Conic epipolar constraints from affine correspondences

Bentolila, J.; Francos, J.M.

doi:10.1016/j.cviu.2014.02.004

Cited by 48 publications

(69 citation statements)

References 15 publications

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“…This is possible if at least two correspondences are taken as it was demonstrated by Perdoch et al [28]. Bentolila et al [8] proved that three affine transformations give sufficient information to estimate the epipole in stereo images. Lakemond et al [20] discussed that an affine transformation gives additional information for feature correspondence matching, useful for wide-baseline stereo reconstruction.…”

Section: Introductionmentioning

confidence: 97%

Computer Vision Meets Geometric Modeling: Multi-view Reconstruction of Surface Points and Normals Using Affine Correspondences

Hajder

Eichhardt

2017

2017 IEEE International Conference on Computer Vision Workshops (ICCVW)

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Section: Introductionmentioning

confidence: 97%

Computer Vision Meets Geometric Modeling: Multi-view Reconstruction of Surface Points and Normals Using Affine Correspondences

Hajder

Eichhardt

2017

2017 IEEE International Conference on Computer Vision Workshops (ICCVW)

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“…A technique, proposed by Perdoch et al [29], approximates the epipolar geometry from one or two affine correspondences by converting them to point pairs. Bentolila and Francos [11] proposed a solution for estimating the fundamental matrix using three affine fea- tures. Raposo et al [31] and Barath et al [6] showed that two correspondences are enough for estimating the relative camera motion.…”

Section: Introductionmentioning

confidence: 99%

Homography From Two Orientation- and Scale-Covariant Features

Baráth

Kúkelová

2019

2019 IEEE/CVF International Conference on Computer Vision (ICCV)

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This paper proposes a geometric interpretation of the angles and scales which the orientation-and scale-covariant feature detectors, e.g. SIFT, provide. Two new general constraints are derived on the scales and rotations which can be used in any geometric model estimation tasks. Using these formulas, two new constraints on homography estimation are introduced. Exploiting the derived equations, a solver for estimating the homography from the minimal number of two correspondences is proposed. Also, it is shown how the normalization of the point correspondences affects the rotation and scale parameters, thus achieving numerically stable results. Due to requiring merely two feature pairs, robust estimators, e.g. RANSAC, do significantly fewer iterations than by using the four-point algorithm. When using covariant features, e.g. SIFT, the information about the scale and orientation is given at no cost. The proposed homography estimation method is tested in a synthetic environment and on publicly available real-world datasets.

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“…In the last three pairs, we manually marked point correspondences and assigned them to planes. The ground truth homographies are computed using the annotated point correspondences 5 .…”

Section: Tests On Real Datamentioning

confidence: 99%

“…Köser [11] showed that 3D points can be precisely triangulated from local affinities. Bentolila et al [5] proved that affine transformations give constraints for estimating the epipoles in the images. Current 3D reconstruction pipelines use point correspondences as well as patches [6,7,24] in order to compute realistic 3D models of real-world objects.…”

Section: Introductionmentioning

confidence: 99%

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Accurate Closed-form Estimation of Local Affine Transformations Consistent with the Epipolar Geometry

Baráth¹,

Matas²,

Hajder³

2016

Procedings of the British Machine Vision Conference 2016

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For a pair of images satisfying the epipolar constraint, a method for accurate estimation of local affine transformations is proposed. The method returns the local affine transformation consistent with the epipolar geometry that is closest in the least squares sense to the initial estimate provided by an affine-covariant detector. The minimized L 2 norm of the affine matrix elements is found in closed-form. We show that the used norm has an intuitive geometric interpretation.The method, with negligible computational requirements, is validated on publicly available benchmarking datasets and on synthetic data. The accuracy of the local affine transformations is improved for all detectors and all image pairs. Implicitly, precision of the tested feature detectors was compared. The Hessian-Affine detector combined with ASIFT view synthesis was the most accurate.

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Conic epipolar constraints from affine correspondences

Cited by 48 publications

References 15 publications

Computer Vision Meets Geometric Modeling: Multi-view Reconstruction of Surface Points and Normals Using Affine Correspondences

Computer Vision Meets Geometric Modeling: Multi-view Reconstruction of Surface Points and Normals Using Affine Correspondences

Homography From Two Orientation- and Scale-Covariant Features

Accurate Closed-form Estimation of Local Affine Transformations Consistent with the Epipolar Geometry

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