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Fast and Robust Numerical Solutions to Minimal Problems for Cameras with Radial Distortion

Byröd, Martin LU ; Kukelova, Zuzana; Josephson, Klas LU ; Pajdla, Tomas and Åström, Karl LU (2008) IEEE Computer Society Conference on Computer Vision and Pattern Recognition Workshops (CVPR Workshops), 2008 In [Host publication title missing] p.2586-2593
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 exist no known practical

algorithm 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... (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 exist no known practical

algorithm 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 on simulated and

real experiments that these two problems can be efficiently solved in

floating point arithmetic. (Less)
Please use this url to cite or link to this publication:
author
organization
publishing date
type
Chapter in Book/Report/Conference proceeding
publication status
published
subject
in
[Host publication title missing]
pages
2586 - 2593
conference name
IEEE Computer Society Conference on Computer Vision and Pattern Recognition Workshops (CVPR Workshops), 2008
external identifiers
  • wos:000259736802039
  • scopus:52249090469
DOI
10.1109/CVPR.2008.4587674
language
English
LU publication?
yes
id
c70b5936-d059-4ed2-b60b-f481482f5392 (old id 1057217)
date added to LUP
2008-07-01 12:09:53
date last changed
2017-08-20 04:53:22
@inproceedings{c70b5936-d059-4ed2-b60b-f481482f5392,
  abstract     = {A number of minimal problems of structure from motion for<br/><br>
cameras with radial distortion have recently been studied and solved<br/><br>
in some cases. These problems are known to be numerically very<br/><br>
challenging and in several cases there exist no known practical<br/><br>
algorithm yielding solutions in floating point arithmetic. We make<br/><br>
some crucial observations concerning the floating point implementation<br/><br>
of Gröbner basis computations and use these new insights to formulate fast and<br/><br>
stable algorithms for two minimal problems with radial distortion<br/><br>
previously solved in exact rational arithmetic only: (i) simultaneous<br/><br>
estimation of essential matrix and a common radial distortion<br/><br>
parameter for two partially calibrated views and six image point<br/><br>
correspondences and (ii) estimation of fundamental matrix and two<br/><br>
different radial distortion parameters for two uncalibrated views and<br/><br>
nine image point correspondences. We demonstrate on simulated and<br/><br>
real experiments that these two problems can be efficiently solved in<br/><br>
floating point arithmetic.},
  author       = {Byröd, Martin and Kukelova, Zuzana and Josephson, Klas and Pajdla, Tomas and Åström, Karl},
  booktitle    = {[Host publication title missing]},
  language     = {eng},
  pages        = {2586--2593},
  title        = {Fast and Robust Numerical Solutions to Minimal Problems for Cameras with Radial Distortion},
  url          = {http://dx.doi.org/10.1109/CVPR.2008.4587674},
  year         = {2008},
}