Extensions and Applications of Affine Shape
(1999) In Doctoral Theses in Mathematical Sciences 1999:7. Abstract
 A central problem in computer vision is to reconstruct the threedimensional structure of a scene from a set of twodimensional 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 threedimensional structure of a scene from a set of twodimensional 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:
https://lup.lub.lu.se/record/40132
 author
 Berthilsson, Rikard ^{LU}
 supervisor
 opponent

 Maybank, Steve, Reader, University of Reading, Dept. of Computer Science, Whiteknights, Reading RG6 6Ay, England
 organization
 publishing date
 1999
 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, SÃ¶lvegatan 18, Lund
 defense date
 19991209 10:15:00
 external identifiers

 other:LUTFMA10091999
 ISSN
 14040034
 ISBN
 9162839152
 language
 English
 LU publication?
 yes
 id
 ac6f0ba25ae24ff7b3dd78dc9e5aca69 (old id 40132)
 date added to LUP
 20160401 17:11:34
 date last changed
 20190521 13:26:49
@phdthesis{ac6f0ba25ae24ff7b3dd78dc9e5aca69, abstract = {{A central problem in computer vision is to reconstruct the threedimensional structure of a scene from a set of twodimensional 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 = {{9162839152}}, issn = {{14040034}}, keywords = {{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}}, 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}}, }