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Global Optimization for One-Dimensional Structure and Motion Problems

Enqvist, Olof LU ; Kahl, Fredrik LU ; Olsson, Carl LU and Åström, Karl LU (2010) In SIAM Journal of Imaging Sciences 3(4). p.1075-1095
Abstract
We study geometric reconstruction problems in one-dimensional retina vision. In such problems, the scene is modeled as a two-dimensional plane, and the camera sensor produces one-dimensional images of the scene. Our main contribution is an efficient method for computing the global optimum to the structure and motion problem with respect to the L-infinity norm of the reprojection errors. One-dimensional cameras have proven useful in several applications, most prominently for autonomous vehicles, where they are used to provide inexpensive and reliable navigational systems. Previous results on one-dimensional vision are limited to the classification and solving of minimal cases, bundle adjustment for finding local optima, and linear... (More)
We study geometric reconstruction problems in one-dimensional retina vision. In such problems, the scene is modeled as a two-dimensional plane, and the camera sensor produces one-dimensional images of the scene. Our main contribution is an efficient method for computing the global optimum to the structure and motion problem with respect to the L-infinity norm of the reprojection errors. One-dimensional cameras have proven useful in several applications, most prominently for autonomous vehicles, where they are used to provide inexpensive and reliable navigational systems. Previous results on one-dimensional vision are limited to the classification and solving of minimal cases, bundle adjustment for finding local optima, and linear algorithms for algebraic cost functions. In contrast, we present an approach for finding globally optimal solutions with respect to the L-infinity norm of the angular reprojection errors. We show how to solve intersection and resection problems as well as the problem of simultaneous localization and mapping (SLAM). The algorithm is robust to use when there are missing data, which means that all points are not necessarily seen in all images. Our approach has been tested on a variety of different scenarios, both real and synthetic. The algorithm shows good performance for intersection and resection and for SLAM with up to five views. For more views the high dimension of the search space tends to give long running times. The experimental section also gives interesting examples showing that for one-dimensional cameras with limited field of view the SLAM problem is often inherently ill-conditioned. (Less)
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author
organization
publishing date
type
Contribution to journal
publication status
published
subject
keywords
geometry, and mapping, simultaneous localization, one-dimensional vision, structure and motion
in
SIAM Journal of Imaging Sciences
volume
3
issue
4
pages
1075 - 1095
publisher
SIAM Publications
external identifiers
  • wos:000285501700015
ISSN
1936-4954
DOI
10.1137/090754510
language
English
LU publication?
yes
id
31463d33-ab1a-402b-a100-ed1d29e07541 (old id 1810916)
date added to LUP
2011-03-16 14:30:22
date last changed
2018-05-29 12:02:46
@article{31463d33-ab1a-402b-a100-ed1d29e07541,
  abstract     = {We study geometric reconstruction problems in one-dimensional retina vision. In such problems, the scene is modeled as a two-dimensional plane, and the camera sensor produces one-dimensional images of the scene. Our main contribution is an efficient method for computing the global optimum to the structure and motion problem with respect to the L-infinity norm of the reprojection errors. One-dimensional cameras have proven useful in several applications, most prominently for autonomous vehicles, where they are used to provide inexpensive and reliable navigational systems. Previous results on one-dimensional vision are limited to the classification and solving of minimal cases, bundle adjustment for finding local optima, and linear algorithms for algebraic cost functions. In contrast, we present an approach for finding globally optimal solutions with respect to the L-infinity norm of the angular reprojection errors. We show how to solve intersection and resection problems as well as the problem of simultaneous localization and mapping (SLAM). The algorithm is robust to use when there are missing data, which means that all points are not necessarily seen in all images. Our approach has been tested on a variety of different scenarios, both real and synthetic. The algorithm shows good performance for intersection and resection and for SLAM with up to five views. For more views the high dimension of the search space tends to give long running times. The experimental section also gives interesting examples showing that for one-dimensional cameras with limited field of view the SLAM problem is often inherently ill-conditioned.},
  author       = {Enqvist, Olof and Kahl, Fredrik and Olsson, Carl and Åström, Karl},
  issn         = {1936-4954},
  keyword      = {geometry,and mapping,simultaneous localization,one-dimensional vision,structure and motion},
  language     = {eng},
  number       = {4},
  pages        = {1075--1095},
  publisher    = {SIAM Publications},
  series       = {SIAM Journal of Imaging Sciences},
  title        = {Global Optimization for One-Dimensional Structure and Motion Problems},
  url          = {http://dx.doi.org/10.1137/090754510},
  volume       = {3},
  year         = {2010},
}