Dynamic modelling for image analysis

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.