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Polynomial Solvers for Geometric Problems - Applications in Computer Vision and Sensor Networks

Kuang, Yubin LU (2014)
Abstract
Given images of a scene taken by a moving camera or recordings of a moving smart phone playing a song by a microphone array, how hard is it to reconstruct the scene structure or the moving trajectory of the phone? In this thesis, we study and solve several fundamental geometric problems in order to provide solutions to these problems.



The key underlying technique for solving such geometric problems is solving systems of polynomial equations. In this thesis, several general techniques are developed. We utilize numerical schemes and explore symmetric structures of polynomial equations to enable fast and stable polynomial solvers.



These enable fast and robust techniques for reconstruction of the scene... (More)
Given images of a scene taken by a moving camera or recordings of a moving smart phone playing a song by a microphone array, how hard is it to reconstruct the scene structure or the moving trajectory of the phone? In this thesis, we study and solve several fundamental geometric problems in order to provide solutions to these problems.



The key underlying technique for solving such geometric problems is solving systems of polynomial equations. In this thesis, several general techniques are developed. We utilize numerical schemes and explore symmetric structures of polynomial equations to enable fast and stable polynomial solvers.



These enable fast and robust techniques for reconstruction of the scene structures using different measurements. One of the examples is structure from sound. By measuring the time-of-arrivals of specific time instances of a song played on a phone, one can reconstruct the trajectory of the phone as well as the positions of the microphones up to precision of centimeters. (Less)
Please use this url to cite or link to this publication:
author
supervisor
opponent
  • Prof. Bartoli, Adrien, University of Auvergne, France
organization
publishing date
type
Thesis
publication status
published
subject
keywords
polynomial solver, geometric problems, computer vision, sensor networks, symmetry
pages
172 pages
defense location
Lecture hall MH:A, Centre for Mathematical Sciences, Sölvegatan 18, Lund University Faculty of Engineering
defense date
2014-05-09 10:15
ISSN
1404-0034
ISBN
978-91-7473-995-4
language
English
LU publication?
yes
id
5bd36ec8-d67f-4f04-af73-bf68a5dd1267 (old id 4393456)
alternative location
http://www.maths.lth.se/matematiklth/personal/yubin/thesis.pdf
date added to LUP
2014-04-17 13:05:08
date last changed
2016-09-19 08:45:01
@misc{5bd36ec8-d67f-4f04-af73-bf68a5dd1267,
  abstract     = {Given images of a scene taken by a moving camera or recordings of a moving smart phone playing a song by a microphone array, how hard is it to reconstruct the scene structure or the moving trajectory of the phone? In this thesis, we study and solve several fundamental geometric problems in order to provide solutions to these problems. <br/><br>
<br/><br>
The key underlying technique for solving such geometric problems is solving systems of polynomial equations. In this thesis, several general techniques are developed. We utilize numerical schemes and explore symmetric structures of polynomial equations to enable fast and stable polynomial solvers. <br/><br>
<br/><br>
These enable fast and robust techniques for reconstruction of the scene structures using different measurements. One of the examples is structure from sound. By measuring the time-of-arrivals of specific time instances of a song played on a phone, one can reconstruct the trajectory of the phone as well as the positions of the microphones up to precision of centimeters.},
  author       = {Kuang, Yubin},
  isbn         = {978-91-7473-995-4},
  issn         = {1404-0034},
  keyword      = {polynomial solver,geometric problems,computer vision,sensor networks,symmetry},
  language     = {eng},
  pages        = {172},
  title        = {Polynomial Solvers for Geometric Problems - Applications in Computer Vision and Sensor Networks},
  year         = {2014},
}