Three-view Focal Length Recovery From Homographies

TL;DR

This paper introduces a new method for estimating camera focal lengths from three-view homographies by deriving explicit constraints and solving polynomial equations, improving speed and accuracy over existing two-view methods.

Contribution

The paper presents a novel approach leveraging three-view homographies to recover focal lengths with explicit constraints, enhancing accuracy and efficiency.

Findings

Focal lengths can be recovered from three-view homographies using derived constraints.

The proposed solvers outperform existing methods in speed and accuracy.

The approach is effective on both synthetic and real data.

Abstract

In this paper, we propose a novel approach for recovering focal lengths from three-view homographies. By examining the consistency of normal vectors between two homographies, we derive new explicit constraints between the focal lengths and homographies using an elimination technique. We demonstrate that three-view homographies provide two additional constraints, enabling the recovery of one or two focal lengths. We discuss four possible cases, including three cameras having an unknown equal focal length, three cameras having two different unknown focal lengths, three cameras where one focal length is known, and the other two cameras have equal or different unknown focal lengths. All the problems can be converted into solving polynomials in one or two unknowns, which can be efficiently solved using Sturm sequence or hidden variable technique. Evaluation using both synthetic and real data shows that the proposed solvers are both faster and more accurate than methods relying on existing two-view solvers. The code and data are available on https://github.com/kocurvik/hf