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Triangulation of Points, Lines and Conics

Josephson, Klas LU and Kahl, Fredrik LU (2008) In Journal of Mathematical Imaging and Vision 32(2). p.215-225
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... (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
organization
publishing date
type
Contribution to journal
publication status
published
subject
keywords
Triangulation, Global optimization, RATIOS PROBLEM, SUM
in
Journal of Mathematical Imaging and Vision
volume
32
issue
2
pages
215 - 225
publisher
Springer
external identifiers
  • wos:000258539200007
  • scopus:49749109115
ISSN
0924-9907
DOI
10.1007/s10851-008-0097-y
language
English
LU publication?
yes
id
ebc465a0-39cb-4b27-b0f8-a05186607a56 (old id 1152267)
alternative location
http://www.maths.lth.se/vision/publdb/reports/pdf/josephson-kahl-jmiv-08.pdf
date added to LUP
2008-10-06 16:17:44
date last changed
2017-08-13 03:50:49
@article{ebc465a0-39cb-4b27-b0f8-a05186607a56,
  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},
  issn         = {0924-9907},
  keyword      = {Triangulation,Global optimization,RATIOS PROBLEM,SUM},
  language     = {eng},
  number       = {2},
  pages        = {215--225},
  publisher    = {Springer},
  series       = {Journal of Mathematical Imaging and Vision},
  title        = {Triangulation of Points, Lines and Conics},
  url          = {http://dx.doi.org/10.1007/s10851-008-0097-y},
  volume       = {32},
  year         = {2008},
}