Pre-Weighted Midpoint Algorithm for Efficient Multiple-View Triangulation

Triangulation is a fundamental module in vision based navigation system, which reconstructs the observed 3D point using cameras with known intrinsic and poses. In this article, we adopt the minimization of the angular residual as the criterion of triangulation and a novel structure of multiple-view triangulation is proposed. A multiple-view triangulation problem is divided into several two-view triangulation problems and a linear algorithm is derived to find the explicit closed form solutions of these two-view triangulation problems. Then, the Cramer–Rao lower bound (CRLB) is employed to calculate their covariances, according to which these solutions are fused to obtain the final result of the multiple-view triangulation. Our proposed algorithm is proved to be efficient based on the theoretical analysis, as it is linear and non-iterative. The simulations on both synthetic and real data show that the proposed algorithm can achieve competitive accuracy within less processing time, comparing with the most state-of-art algorithms.