Bound and Conquer: Improving Triangulation by Enforcing Consistency

TL;DR

This paper investigates how the accuracy of multi-camera triangulation improves with more cameras, showing that consistent algorithms achieve quadratic error decay, outperforming other methods, supported by simulations.

Contribution

We introduce the concept of consistency in triangulation, demonstrating that consistent algorithms attain optimal quadratic error decay as the number of cameras increases.

Findings

Consistent algorithms achieve quadratic error decay with more cameras.

Error decay rate of state-of-the-art algorithms varies, with some achieving optimal decay.

Simulations confirm theoretical error decay rates and advantages of consistency.

Abstract

We study the accuracy of triangulation in multi-camera systems with respect to the number of cameras. We show that, under certain conditions, the optimal achievable reconstruction error decays quadratically as more cameras are added to the system. Furthermore, we analyse the error decay-rate of major state-of-the-art algorithms with respect to the number of cameras. To this end, we introduce the notion of consistency for triangulation, and show that consistent reconstruction algorithms achieve the optimal quadratic decay, which is asymptotically faster than some other methods. Finally, we present simulations results supporting our findings. Our simulations have been implemented in MATLAB and the resulting code is available in the supplementary material.