The Space of Multibody Fundamental Matrices: Rank, Geometry and Projection
Abstract
We study the rank and geometry of the multibody fundamental matrix, a geometric entity characterizing the two-view geometry of dynamic scenes consisting of multiple rigid-body motions. We derive an upper bound on the rank of the multibody fundamental matrix that depends on the number of independent translations. We also derive an algebraic characterization of the SVD of a multibody fundamental matrix in the case of two or odd number of rigid-body motions with a common rotation. This characterization allows us to project an arbitrary matrix onto the space of multibody fundamental matrices using linear algebraic techniques.
Cite
Text
Fan and Vidal. "The Space of Multibody Fundamental Matrices: Rank, Geometry and Projection." European Conference on Computer Vision, 2006. doi:10.1007/978-3-540-70932-9_1Markdown
[Fan and Vidal. "The Space of Multibody Fundamental Matrices: Rank, Geometry and Projection." European Conference on Computer Vision, 2006.](https://mlanthology.org/eccv/2006/fan2006eccv-space/) doi:10.1007/978-3-540-70932-9_1BibTeX
@inproceedings{fan2006eccv-space,
title = {{The Space of Multibody Fundamental Matrices: Rank, Geometry and Projection}},
author = {Fan, Xiaodong and Vidal, René},
booktitle = {European Conference on Computer Vision},
year = {2006},
pages = {1-17},
doi = {10.1007/978-3-540-70932-9_1},
url = {https://mlanthology.org/eccv/2006/fan2006eccv-space/}
}