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Stochastic Modelling and Reconstruction of Random Shapes

Lindgren, Finn LU (2003) In Doctoral Theses in Mathematical Sciences 2003:1.
Abstract
This thesis originates from the problem of reconstructing the three-dimensional shape of objects, when the only available data are two-dimensional images. The solution presented is based on stochastic models for random object shapes and measurements, in combination with practical surface representation and simulation methods.



As a means to handle general, unknown object types, stochastic models for approximating known smooth surfaces as well as generating random smooth surfaces is developed. By also constructing statistical models for measured data, shape estimates can be obtained by application of Bayes' formula. For this purpose, Markov chain Monte Carlo (MCMC) simulation algorithms for the surface models are... (More)
This thesis originates from the problem of reconstructing the three-dimensional shape of objects, when the only available data are two-dimensional images. The solution presented is based on stochastic models for random object shapes and measurements, in combination with practical surface representation and simulation methods.



As a means to handle general, unknown object types, stochastic models for approximating known smooth surfaces as well as generating random smooth surfaces is developed. By also constructing statistical models for measured data, shape estimates can be obtained by application of Bayes' formula. For this purpose, Markov chain Monte Carlo (MCMC) simulation algorithms for the surface models are developed.



Since it is impossible to exactly represent all surfaces in a computer, it is necessary to develop discrete representations, that can be used in estimation algorithms. In this thesis, two spline surface construction methods are developed, one based on triangular Bézier patches, and one based on subdivision techniques. Both methods use control points and normal vectors, so that local control of surface positions and tangent plane orientations is possible.



In addition to surface representations and distributions, an efficient data type and an operator history system are presented, that enable the practical use of variable dimension MCMC simulation, by taking care of the complicated operations necessary to allow changing the structure of the spline surface representation during the simulation. (Less)
Please use this url to cite or link to this publication:
author
supervisor
opponent
  • Professor Rue, Håvard, Norwegian University of Science and Technology, Trondheim
organization
publishing date
type
Thesis
publication status
published
subject
keywords
operations research, Statistics, operationsanalys, Statistik, programmering, aktuariematematik, actuarial mathematics, programming
in
Doctoral Theses in Mathematical Sciences
volume
2003:1
pages
150 pages
publisher
Mathematical Statistics, Centre for Mathematical Sciences, Lund University
defense location
Lecture hall MH:A, Centre for Mathematical Sciences, Sölvegatan 18, Lund Institute of Technology
defense date
2003-06-06 10:15
ISSN
1404-0034
ISBN
91-628-5701-0
language
English
LU publication?
yes
id
8a77516e-9ec1-42ba-9d69-cf58bf644be8 (old id 21282)
date added to LUP
2007-05-28 14:49:16
date last changed
2018-05-29 12:13:18
@phdthesis{8a77516e-9ec1-42ba-9d69-cf58bf644be8,
  abstract     = {This thesis originates from the problem of reconstructing the three-dimensional shape of objects, when the only available data are two-dimensional images. The solution presented is based on stochastic models for random object shapes and measurements, in combination with practical surface representation and simulation methods.<br/><br>
<br/><br>
As a means to handle general, unknown object types, stochastic models for approximating known smooth surfaces as well as generating random smooth surfaces is developed. By also constructing statistical models for measured data, shape estimates can be obtained by application of Bayes' formula. For this purpose, Markov chain Monte Carlo (MCMC) simulation algorithms for the surface models are developed.<br/><br>
<br/><br>
Since it is impossible to exactly represent all surfaces in a computer, it is necessary to develop discrete representations, that can be used in estimation algorithms. In this thesis, two spline surface construction methods are developed, one based on triangular Bézier patches, and one based on subdivision techniques. Both methods use control points and normal vectors, so that local control of surface positions and tangent plane orientations is possible.<br/><br>
<br/><br>
In addition to surface representations and distributions, an efficient data type and an operator history system are presented, that enable the practical use of variable dimension MCMC simulation, by taking care of the complicated operations necessary to allow changing the structure of the spline surface representation during the simulation.},
  author       = {Lindgren, Finn},
  isbn         = {91-628-5701-0},
  issn         = {1404-0034},
  keyword      = {operations research,Statistics,operationsanalys,Statistik,programmering,aktuariematematik,actuarial mathematics,programming},
  language     = {eng},
  pages        = {150},
  publisher    = {Mathematical Statistics, Centre for Mathematical Sciences, Lund University},
  school       = {Lund University},
  series       = {Doctoral Theses in Mathematical Sciences},
  title        = {Stochastic Modelling and Reconstruction of Random Shapes},
  volume       = {2003:1},
  year         = {2003},
}