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Critical Configurations for N-View Projective Reconstruction

Fredrik Kahl, Richard I. Hartley, Kalle Åström
CVPR 2001 pp. II:158-163
doi:10.1109/CVPR.2001.990945 /cvpr/2001/kahl2001cvpr-critical/

Abstract

In this paper we give a characterization of critical configurations for projective reconstruction with any number of points and views. A set of cameras and points is said to be critical if the projected image points are insufficient to determine the placement of the points and the cameras uniquely, up to a projective transformation. For two views, the critical configurations are well-known. In this paper it is shown that a configuration of n 3 cameras and in points all lying on the intersection of two distinct ruled quadrics is critical. In distinction to the two-view case, which in general allows two alternative solutions, there is a family of ambiguous reconstructions for the n-view case. As a partial converse, it Is shown that for any critical configuration, all the points lie on the intersection of two ruled quadrics.

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Text

Kahl et al. "Critical Configurations for N-View Projective Reconstruction." IEEE/CVF Conference on Computer Vision and Pattern Recognition, 2001. doi:10.1109/CVPR.2001.990945

Markdown

[Kahl et al. "Critical Configurations for N-View Projective Reconstruction." IEEE/CVF Conference on Computer Vision and Pattern Recognition, 2001.](https://mlanthology.org/cvpr/2001/kahl2001cvpr-critical/) doi:10.1109/CVPR.2001.990945

BibTeX

@inproceedings{kahl2001cvpr-critical,
  title     = {{Critical Configurations for N-View Projective Reconstruction}},
  author    = {Kahl, Fredrik and Hartley, Richard I. and Åström, Kalle},
  booktitle = {IEEE/CVF Conference on Computer Vision and Pattern Recognition},
  year      = {2001},
  pages     = {II:158-163},
  doi       = {10.1109/CVPR.2001.990945},
  url       = {https://mlanthology.org/cvpr/2001/kahl2001cvpr-critical/}
}