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Triangulation of Points, Lines and Conics

Josephson, Klas LU and Kahl, Fredrik LU (2007) 15th Scandinavian Conference on Image Analysis 4522. p.162-172
Abstract
The problem of reconstructing 3D scene features from multiple views with known camera motion and given image correspondences is considered. This is a classical and one of the most basic geometric problems in computer vision and photogrammetry. Yet, previous methods fail to guarantee optimal reconstructions - they are either plagued by local minima or rely on a non-optimal cost-function. A common framework for the triangulation problem of points, lines and conics is presented. We define what is meant by an optimal triangulation based on statistical principles and then derive an algorithm for computing the globally optimal solution. The method for achieving the global minimum is based on convex and concave relaxations for both fractionals... (More)
The problem of reconstructing 3D scene features from multiple views with known camera motion and given image correspondences is considered. This is a classical and one of the most basic geometric problems in computer vision and photogrammetry. Yet, previous methods fail to guarantee optimal reconstructions - they are either plagued by local minima or rely on a non-optimal cost-function. A common framework for the triangulation problem of points, lines and conics is presented. We define what is meant by an optimal triangulation based on statistical principles and then derive an algorithm for computing the globally optimal solution. The method for achieving the global minimum is based on convex and concave relaxations for both fractionals and monomials. The performance of the method is evaluated on real image data. (Less)
Please use this url to cite or link to this publication:
author
and
organization
publishing date
type
Chapter in Book/Report/Conference proceeding
publication status
published
subject
host publication
Image Analysis (Lecture Notes in Computer Science)
editor
Ersbøll, Bjarne and Pedersen, Kim
volume
4522
pages
162 - 172
publisher
Springer
conference name
15th Scandinavian Conference on Image Analysis
conference location
Aalborg, Denmark
conference dates
2007-06-11 - 2007-06-13
external identifiers
  • wos:000247364000017
  • scopus:38049055922
ISSN
0302-9743
1611-3349
ISBN
978-3-540-73039-2
DOI
10.1007/978-3-540-73040-8_17
language
English
LU publication?
yes
id
ef624834-f2f5-4e1a-b098-926205de3f91 (old id 787760)
date added to LUP
2016-04-01 11:44:37
date last changed
2021-03-16 04:27:19
@inproceedings{ef624834-f2f5-4e1a-b098-926205de3f91,
  abstract     = {The problem of reconstructing 3D scene features from multiple views with known camera motion and given image correspondences is considered. This is a classical and one of the most basic geometric problems in computer vision and photogrammetry. Yet, previous methods fail to guarantee optimal reconstructions - they are either plagued by local minima or rely on a non-optimal cost-function. A common framework for the triangulation problem of points, lines and conics is presented. We define what is meant by an optimal triangulation based on statistical principles and then derive an algorithm for computing the globally optimal solution. The method for achieving the global minimum is based on convex and concave relaxations for both fractionals and monomials. The performance of the method is evaluated on real image data.},
  author       = {Josephson, Klas and Kahl, Fredrik},
  booktitle    = {Image Analysis (Lecture Notes in Computer Science)},
  editor       = {Ersbøll, Bjarne and Pedersen, Kim},
  isbn         = {978-3-540-73039-2},
  issn         = {0302-9743},
  language     = {eng},
  pages        = {162--172},
  publisher    = {Springer},
  title        = {Triangulation of Points, Lines and Conics},
  url          = {https://lup.lub.lu.se/search/ws/files/2621089/1245431.pdf},
  doi          = {10.1007/978-3-540-73040-8_17},
  volume       = {4522},
  year         = {2007},
}