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Homography Estimation from Ellipse Correspondences Based on the Common Self-polar Triangle

  • Yang GuoEmail author
Article
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Abstract

This paper presents new implementation algorithms for estimating the homography from ellipse correspondences based on the common self-polar triangle. Firstly, we propose an analytical solution with a fourfold ambiguity to homography based on converting two ellipse correspondences to three common pole correspondences. Secondly, after exploring the position information of the common poles, we propose the analytical algorithms for estimating the homography from only two ellipse correspondences. We also propose an analytical linear algorithm for estimating the homography by using the common pole correspondences with the known projective scale factors when given three or more ellipse correspondences. Unlike the previous methods, our algorithms are very easy to implement and furthermore may usually provide a unique solution (at most two solutions). Experimental results in synthetic data and real images show the accuracy advantage and the usefulness of our proposed algorithms.

Keywords

Homography Ellipse correspondence Common self-polar triangle Quasi-affine transformation Analytical solution 

Notes

Acknowledgements

The author thanks the anonymous referees for valuable suggestions.

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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of MathematicsNortheastern UniversityShenyangPeople’s Republic of China

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