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RankConstrained Fundamental Matrix Estimation by Polynomial Global Optimization Versus the EightPoint Algorithm
, 2012
"... The fundamental matrix can be estimated from point matches. The current gold standard is to bootstrap the eightpoint algorithm and twoview projective bundle adjustment. The eightpoint algorithm first computes a simple linear least squares solution by minimizing an algebraic cost and then computes ..."
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The fundamental matrix can be estimated from point matches. The current gold standard is to bootstrap the eightpoint algorithm and twoview projective bundle adjustment. The eightpoint algorithm first computes a simple linear least squares solution by minimizing an algebraic cost and then computes the closest rankdeficient matrix. This article proposes a singlestep method that solves both steps of the eightpoint algorithm. Using recent result from polynomial global optimization, our method finds the rankdeficient matrix that exactly minimizes the algebraic cost. The current gold standard is known to be extremely effective but is nonetheless outperformed by our rankconstrained 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.
A Convex Optimization Approach to Robust Fundamental Matrix Estimation ∗
"... This paper considers the problem of estimating the fundamental matrix from corrupted point correspondences. A general nonconvex framework is proposed that explicitly takes into account the rank2 constraint on the fundamental matrix and the presence of noise and outliers. The main result of the pap ..."
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This paper considers the problem of estimating the fundamental matrix from corrupted point correspondences. A general nonconvex framework is proposed that explicitly takes into account the rank2 constraint on the fundamental matrix and the presence of noise and outliers. The main result of the paper shows that this nonconvex problem can be solved by solving a sequence of convex semidefinite programs, obtained by exploiting a combination of polynomial optimization tools and rank minimization techniques. Further, the algorithm can be easily extended to handle the case where only some of the correspondences are labeled, and, to exploit coocurrence information, if available. Consistent experiments show that the proposed method works well, even in scenarios characterized by a very high percentage of outliers. 1.