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arXiv · 0905.3964

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

Mahzad Kalantari·Amir Hashemi·Franck Jung·JeanPierre Guedon
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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.

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Mahzad Kalantari, Amir Hashemi, Franck Jung, JeanPierre Guedon. 2009-05-25. A New Solution to the Relative Orientation Problem using only 3 Points and the Vertical Direction. https://doi.org/10.1007/s10851-010-0234-2

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