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Kruppa Equation Revisited: Its Renormalization and Degeneracy

Ma, Y.; Vidal, R.; Kosecka, J. and Sastry, S. (2000) 6th European Conf. on Computer Vision In Computer Vision — ECCV 2000 : Lecture Notes in Computer Science 1843. p.561-577
Abstract
In this paper, we study general questions about the solvability of the Kruppa equations and show that, in several special cases, the Kruppa equations can be renormalized and become linear. In particular, for cases when the camera motion is such that its rotation axis is parallel or perpendicular to translation, we can obtain linear algorithms for self-calibration. A further study of these cases not only reveals generic difficulties with degeneracy in conventional self-calibration methods based on the nonlinear Kruppa equations, but also clarifies some incomplete discussion in the literature about the solutions of the Kruppa equations. We demonstrate that Kruppa equations do not provide sufficient constraints on camera calibration and give... (More)
In this paper, we study general questions about the solvability of the Kruppa equations and show that, in several special cases, the Kruppa equations can be renormalized and become linear. In particular, for cases when the camera motion is such that its rotation axis is parallel or perpendicular to translation, we can obtain linear algorithms for self-calibration. A further study of these cases not only reveals generic difficulties with degeneracy in conventional self-calibration methods based on the nonlinear Kruppa equations, but also clarifies some incomplete discussion in the literature about the solutions of the Kruppa equations. We demonstrate that Kruppa equations do not provide sufficient constraints on camera calibration and give a complete account of exactly what is missing in Kruppa equations. In particular, a clear relationship between the Kruppa equations and chirality is revealed. The results then resolve the discrepancy between the Kruppa equations and the necessary and sufficient condition for a unique calibration. Simulation results are presented for evaluation of the sensitivity and robustness of the proposed linear algorithms. (Less)
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author
publishing date
type
Chapter in Book/Report/Conference proceeding
publication status
published
subject
in
Computer Vision — ECCV 2000 : Lecture Notes in Computer Science
volume
1843
pages
561 - 577
conference name
6th European Conf. on Computer Vision
external identifiers
  • Scopus:84944041455
ISBN
978-3-540-67686-7
DOI
10.1007/3-540-45053-X_36
language
English
LU publication?
no
id
6eabd533-6b85-41d6-9fe2-55ab83ee1480 (old id 787376)
alternative location
http://citeseer.ist.psu.edu/article/ma00kruppa.html
date added to LUP
2008-09-16 15:31:37
date last changed
2016-10-13 04:59:16
@misc{6eabd533-6b85-41d6-9fe2-55ab83ee1480,
  abstract     = {In this paper, we study general questions about the solvability of the Kruppa equations and show that, in several special cases, the Kruppa equations can be renormalized and become linear. In particular, for cases when the camera motion is such that its rotation axis is parallel or perpendicular to translation, we can obtain linear algorithms for self-calibration. A further study of these cases not only reveals generic difficulties with degeneracy in conventional self-calibration methods based on the nonlinear Kruppa equations, but also clarifies some incomplete discussion in the literature about the solutions of the Kruppa equations. We demonstrate that Kruppa equations do not provide sufficient constraints on camera calibration and give a complete account of exactly what is missing in Kruppa equations. In particular, a clear relationship between the Kruppa equations and chirality is revealed. The results then resolve the discrepancy between the Kruppa equations and the necessary and sufficient condition for a unique calibration. Simulation results are presented for evaluation of the sensitivity and robustness of the proposed linear algorithms.},
  author       = {Ma, Y. and Vidal, R. and Kosecka, J. and Sastry, S.},
  isbn         = {978-3-540-67686-7},
  language     = {eng},
  pages        = {561--577},
  series       = {Computer Vision — ECCV 2000 : Lecture Notes in Computer Science},
  title        = {Kruppa Equation Revisited: Its Renormalization and Degeneracy},
  url          = {http://dx.doi.org/10.1007/3-540-45053-X_36},
  volume       = {1843},
  year         = {2000},
}