Image segmentation is an important task in many image analysis applications,
where it is an essential first stage before further analysis is possible. The levelset
method is an implicit approach to image segmentation problems. The main
advantages are that it can handle an unknown number of regions and can deal
with complicated topological changes in a simple and natural way. The research
presented in this thesis is motivated by the need to develop statistical methodologies
for modelling image data through level sets. The fundamental idea is to
combine the level-set method with statistical modelling based on the Bayesian
framework to produce an attractive approach for tackling a wider range of segmentation
problems in image analysis.
A complete framework for a Bayesian level set model is given to allow a wider
interpretation of model components. The proposed model is described based
on a Gaussian likelihood and exponential prior distributions on object area and
boundary length, and an investigation of uncertainty and a sensitivity analysis
are carried out. The model is then generalized using a more robust noise model
and more flexible prior distributions.
A new Bayesian modelling approach to object identification is introduced. The
proposed model is based on the level set method which assumes the implicit
representation of the object outlines as a zero level set contour of a higher dimensional
function. The Markov chain Monte Carlo (MCMC) algorithm is used
to estimate the model parameters, by generating approximate samples from the
posterior distribution. The proposed method is applied to simulated and real
datasets.
A new temporal model is proposed in a Bayesian framework for level-set based
image sequence segmentation. MCMC methods are used to explore the model
and to obtain information about solution behaviour. The proposed method is
applied to simulated image sequences
