SpatioTemporal Estimation for Mixture Models and Gaussian Markov Random Fields  Applications to Video Analysis and Environmental Modelling
(2008) In Doctoral Theses in Mathematical Sciences 4. Abstract
 In this thesis computationally intensive methods are used to estimate models and to make inference for large, spatiotemporal data sets. The thesis is divided into two parts: the first two papers are concerned with video analysis, while the last three papers model and investigate
environmental data from the Sahel area in northern Africa.
In the first part of the thesis, mixture models are used to
distinguish between moving (foreground) and stationary (background) pixels in video sequences. A recursive estimator for mixtures of Gaussians is derived using an expectation maximisation (EM) algorithm. It is shown that the recursive estimator can be interpreted in a Bayesian framework. With some additional... (More)  In this thesis computationally intensive methods are used to estimate models and to make inference for large, spatiotemporal data sets. The thesis is divided into two parts: the first two papers are concerned with video analysis, while the last three papers model and investigate
environmental data from the Sahel area in northern Africa.
In the first part of the thesis, mixture models are used to
distinguish between moving (foreground) and stationary (background) pixels in video sequences. A recursive estimator for mixtures of Gaussians is derived using an expectation maximisation (EM) algorithm. It is shown that the recursive estimator can be interpreted in a Bayesian framework. With some additional steps, the estimator is
used to construct an algorithm that segments video frames into foreground and background pixels.
Additionally, an extension to existing segmentation algorithms that detects and adjusts for rapid changes in illumination is presented. This extension is shown to work for two segmentation algorithms that model the pixel values using Gaussian mixtures.
In the second part of the thesis, environmental data sets, consisting of precipitation measurements and satellite derived vegetation indices, are examined. First, calibration issues for the vegetation index data are investigated. Thereafter, a Gaussian Markov random field (GMRF) model for estimation of spatially dependent trends is constructed. The parameters in the GMRF model are estimated using an EM algorithm, and the performance of the model is evaluated using simulated data. The model is used to analyse temporal trends in the vegetation data.
Finally, a spatiotemporal GMRF model is used to interpolate the precipitation measurements. The model is created by extending a spatial GMRF to a spatiotemporal model with a first order autoregressive dependence in time. The spatial part of the model consists of a
GMRF that approximates a field with isotropic Matérn covariance. To obtain a model that is defined where the precipitation measurements were taken the spatial GMRF is constructed on a set of irregularly spaced points on the globe. The model is estimated using a Markov chain Monte Carlo approach and the formulation as a Markov field allows for efficient computations, even though the field has more than 30000 nodes. (Less)
Please use this url to cite or link to this publication:
http://lup.lub.lu.se/record/1146245
 author
 Lindström, Johan ^{LU}
 supervisor
 opponent

 Prof Rue, Håvard, NTNU, Trondheim, Norway
 organization
 publishing date
 2008
 type
 Thesis
 publication status
 published
 subject
 keywords
 vegetation, time series analysis, video segmentation, spatiotemporal modelling, precipitation, Markov chain Monte Carlo, Gaussian Markov random fields, expectation maximisation, change point detection, Bayesian recursive estimation, African Sahel, adaptive Gaussian mixtures
 in
 Doctoral Theses in Mathematical Sciences
 volume
 4
 pages
 179 pages
 publisher
 Lund University
 defense location
 Room MH:C, Mathematics Building, Sölvegatan 18, Faculty of Engineering, Lund university, Lund
 defense date
 20080523 09:15
 ISBN
 9789162875022
 language
 English
 LU publication?
 yes
 id
 39b587f7be744e5f9730506062ea9a5f (old id 1146245)
 date added to LUP
 20080429 15:37:17
 date last changed
 20160919 08:45:07
@phdthesis{39b587f7be744e5f9730506062ea9a5f, abstract = {In this thesis computationally intensive methods are used to estimate models and to make inference for large, spatiotemporal data sets. The thesis is divided into two parts: the first two papers are concerned with video analysis, while the last three papers model and investigate<br/><br> environmental data from the Sahel area in northern Africa.<br/><br> <br/><br> In the first part of the thesis, mixture models are used to<br/><br> distinguish between moving (foreground) and stationary (background) pixels in video sequences. A recursive estimator for mixtures of Gaussians is derived using an expectation maximisation (EM) algorithm. It is shown that the recursive estimator can be interpreted in a Bayesian framework. With some additional steps, the estimator is<br/><br> used to construct an algorithm that segments video frames into foreground and background pixels.<br/><br> <br/><br> Additionally, an extension to existing segmentation algorithms that detects and adjusts for rapid changes in illumination is presented. This extension is shown to work for two segmentation algorithms that model the pixel values using Gaussian mixtures.<br/><br> <br/><br> In the second part of the thesis, environmental data sets, consisting of precipitation measurements and satellite derived vegetation indices, are examined. First, calibration issues for the vegetation index data are investigated. Thereafter, a Gaussian Markov random field (GMRF) model for estimation of spatially dependent trends is constructed. The parameters in the GMRF model are estimated using an EM algorithm, and the performance of the model is evaluated using simulated data. The model is used to analyse temporal trends in the vegetation data.<br/><br> <br/><br> Finally, a spatiotemporal GMRF model is used to interpolate the precipitation measurements. The model is created by extending a spatial GMRF to a spatiotemporal model with a first order autoregressive dependence in time. The spatial part of the model consists of a <br/><br> GMRF that approximates a field with isotropic Matérn covariance. To obtain a model that is defined where the precipitation measurements were taken the spatial GMRF is constructed on a set of irregularly spaced points on the globe. The model is estimated using a Markov chain Monte Carlo approach and the formulation as a Markov field allows for efficient computations, even though the field has more than 30000 nodes.}, author = {Lindström, Johan}, isbn = {9789162875022}, keyword = {vegetation,time series analysis,video segmentation,spatiotemporal modelling,precipitation,Markov chain Monte Carlo,Gaussian Markov random fields,expectation maximisation,change point detection,Bayesian recursive estimation,African Sahel,adaptive Gaussian mixtures}, language = {eng}, pages = {179}, publisher = {Lund University}, school = {Lund University}, series = {Doctoral Theses in Mathematical Sciences}, title = {SpatioTemporal Estimation for Mixture Models and Gaussian Markov Random Fields  Applications to Video Analysis and Environmental Modelling}, volume = {4}, year = {2008}, }