Optimal Triangulation Method is Not Really Optimal

Abstract: Triangulation refers to the problem of finding a 3D point from its 2D projections on multiple camera images. For solving this problem, it is the common practice to use so-called optimal triangulation method, which we call the L2 method in this paper. But, the method can be optimal only if we assume no uncertainty in the camera parameters. Through extensive comparison on synthetic and real data, we observed that the L2 method is actually not the best choice when there is uncertainty in the camera parameters. Interestingly, it can be observed that the simple mid-point method outperforms other methods. Apart from its high performance, the mid-point method has a simple closed formed solution for multiple camera images while the L2 method is hard to be used for more than two camera images. Therefore, in contrast to the common practice, we argue that the simple mid-point method should be used in structure-from-motion applications where there is uncertainty in camera parameters.