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The minimal structure and motion problems with missing data for 1D retina vision

Oskarsson, Magnus LU ; Åström, Karl LU and Overgaard, Niels Christian LU (2006) In Journal of Mathematical Imaging and Vision 26(3). p.327-343
Abstract
In this paper we investigate the structure and motion problem for calibrated one-dimensional projections of a two-dimensional environment. The theory of one-dimensional cameras are useful in several areas, e.g. within robotics, autonomous guided vehicles, projection of lines in ordinary vision and vision of vehicles undergoing so called planar motion. In a previous paper the structure and motion problem for all cases with non-missing data was classified and solved. Our aim is here to classify all structure and motion problems, even those with missing data, and to solve them. In the classification we introduce the notion of a prime problem. A prime problem is a minimal problem that does not contain a minimal problem as a sub-problem. We... (More)
In this paper we investigate the structure and motion problem for calibrated one-dimensional projections of a two-dimensional environment. The theory of one-dimensional cameras are useful in several areas, e.g. within robotics, autonomous guided vehicles, projection of lines in ordinary vision and vision of vehicles undergoing so called planar motion. In a previous paper the structure and motion problem for all cases with non-missing data was classified and solved. Our aim is here to classify all structure and motion problems, even those with missing data, and to solve them. In the classification we introduce the notion of a prime problem. A prime problem is a minimal problem that does not contain a minimal problem as a sub-problem. We further show that there are infinitely many such prime problems. We give solutions to four prime problems, and using the duality of Carlsson these can be extended to solutions of seven prime problems. Finally we give some experimental results based on synthetic data. (Less)
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author
organization
publishing date
type
Contribution to journal
publication status
published
subject
in
Journal of Mathematical Imaging and Vision
volume
26
issue
3
pages
327 - 343
publisher
Springer
external identifiers
  • wos:000242704500007
  • scopus:33845490207
ISSN
0924-9907
DOI
10.1007/s10851-006-9003-7
language
English
LU publication?
yes
id
b28799db-ae2d-463e-95b1-9d28bbb1da00 (old id 682462)
date added to LUP
2008-01-06 10:57:38
date last changed
2019-01-06 10:44:24
@article{b28799db-ae2d-463e-95b1-9d28bbb1da00,
  abstract     = {In this paper we investigate the structure and motion problem for calibrated one-dimensional projections of a two-dimensional environment. The theory of one-dimensional cameras are useful in several areas, e.g. within robotics, autonomous guided vehicles, projection of lines in ordinary vision and vision of vehicles undergoing so called planar motion. In a previous paper the structure and motion problem for all cases with non-missing data was classified and solved. Our aim is here to classify all structure and motion problems, even those with missing data, and to solve them. In the classification we introduce the notion of a prime problem. A prime problem is a minimal problem that does not contain a minimal problem as a sub-problem. We further show that there are infinitely many such prime problems. We give solutions to four prime problems, and using the duality of Carlsson these can be extended to solutions of seven prime problems. Finally we give some experimental results based on synthetic data.},
  author       = {Oskarsson, Magnus and Åström, Karl and Overgaard, Niels Christian},
  issn         = {0924-9907},
  language     = {eng},
  number       = {3},
  pages        = {327--343},
  publisher    = {Springer},
  series       = {Journal of Mathematical Imaging and Vision},
  title        = {The minimal structure and motion problems with missing data for 1D retina vision},
  url          = {http://dx.doi.org/10.1007/s10851-006-9003-7},
  volume       = {26},
  year         = {2006},
}