Practical Projective Structure from Motion (P2SfM)

Magerand, Ludovic; Bue, Alessio Del

doi:10.1109/iccv.2017.14

Cited by 13 publications

(19 citation statements)

References 22 publications

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“…As the authors acknowledge, their algorithm is sensitive, and so it was suggested as a refinement to a calibrated method [18]. To avoid calibration, for a fair comparison, we initialized the method with P 2 SfM [15]. Moreover, as the method does not suggest a way to produce projective reconstruction, we used Corollary 1 to obtain camera matrices from its output.…”

Section: Resultsmentioning

confidence: 99%

GPSfM: Global Projective SFM Using Algebraic Constraints on Multi-View Fundamental Matrices

Kasten

Geifman

Galun

2019

2019 IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR)

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This paper addresses the problem of recovering projective camera matrices from collections of fundamental matrices in multiview settings. We make two main contributions. First, given n 2 fundamental matrices computed for n images, we provide a complete algebraic characterization in the form of conditions that are both necessary and sufficient to enabling the recovery of camera matrices. These conditions are based on arranging the fundamental matrices as blocks in a single matrix, called the n-view fundamental matrix, and characterizing this matrix in terms of the signs of its eigenvalues and rank structures. Secondly, we propose a concrete algorithm for projective structure-frommotion that utilizes this characterization. Given a complete or partial collection of measured fundamental matrices, our method seeks camera matrices that minimize a global algebraic error for the measured fundamental matrices. In contrast to existing methods, our optimization, without any initialization, produces a consistent set of fundamental matrices that corresponds to a unique set of cameras (up to a choice of projective frame). Our experiments indicate that our method achieves state of the art performance in both accuracy and running time.

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Section: Resultsmentioning

confidence: 99%

GPSfM: Global Projective SFM Using Algebraic Constraints on Multi-View Fundamental Matrices

Kasten

Geifman

Galun

2019

2019 IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR)

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“…Projective reconstructions for the synthetic data were obtained using the implementation of [18] in [22], followed by a projective bundle adjustment. For the real image sequences, they were obtained using P2SfM [15] with COLMAP [25] for feature matching. Data normalization was used throughout.…”

Section: Resultsmentioning

confidence: 99%

“…From (5b) and (6b), these Schur complements are nonnegative when |θ ij | ≥ 120 • . Hence, the inequalities in (16) hold and so do the LMIs in (15).…”

Section: Lmi Constraints On the Plane At Infinitymentioning

confidence: 98%

“…From (13), we can deduce that S ij (Π ∞ ) ≤ 0 and S ji (Π ∞ ) ≤ 0. For the LMIs in (15) to be satisfied, the following inequalities must hold:…”

Section: Lmi Constraints On the Plane At Infinitymentioning

confidence: 99%

“…The LMIs in (15) further characterize the region of intersection. This region is dependent on the discriminants, which, from (13), can be seen to be constrained by (16) and hence by the LMIs in (15).…”

Section: Lmi Constraints On the Plane At Infinitymentioning

confidence: 99%

See 2 more Smart Citations

QUARCH: A New Quasi-Affine Reconstruction Stratum From Vague Relative Camera Orientation Knowledge

Adlakha

Habed

Morbidi

et al. 2019

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

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We present a new quasi-affine reconstruction of a scene and its application to camera self-calibration. We refer to this reconstruction as QUARCH (QUasi-Affine Reconstruction with respect to Camera centers and the Hodographs of horopters). A QUARCH can be obtained by solving a semidefinite programming problem when, (i) the images have been captured by a moving camera with constant intrinsic parameters, and (ii) a vague knowledge of the relative orientation (under or over 120 •) between camera pairs is available. The resulting reconstruction comes close enough to an affine one allowing thus an easy upgrade of the QUARCH to its affine and metric counterparts. We also present a constrained Levenberg-Marquardt method for nonlinear optimization subject to Linear Matrix Inequality (LMI) constraints so as to ensure that the QUARCH LMIs are satisfied during optimization. Experiments with synthetic and real data show the benefits of QUARCH in reliably obtaining a metric reconstruction.

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Sampling Algebraic Varieties for Robust Camera Autocalibration

Paudel

Gool

2018

Computer Vision – ECCV 2018

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Practical Projective Structure from Motion (P2SfM)

Cited by 13 publications

References 22 publications

GPSfM: Global Projective SFM Using Algebraic Constraints on Multi-View Fundamental Matrices

GPSfM: Global Projective SFM Using Algebraic Constraints on Multi-View Fundamental Matrices

QUARCH: A New Quasi-Affine Reconstruction Stratum From Vague Relative Camera Orientation Knowledge

Sampling Algebraic Varieties for Robust Camera Autocalibration

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