Polynomial Solvers for Geometric Problems - Applications in Computer Vision and Sensor Networks
(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:
https://lup.lub.lu.se/record/4393456
- author
- Kuang, Yubin LU
- supervisor
-
- Karl Åström LU
- opponent
-
- Prof. Bartoli, Adrien, University of Auvergne, France
- organization
- publishing date
- 2014
- 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 10:15:00
- 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
- 2016-04-04 09:37:33
- date last changed
- 2018-11-21 20:54:26
@phdthesis{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}},
keywords = {{polynomial solver; geometric problems; computer vision; sensor networks; symmetry}},
language = {{eng}},
school = {{Lund University}},
title = {{Polynomial Solvers for Geometric Problems - Applications in Computer Vision and Sensor Networks}},
url = {{https://lup.lub.lu.se/search/files/5374142/4393481.pdf}},
year = {{2014}},
}