Triangulation: Why Optimize?
This work addresses a fundamental issue in computer vision for 3D reconstruction, offering a more accurate and stable solution applicable to various camera types, though it is incremental in refining existing triangulation methods.
The paper tackled the problem of two-view triangulation by challenging the traditional approach of minimizing reprojection errors, proposing a novel alternative to the midpoint method that significantly reduces 2D and parallax errors, with results showing improved accuracy for small parallax angles.
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.