Stochastic Modelling and Reconstruction of Random Shapes
(2003) In Doctoral Theses in Mathematical Sciences 2003:1. Abstract
 This thesis originates from the problem of reconstructing the threedimensional shape of objects, when the only available data are twodimensional 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 threedimensional shape of objects, when the only available data are twodimensional 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:
http://lup.lub.lu.se/record/21282
 author
 Lindgren, Finn ^{LU}
 supervisor
 opponent

 Professor Rue, Håvard, Norwegian University of Science and Technology, Trondheim
 organization
 publishing date
 2003
 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
 20030606 10:15
 ISSN
 14040034
 ISBN
 9162857010
 language
 English
 LU publication?
 yes
 id
 8a77516e9ec142ba9d69cf58bf644be8 (old id 21282)
 date added to LUP
 20070528 14:49:16
 date last changed
 20180529 12:13:18
@phdthesis{8a77516e9ec142ba9d69cf58bf644be8, abstract = {This thesis originates from the problem of reconstructing the threedimensional shape of objects, when the only available data are twodimensional 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 = {9162857010}, issn = {14040034}, 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}, }