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Reconstruction of general curves, using factorization and bundle adjustment

Berthilsson, Rikard LU ; Åström, Kalle LU orcid and Heyden, Anders LU (2001) In International Journal of Computer Vision 41(3). p.171-182
Abstract

In this paper, we extend the notion of affine shape, introduced by Sparr, from finite point sets to curves. The extension makes it possible to reconstruct 3D-curves up to projective transformations, from a number of their 2D-projections. We also extend the bundle adjustment technique from point features to curves. The first step of the curve reconstruction algorithm is based on affine shape. It is independent of choice of coordinates, is robust, does not rely on any preselected parameters and works for an arbitrary number of images. In particular this means that, except for a small set of curves (e.g. a moving line), a solution is given to the aperture problem of finding point correspondences between curves. The second step takes... (More)

In this paper, we extend the notion of affine shape, introduced by Sparr, from finite point sets to curves. The extension makes it possible to reconstruct 3D-curves up to projective transformations, from a number of their 2D-projections. We also extend the bundle adjustment technique from point features to curves. The first step of the curve reconstruction algorithm is based on affine shape. It is independent of choice of coordinates, is robust, does not rely on any preselected parameters and works for an arbitrary number of images. In particular this means that, except for a small set of curves (e.g. a moving line), a solution is given to the aperture problem of finding point correspondences between curves. The second step takes advantage of any knowledge of measurement errors in the images. This is possible by extending the bundle adjustment technique to curves. Finally, experiments are performed on both synthetic and real data to show the performance and applicability of the algorithm.

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author
; and
organization
publishing date
type
Contribution to journal
publication status
published
subject
keywords
3D, Affine shape, Bundle adjustment, Curves, Error analysis, Proximity measure, Structure from motion
in
International Journal of Computer Vision
volume
41
issue
3
pages
12 pages
publisher
Springer
external identifiers
  • scopus:0035244983
ISSN
0920-5691
DOI
10.1023/A:1011104020586
language
English
LU publication?
yes
id
edd27086-1d42-4d36-adca-fc186a8c886b
date added to LUP
2020-12-03 13:42:24
date last changed
2021-06-16 03:15:43
@article{edd27086-1d42-4d36-adca-fc186a8c886b,
  abstract     = {<p>In this paper, we extend the notion of affine shape, introduced by Sparr, from finite point sets to curves. The extension makes it possible to reconstruct 3D-curves up to projective transformations, from a number of their 2D-projections. We also extend the bundle adjustment technique from point features to curves. The first step of the curve reconstruction algorithm is based on affine shape. It is independent of choice of coordinates, is robust, does not rely on any preselected parameters and works for an arbitrary number of images. In particular this means that, except for a small set of curves (e.g. a moving line), a solution is given to the aperture problem of finding point correspondences between curves. The second step takes advantage of any knowledge of measurement errors in the images. This is possible by extending the bundle adjustment technique to curves. Finally, experiments are performed on both synthetic and real data to show the performance and applicability of the algorithm.</p>},
  author       = {Berthilsson, Rikard and Åström, Kalle and Heyden, Anders},
  issn         = {0920-5691},
  language     = {eng},
  number       = {3},
  pages        = {171--182},
  publisher    = {Springer},
  series       = {International Journal of Computer Vision},
  title        = {Reconstruction of general curves, using factorization and bundle adjustment},
  url          = {http://dx.doi.org/10.1023/A:1011104020586},
  doi          = {10.1023/A:1011104020586},
  volume       = {41},
  year         = {2001},
}