Averaging Essential and Fundamental Matrices in Collinear Camera Settings

Geifman, Amnon; Kasten, Yoni; Galun, Meirav

doi:10.1109/cvpr42600.2020.00606

Cited by 10 publications

(14 citation statements)

References 28 publications

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“…For non-collinear cameras, [13, Theorem 1] provides necessary and sufficient conditions for compatibility for any n. These conditions rely on the eigenvalues and rank of the n-view fundamental matrix, which is obtained by stacking all fundamental matrices into a 3n × 3n matrix. In the follow-up work, [7,Theorem 2] arrives at a similar condition in the collinear case. Both methods rely on fixing a correct scaling of each matrix and are therefore not projectively well-defined, nor are the conditions expressed in terms of the fundamental matrices and their epipoles, as in the n = 3 case.…”

Section: Introductionmentioning

confidence: 76%

“…Theorem 5.2 (Theorem 1 of [13], Theorem 2 of [7]). Given a complete graph on n ≥ 3 vertices G = K n , a set of real fundamental matrices F ij is compatible with a solution of real cameras whose centers are not all collinear if and only if there exists non-zero scalars λ ij for 1 ≤ i, j ≤ n such that λ ij = λ ji and 1. the n-view fundamental matrix F of λ ij F ij is rank 6 and has exactly three positive and three negative eigenvalues;…”

Section: Compatibility For Complete Graphsmentioning

confidence: 99%

“…Specifically, for the case of n = 4, we establish that a set of six fundamental matrices admits a reconstruction of camera matrices with linearly independent centers only if the triple-wise constraints and an additional polynomial equation involving all six fundamental matrices and their epipoles are satisfied. We also demonstrate, using the computer algebra system Macaulay2 [8], that the eigenvalue conditions from [7,13] are superfluous. We end in Section 6 with a discussion on the viewing graph variety.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Compatibility of Fundamental Matrices for Complete Viewing Graphs

Bråtelund¹,

Rydell²

2023

Preprint

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This paper studies the problem of recovering cameras from a set of fundamental matrices. A set of fundamental matrices is said to be compatible if a set of cameras exists for which they are the fundamental matrices. We focus on the complete graph, where fundamental matrices for each pair of cameras are given. Previous work has established necessary and sufficient conditions for compatibility as rank and eigenvalue conditions on the n-view fundamental matrix obtained by concatenating the individual fundamental matrices. In this work, we show that the eigenvalue condition is redundant. We provide explicit homogeneous polynomials that describe necessary and sufficient conditions for compatibility in terms of the fundamental matrices and their epipoles. In this direction, we find that quadruplewise compatibility is enough to ensure global compatibility for any number of cameras. We demonstrate that for four cameras, compatibility is generically described by triple-wise conditions and one additional equation involving all fundamental matrices.

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Section: Introductionmentioning

confidence: 76%

Section: Compatibility For Complete Graphsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Compatibility of Fundamental Matrices for Complete Viewing Graphs

Bråtelund¹,

Rydell²

2023

Preprint

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“…This makes SfM more robust but inefficient when datasets are large. Global SfM (Cui & Tan, 2015;Geifman et al, 2020;Moulon et al, 2013;Zhuang et al, 2018) considers all images simultaneously by rotation averaging and translation averaging. Hierarchical SfM (Chen et al, 2020;Havlena et al, 2009Havlena et al, , 2010Toldo et al, 2015) adopts a divide-and-conquer scheme, which groups images and performs independent reconstructions, followed by a merging procedure.…”

Section: Rel Ated Workmentioning

confidence: 99%

View‐graph key‐subset extraction for efficient and robust structure from motion

Gong

Zhou

Liu

et al. 2023

The Photogrammetric Record

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Structure from motion (SfM) is used to recover camera poses and the sparse structure of real scenes from multiview images. SfM methods construct a view‐graph from the matching relationships of images. Redundancy and incorrect edges are usually observed in it. Redundancy inhibits the efficiency and incorrect edges result in the misalignment of structures. In addition, the uneven distribution of vertices usually affects the global accuracy. To address these problems, we propose a coarse‐to‐fine approach in which the poses of an extracted key‐subset of images are first computed and then all remaining images are oriented. The core of this approach is view‐graph key‐subset extraction, which not only prunes redundant data and incorrect edges but also obtains properly distributed key‐subset vertices. The extraction approach is based on a replaceability score and an iteration‐update strategy. In this way, only vertices with high SfM importance are preserved in the key‐subset. Different public datasets are used to evaluate our approach. Due to the absence of ground‐truth camera poses in large‐scale datasets, we present new datasets with accurate camera poses and point clouds. The results demonstrate that our approach greatly increases the efficiency of SfM. Furthermore, the robustness and accuracy can be improved.

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“…Recent work [28][29][30] tackle the multiple rotation averaging problem by exploiting rank constraints on the global fundamental matrices. While the factorization-based methods show high accuracy dealing with large-scale datasets, it is much slower and costly than local iterative solver-based approaches.…”

Section: Related Workmentioning

confidence: 99%

On the Robustness of Multi-View Rotation Averaging

Li,

Ling

2021

Preprint

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Rotation averaging is a synchronization process on single or multiple rotation groups, and is a fundamental problem in many computer vision tasks such as multi-view structure from motion (SfM). Specifically, rotation averaging involves the recovery of an underlying pose-graph consistency from pairwise relative camera poses. Specifically, given pairwise motion in rotation groups, especially 3dimensional rotation groups (e.g., SO(3)), one is interested in recovering the original signal of multiple rotations with respect to a fixed frame. In this paper, we propose a robust framework to solve multiple rotation averaging problem, especially in the cases that a significant amount of noisy measurements are present. By introducing the -cycle consistency term into the solver, we enable the robust initialization scheme to be implemented into the IRLS solver. Instead of conducting the costly edge removal, we implicitly constrain the negative effect of erroneous measurements by weight reducing, such that IRLS failures caused by poor initialization can be effectively avoided. Experiment results demonstrate that our proposed approach outperforms state of the arts on various benchmarks.

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Averaging Essential and Fundamental Matrices in Collinear Camera Settings

Cited by 10 publications

References 28 publications

Compatibility of Fundamental Matrices for Complete Viewing Graphs

Compatibility of Fundamental Matrices for Complete Viewing Graphs

View‐graph key‐subset extraction for efficient and robust structure from motion

On the Robustness of Multi-View Rotation Averaging

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