ML Anthology

A Dimensionality Result for Multiple Homography Matrices

Wojciech Chojnacki, Anton van den Hengel
ICCV 2011 pp. 2104-2109
doi:10.1109/ICCV.2011.6126485 /iccv/2011/chojnacki2011iccv-dimensionality/

Abstract

It is shown that the set of all I-element collections of interdependent homography matrices describing homographies induced by I planes in the 3D scene between two views has dimension 4I + 7. This improves on an earlier result which gave an upper bound for the dimension in question, and solves a long-standing open problem. The significance of the present result lies in that it is critical to the identification of the full set of constraints to which collections of interdependent homography matrices are subject, which in turn is critical to the design of constrained optimisation techniques for estimating such collections from image data.

ICCV Semantic Scholar

Cite

Text

Chojnacki and van den Hengel. "A Dimensionality Result for Multiple Homography Matrices." IEEE/CVF International Conference on Computer Vision, 2011. doi:10.1109/ICCV.2011.6126485

Markdown

[Chojnacki and van den Hengel. "A Dimensionality Result for Multiple Homography Matrices." IEEE/CVF International Conference on Computer Vision, 2011.](https://mlanthology.org/iccv/2011/chojnacki2011iccv-dimensionality/) doi:10.1109/ICCV.2011.6126485

BibTeX

@inproceedings{chojnacki2011iccv-dimensionality,
  title     = {{A Dimensionality Result for Multiple Homography Matrices}},
  author    = {Chojnacki, Wojciech and van den Hengel, Anton},
  booktitle = {IEEE/CVF International Conference on Computer Vision},
  year      = {2011},
  pages     = {2104-2109},
  doi       = {10.1109/ICCV.2011.6126485},
  url       = {https://mlanthology.org/iccv/2011/chojnacki2011iccv-dimensionality/}
}