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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)
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author
organization
publishing date
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
2009-05-15 15:07:53
date last changed
2018-05-29 10:18:32
@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},
  keyword      = {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          = {http://dx.doi.org/10.1016/j.cviu.2008.11.008},
  volume       = {114},
  year         = {2010},
}