A Practical Rank-Constrained Eight-Point Algorithm for Fundamental Matrix Estimation

Zheng, Yinqiang; Sugimoto, Shigeki; Okutomi, Masatoshi

doi:10.1109/cvpr.2013.203

Cited by 14 publications

(7 citation statements)

References 23 publications

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“…Finally, in a very recent work [28], the algebraic error is globally minimized thanks to the resolution of seven subproblems. Each subproblem is reduced to a polynomial equation system solved via a Gröbner basis solver.…”

Section: The Proposed Methodsmentioning

confidence: 99%

Rank-Constrained Fundamental Matrix Estimation by Polynomial Global Optimization Versus the Eight-Point Algorithm

et al. 2014

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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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Section: The Proposed Methodsmentioning

confidence: 99%

Rank-Constrained Fundamental Matrix Estimation by Polynomial Global Optimization Versus the Eight-Point Algorithm

et al. 2014

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“…In addition, it would be possible to add the observation weights directly and to use weighted linear least-squares techniques [46]. However, using this option is quite risky, as it influences the estimation of F if the coefficient F 33 approaches zero ( [47]. Such situations (F 33 → 0) can be raised in cases that we will call poor camera models.…”

Section: Fundamental Theories: Two-view Epipolar Geometrymentioning

confidence: 99%

Evolutionary Optimization for Robust Epipolar-Geometry Estimation and Outlier Detection

2017

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Abstract:In this paper, a robust technique based on a genetic algorithm is proposed for estimating two-view epipolar-geometry of uncalibrated perspective stereo images from putative correspondences containing a high percentage of outliers. The advantages of this technique are three-fold: (i) replacing random search with evolutionary search applying new strategies of encoding and guided sampling; (ii) robust and fast estimation of the epipolar geometry via detecting a more-than-enough set of inliers without making any assumptions about the probability distribution of the residuals; (iii) determining the inlier-outlier threshold based on the uncertainty of the estimated model. The proposed method was evaluated both on synthetic data and real images. The results were compared with the most popular techniques from the state-of-the-art, including RANSAC (random sample consensus), MSAC, MLESAC, Cov-RANSAC, LO-RANSAC, StaRSAC, Multi-GS RANSAC and least median of squares (LMedS). Experimental results showed that the proposed approach performed better than other methods regarding the accuracy of inlier detection and epipolar-geometry estimation, as well as the computational efficiency for datasets majorly contaminated by outliers and noise.

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“…Knowledge of explicit formulae for homography constraints would be advantageous for several reasons: (1) it would give rise to novel homography estimation methods that enforce full compatibility without recourse to latent variables; (2) it would spur the development of new global optimisation methods for multi-homography estimation, analogous to what has recently been achieved for fundamental matrix estimation [37,38]; and (3) it would lead to a new generation of robust multi-structure fitting methods that, unlike existing methods, yield estimates with consistent epipolar geometry.…”

Section: Benefits Of Explicit Constraintsmentioning

confidence: 99%

Robust multiple homography estimation: An ill-solved problem

Szpak

Chojnacki

Hengel

2015

2015 IEEE Conference on Computer Vision and Pattern Recognition (CVPR)

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The estimation of multiple homographies between two piecewise planar views of a rigid scene is often assumed to be a solved problem. We show that contrary to popular opinion various crucial aspects of the task have not been adequately emphasised. We are motivated by a growing body of literature in robust multi-structure estimation that purports to solve the multi-homography estimation problem but in fact does not. We demonstrate that the estimation of multiple homographies is an ill-solved problem by deriving new constraints that a set of mutually compatible homographies must satisfy, and by showing that homographies estimated with prevailing methods fail to satisfy the requisite constraints on real-world data. We also explain why incompatible homographies imply inconsistent epipolar geometries. The arguments and experiments presented in this paper signal the need for a new generation of robust multi-structure estimation methods that have the capacity to enforce constraints on projective entities such as homography matrices.

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A Practical Rank-Constrained Eight-Point Algorithm for Fundamental Matrix Estimation

Cited by 14 publications

References 23 publications

Rank-Constrained Fundamental Matrix Estimation by Polynomial Global Optimization Versus the Eight-Point Algorithm

Rank-Constrained Fundamental Matrix Estimation by Polynomial Global Optimization Versus the Eight-Point Algorithm

Evolutionary Optimization for Robust Epipolar-Geometry Estimation and Outlier Detection

Robust multiple homography estimation: An ill-solved problem

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