A New Rank Constraint on Multi-View Fundamental Matrices, and Its Application to Camera Location Recovery

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.

Cite

Text

Sengupta et al. "A New Rank Constraint on Multi-View Fundamental Matrices, and Its Application to Camera Location Recovery." Conference on Computer Vision and Pattern Recognition, 2017. doi:10.1109/CVPR.2017.259

Markdown

[Sengupta et al. "A New Rank Constraint on Multi-View Fundamental Matrices, and Its Application to Camera Location Recovery." Conference on Computer Vision and Pattern Recognition, 2017.](https://mlanthology.org/cvpr/2017/sengupta2017cvpr-new/) doi:10.1109/CVPR.2017.259

BibTeX

@inproceedings{sengupta2017cvpr-new,
  title     = {{A New Rank Constraint on Multi-View Fundamental Matrices, and Its Application to Camera Location Recovery}},
  author    = {Sengupta, Soumyadip and Amir, Tal and Galun, Meirav and Goldstein, Tom and Jacobs, David W. and Singer, Amit and Basri, Ronen},
  booktitle = {Conference on Computer Vision and Pattern Recognition},
  year      = {2017},
  doi       = {10.1109/CVPR.2017.259},
  url       = {https://mlanthology.org/cvpr/2017/sengupta2017cvpr-new/}
}