Rank-constrained fundamental matrix estimation by polynomial global optimization versus the eight-point algorithm
Résumé
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 computes the closest rank-deficient matrix. This article proposes a single-step method that solves both steps of the eight-point algorithm. Using recent result from polynomial global optimization, our method finds the rank-deficient matrix that exactly minimizes the algebraic cost. The current gold standard is known to be extremely effective but is nonetheless outperformed by our rank-constrained method boostrapping 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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