Triangulation: Why Optimize?

Seong Hun Lee, Javier Civera

Abstract:

For decades, it has been widely accepted that the gold standard for two-view triangulation is to minimize the cost based on reprojection errors. In this work, we challenge this
idea. We propose a novel alternative to the classic midpoint method that leads to significantly lower 2D errors and parallax errors. It provides a numerically stable closed-form
solution based solely on a pair of backprojected rays. Since our solution is rotationally invariant, it can also be applied for fisheye and omnidirectional cameras. We show that for
small parallax angles, our method outperforms the state-of-the-art in terms of combined
2D, 3D and parallax accuracy, while achieving comparable speed.