Reconstruction of general curves, using factorization and bundle adjustment
(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
- Berthilsson, Rikard LU ; Åström, Kalle LU and Heyden, Anders LU
- organization
- publishing date
- 2001-02
- 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
- 2023-09-10 17:08:34
@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}}, keywords = {{3D; Affine shape; Bundle adjustment; Curves; Error analysis; Proximity measure; Structure from motion}}, 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}}, }