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New Results on Triangulation, Polynomial Equation Solving and Their Application in Global Localization

Josephson, Klas LU (2008)
Abstract
This thesis addresses the problem of global localization from images. The overall goal is to find the location and the direction of a camera given an image taken with the camera relative a 3D world model. In order to solve the problem several subproblems have to be handled. The two main steps for constructing a system for global localization consist of model building and localization. For the model construction phase we give a new method for triangulation that guarantees that the globally optimal position is attained under the assumption of Gaussian noise in the image measurements. A common framework for the triangulation of points, lines and conics is presented. The second contribution of the thesis is in the field of solving systems of... (More)
This thesis addresses the problem of global localization from images. The overall goal is to find the location and the direction of a camera given an image taken with the camera relative a 3D world model. In order to solve the problem several subproblems have to be handled. The two main steps for constructing a system for global localization consist of model building and localization. For the model construction phase we give a new method for triangulation that guarantees that the globally optimal position is attained under the assumption of Gaussian noise in the image measurements. A common framework for the triangulation of points, lines and conics is presented. The second contribution of the thesis is in the field of solving systems of polynomial equations. Many problems in geometrical computer vision lead to computing the real roots of a system of polynomial equations, and several such geometry problems appear in the localization problem. The method presented in the thesis gives a significant improvement in the numerics when Gröbner basis methods are applied. Such methods are often plagued by numerical problems, but by using the fact that the complete Gröbner basis is not needed, the numerics can be improved. In the final part of the thesis we present several new minimal, geometric problems that have not been solved previously. These minimal cases make use of both two and three dimensional correspondences at the same time. The solutions to these minimal problems form the basis of a localization system which aims at improving robustness compared to the state of the art. (Less)
Please use this url to cite or link to this publication:
author
supervisor
organization
publishing date
type
Thesis
publication status
published
subject
pages
115 pages
ISBN
978-91-633-2870-1
language
English
LU publication?
yes
id
12953a4c-e140-4cde-b6f1-3834d1105b77 (old id 1051275)
alternative location
http://www.maths.lth.se/vision/publdb/reports/pdf/josephson-lic-08.pdf
date added to LUP
2008-07-01 09:47:59
date last changed
2016-09-19 08:45:15
@misc{12953a4c-e140-4cde-b6f1-3834d1105b77,
  abstract     = {This thesis addresses the problem of global localization from images. The overall goal is to find the location and the direction of a camera given an image taken with the camera relative a 3D world model. In order to solve the problem several subproblems have to be handled. The two main steps for constructing a system for global localization consist of model building and localization. For the model construction phase we give a new method for triangulation that guarantees that the globally optimal position is attained under the assumption of Gaussian noise in the image measurements. A common framework for the triangulation of points, lines and conics is presented. The second contribution of the thesis is in the field of solving systems of polynomial equations. Many problems in geometrical computer vision lead to computing the real roots of a system of polynomial equations, and several such geometry problems appear in the localization problem. The method presented in the thesis gives a significant improvement in the numerics when Gröbner basis methods are applied. Such methods are often plagued by numerical problems, but by using the fact that the complete Gröbner basis is not needed, the numerics can be improved. In the final part of the thesis we present several new minimal, geometric problems that have not been solved previously. These minimal cases make use of both two and three dimensional correspondences at the same time. The solutions to these minimal problems form the basis of a localization system which aims at improving robustness compared to the state of the art.},
  author       = {Josephson, Klas},
  isbn         = {978-91-633-2870-1},
  language     = {eng},
  note         = {Licentiate Thesis},
  pages        = {115},
  title        = {New Results on Triangulation, Polynomial Equation Solving and Their Application in Global Localization},
  year         = {2008},
}