cameras. The results show that the optimal triangulation method is actually not the best choice when there is uncertainty in extrinsic parameters. Interestingly, it can be observed that the simple midpoint method works equally well or outperforms the optimal triangulation and many other methods. Apart from its high performance, the midpoint method has a simple closed form solution for multiple views while the optimal triangulation method is hard to be used for more than two views. Therefore, in contrast to the common practice, we argue that the simple midpoint method can be a good choice in the structure‐from‐motion process where there is uncertainty in extrinsic camera parameters.