Beyond Grobner Bases: Basis Selection for Minimal Solvers

Larsson, Viktor; Oskarsson, Magnus; Åström, Kalle; Wallis, A.F.; Pajdla, Tomáš; Kúkelová, Zuzana

doi:10.1109/cvpr.2018.00415

Cited by 50 publications

(68 citation statements)

References 45 publications

(95 reference statements)

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“…E.g., Pritts et al in [13], [15] were unable to reduce the degree of their constraint equations used for the H DES 222 lλ solver, which resulted in slow solver (see Table 4). Furthermore, stability sampling was required to generate useful solvers [46].…”

Section: Discussionmentioning

confidence: 99%

Minimal Solvers for Rectifying from Radially-Distorted Scales and Change of Scales

et al. 2020

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This paper introduces minimal solvers that jointly solve for affine-rectification and radial lens undistortion from the image of translated and reflected coplanar features. The proposed solvers use the invariant that the affine-rectified image of the meet of the joins of radially-distorted conjugately-translated point correspondences is on the line at infinity. The hidden-variable trick from algebraic geometry is used to reformulate and simplify the constraints so that the generated solvers are stable, small and fast. Multiple solvers are proposed to accommodate various local feature types and sampling strategies, and, remarkably, three of the proposed solvers can recover rectification and lens undistortion from only one radially-distorted conjugately-translated affine-covariant region correspondence. Synthetic and real-image experiments confirm that the proposed solvers demonstrate superior robustness to noise compared to the state of the art. Accurate rectifications on imagery taken with narrow to fisheye field-of-view lenses demonstrate the wide applicability of the proposed method. The method is fully automatic.

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Section: Discussionmentioning

confidence: 99%

Minimal Solvers for Rectifying from Radially-Distorted Scales and Change of Scales

et al. 2020

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“…Experiments on synthetic data (see Section 5.1) revealed that using the standard GRevLex bases in the generator of [12] gave solvers with poor numerical stability. To generate stable solvers we used the recently proposed basis sampling technique from Larsson et al [16]. In [16] the authors propose a method for randomly sampling feasible monomial bases, which can be used to construct polynomial solvers.…”

Section: Creating the Solversmentioning

confidence: 99%

“…Recently, Larsson et al [16] sampled feasible monomial bases, which can be used in the action-matrix method. In [16] basis sampling was used to minimize the size of the solver. We modified the objective of [16] to maximize for solver stability.…”

Section: Introductionmentioning

confidence: 99%

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Rectification from Radially-Distorted Scales

Pritts

Kúkelová

Larsson

et al. 2019

Computer Vision – ACCV 2018

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This paper introduces the first minimal solvers that jointly estimate lens distortion and affine rectification from repetitions of rigidly-transformed coplanar local features. The proposed solvers incorporate lens distortion into the camera model and extend accurate rectification to wide-angle images that contain nearly any type of coplanar repeated content. We demonstrate a principled approach to generating stable minimal solvers by the Gröbner basis method, which is accomplished by sampling feasible monomial bases to maximize numerical stability. Synthetic and real-image experiments confirm that the solvers give accurate rectifications from noisy measurements if used in a RANSAC-based estimator. The proposed solvers demonstrate superior robustness to noise compared to the state of the art. The solvers work on scenes without straight lines and, in general, relax strong assumptions about scene content made by the state of the art. Accurate rectifications on imagery taken with narrow focal length to fisheye lenses demonstrate the wide applicability of the proposed method. The method is automatic, and the code is published at https://github.com/prittjam/repeats.

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“…They then used this basis to construct an action matrix whose eigen-system returns the 64 complex solutions of the problem. Later work by Larsson et al [21,22], inspired by [19], introduced an automatic generator of action matrices, which they applied to Stewenius et al's formulation.…”

Section: Related Workmentioning

confidence: 99%

Resultant Based Incremental Recovery of Camera Pose From Pairwise Matches

Kasten

Galun

2019

2019 IEEE Winter Conference on Applications of Computer Vision (WACV)

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Incremental (online) structure from motion pipelines seek to recover the camera matrix associated with an image I n given n − 1 images, I 1 , ..., I n−1 , whose camera matrices have already been recovered. In this paper, we introduce a novel solution to the six-point online algorithm to recover the exterior parameters associated with I n . Our algorithm uses just six corresponding pairs of 2D points, extracted each from I n and from any of the preceding n − 1 images, allowing the recovery of the full six degrees of freedom of the n'th camera, and unlike common methods, does not require tracking feature points in three or more images. Our novel solution is based on constructing a Dixon resultant, yielding a solution method that is both efficient and accurate compared to existing solutions. We further use Bernstein's theorem to prove a tight bound on the number of complex solutions. Our experiments demonstrate the utility of our approach.

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Beyond Grobner Bases: Basis Selection for Minimal Solvers

Cited by 50 publications

References 45 publications

Minimal Solvers for Rectifying from Radially-Distorted Scales and Change of Scales

Minimal Solvers for Rectifying from Radially-Distorted Scales and Change of Scales

Rectification from Radially-Distorted Scales

Resultant Based Incremental Recovery of Camera Pose From Pairwise Matches

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