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

Martin Byröd; Zuzana Kukelova; Klas Josephson; Tomas Pajdla; Karl Åström

doi:10.1109/CVPR.2008.4587674

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

Martin Byröd, Zuzana Kukelova, Klas Josephson, Tomas Pajdla, Karl Åström

Research output: Chapter in Book/Report/Conference proceeding › Paper in conference proceeding › peer-review

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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 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.

Original language	English
Title of host publication	[Host publication title missing]
Pages	2586-2593
DOIs	https://doi.org/10.1109/CVPR.2008.4587674
Publication status	Published - 2008
Event	IEEE Computer Society Conference on Computer Vision and Pattern Recognition Workshops (CVPR Workshops), 2008 - Anchorage, AK, Anchorage, Alaska, United States Duration: 2008 Jun 23 → 2008 Jun 28

Conference

Conference	IEEE Computer Society Conference on Computer Vision and Pattern Recognition Workshops (CVPR Workshops), 2008
Country/Territory	United States
City	Anchorage, Alaska
Period	2008/06/23 → 2008/06/28

Subject classification (UKÄ)

Mathematics
Computer Vision and Robotics (Autonomous Systems)

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10.1109/CVPR.2008.4587674

byrod-kukelova-etal-cvpr_08

1 Article

Fast and Robust Numerical Solutions to Minimal Problems for Cameras with Radial Distortion
Kukelova, Z., Byröd, M., Josephson, K., Pajdla, T. & Åström, K., 2010, In: Computer Vision and Image Understanding. 114, 2, p. 234-244
Research output: Contribution to journal › Article › peer-review

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Cite this

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title = "Fast and Robust Numerical Solutions to Minimal Problems for Cameras with Radial Distortion",

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 Gr{\"o}bner 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.",

author = "Martin Byr{\"o}d and Zuzana Kukelova and Klas Josephson and Tomas Pajdla and Karl {\AA}str{\"o}m",

year = "2008",

doi = "10.1109/CVPR.2008.4587674",

language = "English",

pages = "2586--2593",

booktitle = "[Host publication title missing]",

note = "IEEE Computer Society Conference on Computer Vision and Pattern Recognition Workshops (CVPR Workshops), 2008 ; Conference date: 23-06-2008 Through 28-06-2008",

}

Byröd, M, Kukelova, Z, Josephson, K, Pajdla, T & Åström, K 2008, Fast and Robust Numerical Solutions to Minimal Problems for Cameras with Radial Distortion. in [Host publication title missing]. pp. 2586-2593, IEEE Computer Society Conference on Computer Vision and Pattern Recognition Workshops (CVPR Workshops), 2008, Anchorage, Alaska, United States, 2008/06/23. https://doi.org/10.1109/CVPR.2008.4587674

TY - GEN

T1 - Fast and Robust Numerical Solutions to Minimal Problems for Cameras with Radial Distortion

AU - Byröd, Martin

AU - Kukelova, Zuzana

AU - Josephson, Klas

AU - Pajdla, Tomas

AU - Åström, Karl

PY - 2008

Y1 - 2008

N2 - 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.

AB - 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.

U2 - 10.1109/CVPR.2008.4587674

DO - 10.1109/CVPR.2008.4587674

M3 - Paper in conference proceeding

SP - 2586

EP - 2593

BT - [Host publication title missing]

T2 - IEEE Computer Society Conference on Computer Vision and Pattern Recognition Workshops (CVPR Workshops), 2008

Y2 - 23 June 2008 through 28 June 2008

ER -

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

Abstract

Conference

Subject classification (UKÄ)

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Research output

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

Cite this