Essential Matrix Estimation Using Adaptive Penalty Formulations

Mohammed Fathy and Michael Rotkowitz

In Proceedings British Machine Vision Conference 2014


Given 6 or more pairs of corresponding points on two calibrated images, existing schemes for estimating the essential matrix (EsM) use some manifold representation to tackle the non-convex constraints of the problem. To the best of our knowledge, no attempts were made to use the more straightforward approach of integrating the EsM constraint functions directly into the optimization using Adaptive Penalty Formulations (APFs). One possible reason is that the constraints characterizing the EsM are nonlinear dependent their number exceeds the number of free parameters in the optimization variable. This paper presents an iterative optimization scheme based on penalty methods that integrates the EsM constraints into the optimization without the use of manifold-based techniques and differential geometry tools. The scheme can be used with algebraic, geometric, and/or robust cost functions. Experimental validations using synthetic and real data show that the proposed scheme outperforms manifold-based algorithms with either global or local parametrizations.


Poster Session


Extended Abstract (PDF, 1 page, 482K)
Paper (PDF, 12 pages, 1.8M)
Bibtex File


Mohammed Fathy and Michael Rotkowitz. Essential Matrix Estimation Using Adaptive Penalty Formulations. Proceedings of the British Machine Vision Conference. BMVA Press, September 2014.


	title = {Essential Matrix Estimation Using Adaptive Penalty Formulations},
	author = {Fathy, Mohammed and Rotkowitz, Michael},
	year = {2014},
	booktitle = {Proceedings of the British Machine Vision Conference},
	publisher = {BMVA Press},
	editors = {Valstar, Michel and French, Andrew and Pridmore, Tony}
	doi = { }