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Rank-constrained fundamental matrix estimation by polynomial global optimization versus the eight-point algorithm

Abstract : The fundamental matrix can be estimated from point matches. The current gold standard is to bootstrap the eight-point algorithm and two-view projective bundle adjustment. The eight-point algorithm first computes a simple linear least squares solution by minimizing an algebraic cost and then projects the result to the closest rank-deficient matrix. We propose a single-step method that solves both steps of the eight-point algorithm. Using recent results from polynomial global optimization, our method finds the rank-deficient matrix that exactly minimizes the algebraic cost. In this special case, the optimization method is reduced to the resolution of very short sequences of convex linear problems which are computationally efficient and numerically stable. The current gold standard is known to be extremely effective but is nonetheless outperformed by our rank-constrained method for bootstrapping bundle adjustment. This is here demonstrated on simulated and standard real datasets. With our initialization, bundle adjustment consistently finds a better local minimum (achieves a lower reprojection error) and takes less iterations to converge.
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https://hal.archives-ouvertes.fr/hal-00723015
Contributor : Didier Henrion <>
Submitted on : Wednesday, March 19, 2014 - 11:19:21 AM
Last modification on : Wednesday, June 24, 2020 - 4:18:53 PM
Long-term archiving on: : Thursday, June 19, 2014 - 11:24:41 AM

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  • HAL Id : hal-00723015, version 2
  • ARXIV : 1403.4806

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Florian Bugarin, Adrien Bartoli, Didier Henrion, Jean-Bernard Lasserre, Jean-José Orteu, et al.. Rank-constrained fundamental matrix estimation by polynomial global optimization versus the eight-point algorithm. Journal of Mathematical Imaging and Vision, Springer Verlag, 2015, 53 (1), pp.42-60. ⟨hal-00723015v2⟩

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