Algorithms for Batch Matrix Factorization with Application to Structure-from-Motion
Abstract
Matrix factorization is a key component for solving several computer vision problems. It is particularly challenging in the presence of missing or erroneous data, which often arise in structure-from-motion. We propose batch algorithms for matrix factorization. They are based on closure and basis constraints, that are used either on the cameras or the structure, leading to four possible algorithms. The constraints are robustly computed from complete measurement sub-matrices with e.g. random data sampling. The cameras and 3D structure are then recovered through linear least squares. Prior information about the scene such as identical camera positions or orientations, smooth camera trajectory, known 3D points and coplanarity of some 3D points can be directly incorporated. We demonstrate our algorithms on challenging image sequences with tracking error and more than 95% missing data.
Cite
Text
Tardif et al. "Algorithms for Batch Matrix Factorization with Application to Structure-from-Motion." IEEE/CVF Conference on Computer Vision and Pattern Recognition, 2007. doi:10.1109/CVPR.2007.383062Markdown
[Tardif et al. "Algorithms for Batch Matrix Factorization with Application to Structure-from-Motion." IEEE/CVF Conference on Computer Vision and Pattern Recognition, 2007.](https://mlanthology.org/cvpr/2007/tardif2007cvpr-algorithms/) doi:10.1109/CVPR.2007.383062BibTeX
@inproceedings{tardif2007cvpr-algorithms,
title = {{Algorithms for Batch Matrix Factorization with Application to Structure-from-Motion}},
author = {Tardif, Jean-Philippe and Bartoli, Adrien and Trudeau, Martin and Guilbert, Nicolas and Roy, Sébastien},
booktitle = {IEEE/CVF Conference on Computer Vision and Pattern Recognition},
year = {2007},
doi = {10.1109/CVPR.2007.383062},
url = {https://mlanthology.org/cvpr/2007/tardif2007cvpr-algorithms/}
}