Robust Three-view Triangulation Done Fast

Johan Hedborg, Andreas Robinson, Michael Felsberg; Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (CVPR) Workshops, 2014, pp. 152-157

Estimating the position of a 3-dimensional world point given its 2-dimensional projections in a set of images is a key component in numerous computer vision systems. There are several methods dealing with this problem, ranging from sub-optimal, linear least square triangulation in two views, to finding the world point that minimized the L2-reprojection error in three views. This leads to the statistically optimal estimate under the assumption of Gaussian noise. In this paper we present a solution to the optimal triangulation in three views. The standard approach for solving the three-view triangulation problem is to find a closed-form solution. In contrast to this, we propose a new method based on an iterative scheme. The method is rigorously tested on both synthetic and real image data with corresponding ground truth, on a midrange desktop PC and a Raspberry Pi, a low-end mobile platform. We are able to improve the precision achieved by the closed-form solvers and reach a speed-up of two orders of magnitude compared to the current state-of-the-art solver. In numbers, this amounts to around 300K triangulations per second on the PC and 30K triangulations per second on Raspberry Pi.