Fast and Robust Numerical Solutions to Minimal Problems for Cameras with Radial Distortion
Kukelova, Zuzana ; Byröd, Martin LU ; Josephson, Klas LU ; Pajdla, Tomas and Åström, Karl LU
(2010)
In Computer Vision and Image Understanding
114(2).
p.234-244
- Abstract
- A number of minimal problems of structure from motion for cameras with radial distortion have recently been studied and solved in some cases. These problems are known to be numerically very challenging and in several cases there were no practical algorithms yielding solutions in floating point arithmetic. We make some crucial observations concerning the floating point implementation of Gröbner basis computations and use these new insights to formulate fast and stable algorithms for two minimal problems with radial distortion previously solved in exact rational arithmetic only: (i) simultaneous estimation of essential matrix and a common radial distortion parameter for two partially calibrated views and six image point correspondences and... (More)
- A number of minimal problems of structure from motion for cameras with radial distortion have recently been studied and solved in some cases. These problems are known to be numerically very challenging and in several cases there were no practical algorithms yielding solutions in floating point arithmetic. We make some crucial observations concerning the floating point implementation of Gröbner basis computations and use these new insights to formulate fast and stable algorithms for two minimal problems with radial distortion previously solved in exact rational arithmetic only: (i) simultaneous estimation of essential matrix and a common radial distortion parameter for two partially calibrated views and six image point correspondences and (ii) estimation of fundamental matrix and two different radial distortion parameters for two uncalibrated views and nine image point correspondences. We demonstrate that these two problems can be efficiently solved in floating point arithmetic in simulated and real experiments. For comparison we have also invented a new non-minimal algorithm for estimating fundamental matrix and two different radial distortion parameters for two uncalibrated views and twelve image point correspondences based on a generalized eigenvalue problem. (Less)
Please use this url to cite or link to this publication:
https://lup.lub.lu.se/record/1276955
- author
- Kukelova, Zuzana
; Byröd, Martin
LU
; Josephson, Klas
LU
; Pajdla, Tomas
and Åström, Karl
LU
- organization
- publishing date
- 2010
- type
- Contribution to journal
- publication status
- published
- subject
- keywords
- Radial distotion calibration, Minimal problems, Gröbner Basis
- in
- Computer Vision and Image Understanding
- volume
- 114
- issue
- 2
- pages
- 234 - 244
- publisher
- Elsevier
- external identifiers
-
- wos:000274337400007
- scopus:74449086549
- ISSN
- 1077-3142
- DOI
- 10.1016/j.cviu.2008.11.008
- language
- English
- LU publication?
- yes
- id
- 1006b265-0960-45d3-b1bb-36dfc5cec3c3 (old id 1276955)
- date added to LUP
- 2016-04-01 10:43:33
- date last changed
- 2022-01-26 01:52:55
@article{1006b265-0960-45d3-b1bb-36dfc5cec3c3,
abstract = {{A number of minimal problems of structure from motion for cameras with radial distortion have recently been studied and solved in some cases. These problems are known to be numerically very challenging and in several cases there were no practical algorithms yielding solutions in floating point arithmetic. We make some crucial observations concerning the floating point implementation of Gröbner basis computations and use these new insights to formulate fast and stable algorithms for two minimal problems with radial distortion previously solved in exact rational arithmetic only: (i) simultaneous estimation of essential matrix and a common radial distortion parameter for two partially calibrated views and six image point correspondences and (ii) estimation of fundamental matrix and two different radial distortion parameters for two uncalibrated views and nine image point correspondences. We demonstrate that these two problems can be efficiently solved in floating point arithmetic in simulated and real experiments. For comparison we have also invented a new non-minimal algorithm for estimating fundamental matrix and two different radial distortion parameters for two uncalibrated views and twelve image point correspondences based on a generalized eigenvalue problem.}},
author = {{Kukelova, Zuzana and Byröd, Martin and Josephson, Klas and Pajdla, Tomas and Åström, Karl}},
issn = {{1077-3142}},
keywords = {{Radial distotion calibration; Minimal problems; Gröbner Basis}},
language = {{eng}},
number = {{2}},
pages = {{234--244}},
publisher = {{Elsevier}},
series = {{Computer Vision and Image Understanding}},
title = {{Fast and Robust Numerical Solutions to Minimal Problems for Cameras with Radial Distortion}},
url = {{https://lup.lub.lu.se/search/files/2084497/1276956.pdf}},
doi = {{10.1016/j.cviu.2008.11.008}},
volume = {{114}},
year = {{2010}},
}