TY - GEN
T1 - A new rank constraint on multi-view fundamental matrices, and its application to camera location recovery
AU - Sengupta, Soumyadip
AU - Amir, Tal
AU - Galun, Meirav
AU - Goldstein, Tom
AU - Jacobs, David W.
AU - Singer, Amit
AU - Basri, Ronen
N1 - Funding Information:
This material is based upon work supported by the National Science Foundation under grant no. IIS-1526234, by the Israel Science Foundation grant no. 1265/14 and by the Minerva Foundation with funding from the Federal German Ministry of Education and research. TG was supported by the US Office of Naval Research (N00014-17-1-2078), and the National Science Foundation (CCF-1535902). AS was supported by AFOSR FA9550-12-1-0317, Simons Investigator Award, and the Moore Foundation Data-Driven Discovery Investigator Award.
Publisher Copyright:
© 2017 IEEE.
PY - 2017/11/6
Y1 - 2017/11/6
N2 - 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.
AB - 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.
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U2 - 10.1109/CVPR.2017.259
DO - 10.1109/CVPR.2017.259
M3 - Conference contribution
AN - SCOPUS:85044299031
T3 - Proceedings - 30th IEEE Conference on Computer Vision and Pattern Recognition, CVPR 2017
SP - 2413
EP - 2421
BT - Proceedings - 30th IEEE Conference on Computer Vision and Pattern Recognition, CVPR 2017
PB - Institute of Electrical and Electronics Engineers Inc.
T2 - 30th IEEE Conference on Computer Vision and Pattern Recognition, CVPR 2017
Y2 - 21 July 2017 through 26 July 2017
ER -