Triangulation: Why Optimize?

TL;DR

This paper introduces a new triangulation method that minimizes 2D and parallax errors, offering a stable, closed-form solution applicable to various camera types, outperforming traditional reprojection error minimization especially at small parallax angles.

Contribution

It presents a novel triangulation approach that improves accuracy and stability over classic methods, applicable to fisheye and omnidirectional cameras.

Findings

Lower 2D and parallax errors compared to traditional methods

Numerically stable closed-form solution based on backprojected rays

Outperforms state-of-the-art at small parallax angles

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.