Direct Triangulation with Spherical Projection for Omnidirectional Cameras

TL;DR

This paper introduces a closed-form, non-iterative triangulation method for calibrated omnidirectional cameras using spherical projection, which is computationally efficient and applicable to narrow field-of-view cameras.

Contribution

It presents a novel triangulation approach based on ray-pair optimization on the projective sphere, offering a simple, fast solution compared to previous methods.

Findings

The method is closed-form and non-iterative.

It is computationally inexpensive.

Applicable to both omnidirectional and narrow FOV cameras.

Abstract

In this paper, it is proposed to solve the problem of triangulation for calibrated omnidirectional cameras through the optimisation of ray-pairs on the projective sphere. The proposed solution boils down to finding the roots of a quadratic function, and as such is closed form, completely non-iterative and computationally inexpensive when compared to previous methods. In addition, even thought the motivation is clearly to solve the triangulation problem for omnidirectional cameras, it is demonstrated that the proposed methods can be applied to non-omnidirectional, narrow field-of-view cameras.