Advanced

Extensions and Applications of Affine Shape

Berthilsson, Rikard LU (1999) In Doctoral theses in mathematical sciences 1999:7.
Abstract
A central problem in computer vision is to reconstruct the three-dimensional structure of a scene from a set of two-dimensional images. Traditionally this is done by extracting a set of characteristic points in the scene and to compute a reconstruction of these points. In this thesis we propose a novel method that allows reconstruction of a wider class of objects, including curves and surfaces. As always when dealing with measured data, the handling of noise is crucial. In this thesis we analyze the impact of uncertainty in measurements on feature parameters, and how these can be estimated in maximum likelihood sense.



The thesis consists of an introduction and six separate papers. The introduction gives an overview and... (More)
A central problem in computer vision is to reconstruct the three-dimensional structure of a scene from a set of two-dimensional images. Traditionally this is done by extracting a set of characteristic points in the scene and to compute a reconstruction of these points. In this thesis we propose a novel method that allows reconstruction of a wider class of objects, including curves and surfaces. As always when dealing with measured data, the handling of noise is crucial. In this thesis we analyze the impact of uncertainty in measurements on feature parameters, and how these can be estimated in maximum likelihood sense.



The thesis consists of an introduction and six separate papers. The introduction gives an overview and motivation for the contents of the thesis. Paper I presents an extension of the so called affine shape of finite point configuration to affine shape of for example curves and surfaces. An algorithm for reconstructing curves is also presented. In paper II it is shown how the extension of affine shape can be used to recognize curves and in particular how it can be used to interpret handwriting. Paper III presents an extension to surfaces of the method for reconstructing curves in paper I based on affine shape. The paper also uses results from paper IV, where it is shown how images can be matched by allowing for deformations and using correlation. The matching is done by an iterative algorithm, where the fast Fourier transformation is used in each iteration to speed up computations. Papers V and VI consider statistical issues in computer vision. In paper V we discuss how uncertainties in measurements of point configurations are influencing the shape. More precisely, it is shown how the probability measure of shape can be computed from the probability measure of the point configurations. In paper VI we discuss how the characteristic function can be used to compute maximum likelihood estimates of matching constraints and how to obtain densities of estimated parameters. In particular, we present a novel method for estimating the fundamental matrix. (Less)
Please use this url to cite or link to this publication:
author
opponent
  • Maybank, Steve, Reader, University of Reading, Dept. of Computer Science, Whiteknights, Reading RG6 6Ay, England
organization
publishing date
type
Thesis
publication status
published
subject
keywords
Systems engineering, Matematik, Mathematics, density of shape, maximum likelihood, matching constraint, surface, curve, handwriting, recognition, affine shape, reconstruction, computer technology, Data- och systemvetenskap
in
Doctoral theses in mathematical sciences
volume
1999:7
pages
188 pages
publisher
Centre for Mathematical Sciences, Lund University
defense location
Room C, Matematikcentrum, Sölvegatan 18, Lund
defense date
1999-12-09 10:15
external identifiers
  • other:LUTFMA-1009-1999
ISSN
1404-0034
ISBN
91-628-3915-2
language
English
LU publication?
yes
id
ac6f0ba2-5ae2-4ff7-b3dd-78dc9e5aca69 (old id 40132)
date added to LUP
2007-06-20 11:59:55
date last changed
2016-09-19 08:44:59
@phdthesis{ac6f0ba2-5ae2-4ff7-b3dd-78dc9e5aca69,
  abstract     = {A central problem in computer vision is to reconstruct the three-dimensional structure of a scene from a set of two-dimensional images. Traditionally this is done by extracting a set of characteristic points in the scene and to compute a reconstruction of these points. In this thesis we propose a novel method that allows reconstruction of a wider class of objects, including curves and surfaces. As always when dealing with measured data, the handling of noise is crucial. In this thesis we analyze the impact of uncertainty in measurements on feature parameters, and how these can be estimated in maximum likelihood sense.<br/><br>
<br/><br>
The thesis consists of an introduction and six separate papers. The introduction gives an overview and motivation for the contents of the thesis. Paper I presents an extension of the so called affine shape of finite point configuration to affine shape of for example curves and surfaces. An algorithm for reconstructing curves is also presented. In paper II it is shown how the extension of affine shape can be used to recognize curves and in particular how it can be used to interpret handwriting. Paper III presents an extension to surfaces of the method for reconstructing curves in paper I based on affine shape. The paper also uses results from paper IV, where it is shown how images can be matched by allowing for deformations and using correlation. The matching is done by an iterative algorithm, where the fast Fourier transformation is used in each iteration to speed up computations. Papers V and VI consider statistical issues in computer vision. In paper V we discuss how uncertainties in measurements of point configurations are influencing the shape. More precisely, it is shown how the probability measure of shape can be computed from the probability measure of the point configurations. In paper VI we discuss how the characteristic function can be used to compute maximum likelihood estimates of matching constraints and how to obtain densities of estimated parameters. In particular, we present a novel method for estimating the fundamental matrix.},
  author       = {Berthilsson, Rikard},
  isbn         = {91-628-3915-2},
  issn         = {1404-0034},
  keyword      = {Systems engineering,Matematik,Mathematics,density of shape,maximum likelihood,matching constraint,surface,curve,handwriting,recognition,affine shape,reconstruction,computer technology,Data- och systemvetenskap},
  language     = {eng},
  pages        = {188},
  publisher    = {Centre for Mathematical Sciences, Lund University},
  school       = {Lund University},
  series       = {Doctoral theses in mathematical sciences},
  title        = {Extensions and Applications of Affine Shape},
  volume       = {1999:7},
  year         = {1999},
}