Advanced

Ambiguous configurations for the 1D structure and motion problem

Åström, Karl LU and Kahl, Fredrik LU (2003) In Journal of Mathematical Imaging and Vision 18(2). p.191-203
Abstract
In this paper we investigate, determine and classify the critical configurations for solving structure and motion problems for 1D retina vision. We give a complete categorization of all ambiguous configurations for a 1D (calibrated or uncalibrated) perspective camera irrespective of the number of points and views. It is well-known that the calibrated and uncalibrated case are linked through the circular points. This link enables us to solve for both cases simultaneously. Another important tool is the duality in exchanging points and cameras and its corresponding Cremona transformation. These concepts are generalized to the 1D case and used for the investigation of ambiguous configurations. Several examples and illustrations are also... (More)
In this paper we investigate, determine and classify the critical configurations for solving structure and motion problems for 1D retina vision. We give a complete categorization of all ambiguous configurations for a 1D (calibrated or uncalibrated) perspective camera irrespective of the number of points and views. It is well-known that the calibrated and uncalibrated case are linked through the circular points. This link enables us to solve for both cases simultaneously. Another important tool is the duality in exchanging points and cameras and its corresponding Cremona transformation. These concepts are generalized to the 1D case and used for the investigation of ambiguous configurations. Several examples and illustrations are also provided to explain the results and to provide geometrical insight. (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
critical configuration, structure and motion, Cremona transformation
in
Journal of Mathematical Imaging and Vision
volume
18
issue
2
pages
191 - 203
publisher
Springer
external identifiers
  • wos:000180586000006
  • scopus:0037343493
ISSN
0924-9907
DOI
10.1023/A:1022120702016
language
English
LU publication?
yes
id
794139fc-57fc-4fed-8440-033327d1e87b (old id 319520)
date added to LUP
2007-08-02 11:33:24
date last changed
2018-01-07 09:08:30
@article{794139fc-57fc-4fed-8440-033327d1e87b,
  abstract     = {In this paper we investigate, determine and classify the critical configurations for solving structure and motion problems for 1D retina vision. We give a complete categorization of all ambiguous configurations for a 1D (calibrated or uncalibrated) perspective camera irrespective of the number of points and views. It is well-known that the calibrated and uncalibrated case are linked through the circular points. This link enables us to solve for both cases simultaneously. Another important tool is the duality in exchanging points and cameras and its corresponding Cremona transformation. These concepts are generalized to the 1D case and used for the investigation of ambiguous configurations. Several examples and illustrations are also provided to explain the results and to provide geometrical insight.},
  author       = {Åström, Karl and Kahl, Fredrik},
  issn         = {0924-9907},
  keyword      = {critical configuration,structure and motion,Cremona transformation},
  language     = {eng},
  number       = {2},
  pages        = {191--203},
  publisher    = {Springer},
  series       = {Journal of Mathematical Imaging and Vision},
  title        = {Ambiguous configurations for the 1D structure and motion problem},
  url          = {http://dx.doi.org/10.1023/A:1022120702016},
  volume       = {18},
  year         = {2003},
}