Fury of the Swarm: Efficient and Very Accurate Triangulation for Multi-view Scene Reconstruction

This paper presents a novel framework for practical and accurate N-view triangulation of scene points. The algorithm is based on applying swarm optimization inside a robustly-computed bounding box, using an angular error-based L₁ cost function which is more robust to outliers and less susceptible to local minima than cost functions such as L₂ on reprojection error. Extensive testing on synthetic data with ground-truth has determined an accurate position over 99.9% of the time, on thousands of camera configurations with varying degrees of feature tracking errors. Opposed to existing polynomial methods developed for a small number of cameras, the proposed algorithm is at best linear in the number of cameras and does not suffer from inaccuracies inherent in solving high-order polynomials or Grobner bases. In the specific case of three views, there is a two to three order of magnitude performance increase with respect to such methods. Results are provided to highlight performance for arbitrary camera configurations, numbers of cameras and under noise, which has not been previously achieved in the triangulation literature. Results on real data also prove that reprojection error is improved with respect to other methods.