Gröbner Basis Methods for Minimal Problems in Computer Vision
(2005) In Doctoral Theses in Mathematical Sciences 2005:1.- Abstract
- A method is presented for building solvers
for classes of multivariate polynomial equations.
The method is based on solving an analogous
template problem over a finite field, and
then using the elimination order established
for this problem for the original
class of problems. A strength of this method
is that this permits pivoting in the elimination.
Solvers for several minimal problems in
computer vision are presented. Relative
pose is solved both for a generalised camera,
and for a camera with unknown focal length,
... (More) - A method is presented for building solvers
for classes of multivariate polynomial equations.
The method is based on solving an analogous
template problem over a finite field, and
then using the elimination order established
for this problem for the original
class of problems. A strength of this method
is that this permits pivoting in the elimination.
Solvers for several minimal problems in
computer vision are presented. Relative
pose is solved both for a generalised camera,
and for a camera with unknown focal length,
both in two positions with six visible points.
A solver for optimal triangulation in
three images is presented.
Model-free calibration for pinhole cameras
is investigated. It is shown that for a smooth
deformation of the image plane, the image plane
can be projectively reconstructed from two
flow-fields from purely translating cameras.
Methods for hand-eye calibration using the
multilinear constraints and
vehicle-eye for laser-scanner based
navigation systems are presented. (Less)
Please use this url to cite or link to this publication:
https://lup.lub.lu.se/record/24960
- author
- Stewenius, Henrik LU
- supervisor
-
- Karl Åström LU
- opponent
-
- professor Triggs, William, INRIA Alpes
- organization
- publishing date
- 2005
- type
- Thesis
- publication status
- published
- subject
- keywords
- computer vision, minimal problems, gröbner basis, Matematik, Teknik, Mathematics, Technological sciences
- in
- Doctoral Theses in Mathematical Sciences
- volume
- 2005:1
- pages
- 183 pages
- publisher
- Centre for Mathematical Sciences, Lund University
- defense location
- Matematikhuset, sal C.
- defense date
- 2005-04-15 13:15:00
- ISSN
- 1404-0034
- ISBN
- 91-628-6410-6
- language
- English
- LU publication?
- yes
- id
- 7e8e0c17-c54e-4683-a0c7-ce836867362f (old id 24960)
- date added to LUP
- 2016-04-01 16:24:47
- date last changed
- 2019-05-21 13:32:21
@phdthesis{7e8e0c17-c54e-4683-a0c7-ce836867362f,
abstract = {{A method is presented for building solvers<br/><br>
<br/><br>
for classes of multivariate polynomial equations.<br/><br>
<br/><br>
The method is based on solving an analogous<br/><br>
<br/><br>
template problem over a finite field, and<br/><br>
<br/><br>
then using the elimination order established<br/><br>
<br/><br>
for this problem for the original<br/><br>
<br/><br>
class of problems. A strength of this method<br/><br>
<br/><br>
is that this permits pivoting in the elimination.<br/><br>
<br/><br>
Solvers for several minimal problems in<br/><br>
<br/><br>
computer vision are presented. Relative<br/><br>
<br/><br>
pose is solved both for a generalised camera,<br/><br>
<br/><br>
and for a camera with unknown focal length,<br/><br>
<br/><br>
both in two positions with six visible points.<br/><br>
<br/><br>
A solver for optimal triangulation in<br/><br>
<br/><br>
three images is presented.<br/><br>
<br/><br>
Model-free calibration for pinhole cameras<br/><br>
<br/><br>
is investigated. It is shown that for a smooth<br/><br>
<br/><br>
deformation of the image plane, the image plane<br/><br>
<br/><br>
can be projectively reconstructed from two<br/><br>
<br/><br>
flow-fields from purely translating cameras.<br/><br>
<br/><br>
Methods for hand-eye calibration using the<br/><br>
<br/><br>
multilinear constraints and<br/><br>
<br/><br>
vehicle-eye for laser-scanner based<br/><br>
<br/><br>
navigation systems are presented.}},
author = {{Stewenius, Henrik}},
isbn = {{91-628-6410-6}},
issn = {{1404-0034}},
keywords = {{computer vision; minimal problems; gröbner basis; Matematik; Teknik; Mathematics; Technological sciences}},
language = {{eng}},
publisher = {{Centre for Mathematical Sciences, Lund University}},
school = {{Lund University}},
series = {{Doctoral Theses in Mathematical Sciences}},
title = {{Gröbner Basis Methods for Minimal Problems in Computer Vision}},
volume = {{2005:1}},
year = {{2005}},
}