# A New Rank Constraint on Multi-view Fundamental Matrices, and its Application to Camera Location Recovery

## Author(s): Sengupta, Soumyadip; Amir, Tal; Galun, Meirav; Goldstein, Tom; Jacobs, David W; et al

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 Abstract: Accurate estimation of camera matrices is an important step in structure from motion algorithms. In this paper we introduce a novel rank constraint on collections of fundamental matrices in multi-view settings. We show that in general, with the selection of proper scale factors, a matrix formed by stacking fundamental matrices between pairs of images has rank 6. Moreover, this matrix forms the symmetric part of a rank 3 matrix whose factors relate directly to the corresponding camera matrices. We use this new characterization to produce better estimations of fundamental matrices by optimizing an L1-cost function using Iterative Re-weighted Least Squares and Alternate Direction Method of Multiplier. We further show that this procedure can improve the recovery of camera locations, particularly in multi-view settings in which fewer images are available. Publication Date: 2017 Electronic Publication Date: 9-Nov-2017 Citation: Sengupta, Soumyadip, Amir, Tal, Galun, Meirav, Goldstein, Tom, Jacobs, David W, Singer, Amit, Basri, Ronen. (2017). A New Rank Constraint on Multi-view Fundamental Matrices, and its Application to Camera Location Recovery. 30TH IEEE CONFERENCE ON COMPUTER VISION AND PATTERN RECOGNITION (CVPR 2017), 2413 - 2421. doi:10.1109/CVPR.2017.259 DOI: doi:10.1109/CVPR.2017.259 ISSN: 1063-6919 Pages: 2413 - 2421 Type of Material: Conference Article Journal/Proceeding Title: 30TH IEEE CONFERENCE ON COMPUTER VISION AND PATTERN RECOGNITION (CVPR 2017) Version: Author's manuscript