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Critical curves and surfaces for euclidean reconstruction

Kahl, Fredrik LU and Hartley, Richard (2002) Computer Vision - ECCV 2002. 7th European Conference on Computer Vision. In Computer Vision - ECCV 2002, PT II 2351. p.447-462
Abstract
The problem of recovering scene structure and camera motion from images has a number of inherent ambiguities. In this paper, configurations of points and cameras are analyzed for which the image points alone are insufficient to recover the scene geometry uniquely. Such configurations are said to be critical. For two views, it is well-known that a configuration is critical only if the two camera centres and all points lie on a ruled quadric. However, this is only a necessary condition. We give a complete characterization of the critical surfaces for two calibrated cameras and any number of points. Both algebraic and geometric characterizations of such surfaces are given. The existence of critical sets for n-view projective reconstruction... (More)
The problem of recovering scene structure and camera motion from images has a number of inherent ambiguities. In this paper, configurations of points and cameras are analyzed for which the image points alone are insufficient to recover the scene geometry uniquely. Such configurations are said to be critical. For two views, it is well-known that a configuration is critical only if the two camera centres and all points lie on a ruled quadric. However, this is only a necessary condition. We give a complete characterization of the critical surfaces for two calibrated cameras and any number of points. Both algebraic and geometric characterizations of such surfaces are given. The existence of critical sets for n-view projective reconstruction has recently been reported in the literature. We show that there are critical sets for n-view Euclidean reconstruction as well. For example, it is shown that for any placement of three calibrated cameras, there always exists a critical set consisting of any number of points on a fourth-degree curve. (Less)
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author
organization
publishing date
type
Chapter in Book/Report/Conference proceeding
publication status
published
subject
keywords
Euclidean reconstruction, critical surfaces, critical curves, scene structure, fourth-degree curve, n-view projective reconstruction, calibrated cameras, scene geometry, camera motion
in
Computer Vision - ECCV 2002, PT II
volume
2351
pages
447 - 462
publisher
Springer
conference name
Computer Vision - ECCV 2002. 7th European Conference on Computer Vision.
external identifiers
  • wos:000179968800030
  • scopus:84948949988
ISSN
1611-3349
0302-9743
ISBN
3-540-43744-4
language
English
LU publication?
yes
id
8086bda4-43ce-497d-b4f1-2ef9873d6832 (old id 321062)
alternative location
http://www.springerlink.com/content/5tul14dkugfnm23y
date added to LUP
2007-11-28 08:44:17
date last changed
2017-06-04 03:46:38
@inproceedings{8086bda4-43ce-497d-b4f1-2ef9873d6832,
  abstract     = {The problem of recovering scene structure and camera motion from images has a number of inherent ambiguities. In this paper, configurations of points and cameras are analyzed for which the image points alone are insufficient to recover the scene geometry uniquely. Such configurations are said to be critical. For two views, it is well-known that a configuration is critical only if the two camera centres and all points lie on a ruled quadric. However, this is only a necessary condition. We give a complete characterization of the critical surfaces for two calibrated cameras and any number of points. Both algebraic and geometric characterizations of such surfaces are given. The existence of critical sets for n-view projective reconstruction has recently been reported in the literature. We show that there are critical sets for n-view Euclidean reconstruction as well. For example, it is shown that for any placement of three calibrated cameras, there always exists a critical set consisting of any number of points on a fourth-degree curve.},
  author       = {Kahl, Fredrik and Hartley, Richard},
  booktitle    = {Computer Vision - ECCV 2002, PT II},
  isbn         = {3-540-43744-4},
  issn         = {1611-3349},
  keyword      = {Euclidean reconstruction,critical surfaces,critical curves,scene structure,fourth-degree curve,n-view projective reconstruction,calibrated cameras,scene geometry,camera motion},
  language     = {eng},
  pages        = {447--462},
  publisher    = {Springer},
  title        = {Critical curves and surfaces for euclidean reconstruction},
  volume       = {2351},
  year         = {2002},
}