Revisiting Viewing Graph Solvability: an Effective Approach Based on Cycle Consistency

Arrigoni, Federica; Fusiello, Andrea; Rizzi, Roméo; Ricci, Elisa; Pajdla, Tomáš

doi:10.1109/tpami.2022.3212595

Cited by 6 publications

(2 citation statements)

References 35 publications

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“…Solvability. There has been extensive research on the topic of solvability of viewing graphs in computer vision, as evidenced by various studies such as [2,3,15,17,20,25,26]. A viewing graph is considered solvable if, given a generic set of cameras, their fundamental matrices have a unique solution in terms of cameras up to global projective transformation.…”

Section: Related Workmentioning

confidence: 99%

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: Related Workmentioning

confidence: 99%

Compatibility of Fundamental Matrices for Complete Viewing Graphs

Bråtelund¹,

Rydell²

2023

Preprint

View full text Add to dashboard Cite

show abstract

“…Solvability. There has been extensive research on the topic of solvability of viewing graphs in computer vision, as evidenced by various studies such as [3,4,17,19,22,27,28]. A viewing graph is considered solvable if, given a generic set of cameras, their fundamental matrices have a unique solution in terms of cameras up to global projective transformation.…”

Section: Related Workmentioning

confidence: 99%

Compatibility of Fundamental Matrices for Complete Viewing Graphs

Bråtelund,

Rydell

2023

2023 IEEE/CVF International Conference on Computer Vision (ICCV)

View full text Add to dashboard Cite

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 in the generic and collinear cases. 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 quadruple-wise 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.

show abstract