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Gröbner Basis Methods for Minimal Problems in Computer Vision

Stewenius, Henrik LU (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:
author
supervisor
opponent
  • professor Triggs, William, INRIA Alpes
organization
publishing date
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
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
2007-06-01 09:02:41
date last changed
2016-09-19 08:44:56
@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},
  keyword      = {computer vision,minimal problems,gröbner basis,Matematik,Teknik,Mathematics,Technological sciences},
  language     = {eng},
  pages        = {183},
  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},
}