A New Solution to the Relative Orientation Problem using only 3 Points and the Vertical Direction

TL;DR

This paper introduces a novel method for estimating relative camera pose using only three points and vertical direction information, simplifying computations and enabling real-time applications.

Contribution

It presents a new minimal solver for relative orientation that leverages vertical direction data to reduce the problem to three points and algebraic solving with Grobner bases.

Findings

Effective on real and synthetic data

Simplifies relative orientation computation

Enables real-time implementation

Abstract

This paper presents a new method to recover the relative pose between two images, using three points and the vertical direction information. The vertical direction can be determined in two ways: 1- using direct physical measurement like IMU (inertial measurement unit), 2- using vertical vanishing point. This knowledge of the vertical direction solves 2 unknowns among the 3 parameters of the relative rotation, so that only 3 homologous points are requested to position a couple of images. Rewriting the coplanarity equations leads to a simpler solution. The remaining unknowns resolution is performed by an algebraic method using Grobner bases. The elements necessary to build a specific algebraic solver are given in this paper, allowing for a real-time implementation. The results on real and synthetic data show the efficiency of this method.