The Rank 4 Constraint in Multiple (>=3) View Geometry
Abstract
It has been established that certain trilinear froms of three perspective views give rise to a tensor of 27 intrinsic coefficients [8]. Further investigations have shown the existence of quadlinear forms across four views with the negative result that further views would not add any new constraints [3, 12, 5]. We show in this paper first general results on any number of views. Rather than seeking new constraints (which we know now is not possible) we seek connections across trilinear tensors of triplets of views. Two main results are shown: (i) trilinear tensors across m >3 views are embedded in a low dimensional linear subspace, (ii) given two views, all the induced homography matrices are embedded in a four-dimensional linear subspace. The two results, separately and combined, offer new possibilities of handling the consistency across multiple views in a linear manner (via factorization), some of which are further detailed in this paper.
Cite
Text
Shashua and Avidan. "The Rank 4 Constraint in Multiple (>=3) View Geometry." European Conference on Computer Vision, 1996. doi:10.1007/3-540-61123-1_139Markdown
[Shashua and Avidan. "The Rank 4 Constraint in Multiple (>=3) View Geometry." European Conference on Computer Vision, 1996.](https://mlanthology.org/eccv/1996/shashua1996eccv-rank/) doi:10.1007/3-540-61123-1_139BibTeX
@inproceedings{shashua1996eccv-rank,
title = {{The Rank 4 Constraint in Multiple (>=3) View Geometry}},
author = {Shashua, Amnon and Avidan, Shai},
booktitle = {European Conference on Computer Vision},
year = {1996},
pages = {196-206},
doi = {10.1007/3-540-61123-1_139},
url = {https://mlanthology.org/eccv/1996/shashua1996eccv-rank/}
}