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Multiple View Geometry Under the L-infinity Norm

Kahl, Fredrik LU and Hartley, Richard (2008) In IEEE Transactions on Pattern Analysis and Machine Intelligence 30(9). p.1603-1617
Abstract
This paper presents a new framework for solving geometric structure and motion problems based on the L-infinity-norm. Instead of using the common sum-of-squares cost function, that is, the L-2-norm, the model-fitting errors are measured using the L-infinity-norm. Unlike traditional methods based on L-2, our framework allows for the efficient computation of global estimates. We show that a variety of structure and motion problems, for example, triangulation, camera resectioning, and homography estimation, can be recast as quasi-convex optimization problems within this framework. These problems can be efficiently solved using second-order cone programming (SOCP), which is a standard technique in convex optimization. The methods have been... (More)
This paper presents a new framework for solving geometric structure and motion problems based on the L-infinity-norm. Instead of using the common sum-of-squares cost function, that is, the L-2-norm, the model-fitting errors are measured using the L-infinity-norm. Unlike traditional methods based on L-2, our framework allows for the efficient computation of global estimates. We show that a variety of structure and motion problems, for example, triangulation, camera resectioning, and homography estimation, can be recast as quasi-convex optimization problems within this framework. These problems can be efficiently solved using second-order cone programming (SOCP), which is a standard technique in convex optimization. The methods have been implemented in Matlab and the resulting toolbox has been made publicly available. The algorithms have been validated on real data in different settings on problems with small and large dimensions and with excellent performance. (Less)
Please use this url to cite or link to this publication:
author
organization
publishing date
type
Contribution to journal
publication status
published
subject
in
IEEE Transactions on Pattern Analysis and Machine Intelligence
volume
30
issue
9
pages
1603 - 1617
publisher
IEEE--Institute of Electrical and Electronics Engineers Inc.
external identifiers
  • wos:000257504400008
  • scopus:48049089853
ISSN
1939-3539
DOI
10.1109/TPAMI.2007.70824
language
English
LU publication?
yes
id
8c6a7da9-bf52-432a-9813-35b6a78fb1a6 (old id 788368)
date added to LUP
2008-01-09 17:10:03
date last changed
2017-11-05 04:11:43
@article{8c6a7da9-bf52-432a-9813-35b6a78fb1a6,
  abstract     = {This paper presents a new framework for solving geometric structure and motion problems based on the L-infinity-norm. Instead of using the common sum-of-squares cost function, that is, the L-2-norm, the model-fitting errors are measured using the L-infinity-norm. Unlike traditional methods based on L-2, our framework allows for the efficient computation of global estimates. We show that a variety of structure and motion problems, for example, triangulation, camera resectioning, and homography estimation, can be recast as quasi-convex optimization problems within this framework. These problems can be efficiently solved using second-order cone programming (SOCP), which is a standard technique in convex optimization. The methods have been implemented in Matlab and the resulting toolbox has been made publicly available. The algorithms have been validated on real data in different settings on problems with small and large dimensions and with excellent performance.},
  author       = {Kahl, Fredrik and Hartley, Richard},
  issn         = {1939-3539},
  language     = {eng},
  number       = {9},
  pages        = {1603--1617},
  publisher    = {IEEE--Institute of Electrical and Electronics Engineers Inc.},
  series       = {IEEE Transactions on Pattern Analysis and Machine Intelligence},
  title        = {Multiple View Geometry Under the L-infinity Norm},
  url          = {http://dx.doi.org/10.1109/TPAMI.2007.70824},
  volume       = {30},
  year         = {2008},
}