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A quasiconvex formulation for radial cameras

Olsson, Carl LU ; Larsson, Viktor LU and Kahl, Fredrik LU (2021) 2021 IEEE/CVF Conference on Computer Vision and Pattern Recognition, CVPR 2021 In Proceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition p.14571-14580
Abstract

In this paper we study structure from motion problems for 1D radial cameras. Under this model the projection of a 3D point is a line in the image plane going through the principal point, which makes the model invariant to radial distortion and changes in focal length. It can therefore effectively be applied to uncalibrated image collections without the need for explicit estimation of camera intrinsics. We show that the reprojection errors of 1D radial cameras are examples of quasiconvex functions. This opens up the possibility to solve a general class of relevant reconstruction problems globally optimally using tools from convex optimization. In fact, our resulting algorithm is based on solving a series of LP problems. We perform an... (More)

In this paper we study structure from motion problems for 1D radial cameras. Under this model the projection of a 3D point is a line in the image plane going through the principal point, which makes the model invariant to radial distortion and changes in focal length. It can therefore effectively be applied to uncalibrated image collections without the need for explicit estimation of camera intrinsics. We show that the reprojection errors of 1D radial cameras are examples of quasiconvex functions. This opens up the possibility to solve a general class of relevant reconstruction problems globally optimally using tools from convex optimization. In fact, our resulting algorithm is based on solving a series of LP problems. We perform an extensive experimental evaluation, on both synthetic and real data, showing that a whole class of multiview geometry problems across a range of different cameras models with varying and unknown intrinsic calibration can be reliably and accurately solved within the same framework.

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author
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organization
publishing date
type
Chapter in Book/Report/Conference proceeding
publication status
published
subject
host publication
Proceedings - 2021 IEEE/CVF Conference on Computer Vision and Pattern Recognition, CVPR 2021
series title
Proceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition
pages
10 pages
publisher
IEEE Computer Society
conference name
2021 IEEE/CVF Conference on Computer Vision and Pattern Recognition, CVPR 2021
conference location
Virtual, Online, United States
conference dates
2021-06-19 - 2021-06-25
external identifiers
  • scopus:85123218633
ISSN
1063-6919
ISBN
9781665445092
DOI
10.1109/CVPR46437.2021.01434
language
English
LU publication?
yes
id
36f51d11-fe61-4ea4-b95f-fea003681f22
date added to LUP
2022-03-23 13:54:02
date last changed
2025-04-04 14:01:59
@inproceedings{36f51d11-fe61-4ea4-b95f-fea003681f22,
  abstract     = {{<p>In this paper we study structure from motion problems for 1D radial cameras. Under this model the projection of a 3D point is a line in the image plane going through the principal point, which makes the model invariant to radial distortion and changes in focal length. It can therefore effectively be applied to uncalibrated image collections without the need for explicit estimation of camera intrinsics. We show that the reprojection errors of 1D radial cameras are examples of quasiconvex functions. This opens up the possibility to solve a general class of relevant reconstruction problems globally optimally using tools from convex optimization. In fact, our resulting algorithm is based on solving a series of LP problems. We perform an extensive experimental evaluation, on both synthetic and real data, showing that a whole class of multiview geometry problems across a range of different cameras models with varying and unknown intrinsic calibration can be reliably and accurately solved within the same framework.</p>}},
  author       = {{Olsson, Carl and Larsson, Viktor and Kahl, Fredrik}},
  booktitle    = {{Proceedings - 2021 IEEE/CVF Conference on Computer Vision and Pattern Recognition, CVPR 2021}},
  isbn         = {{9781665445092}},
  issn         = {{1063-6919}},
  language     = {{eng}},
  pages        = {{14571--14580}},
  publisher    = {{IEEE Computer Society}},
  series       = {{Proceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition}},
  title        = {{A quasiconvex formulation for radial cameras}},
  url          = {{http://dx.doi.org/10.1109/CVPR46437.2021.01434}},
  doi          = {{10.1109/CVPR46437.2021.01434}},
  year         = {{2021}},
}