This thesis addresses the automatic extraction of a reference tissue region, devoid of receptor sites, which can then be used as an input for a reference tissue model, allowing for the quantification of receptor sites. It is shown that this segmentation can be determined from the time-activity curves associated with each voxel within the 3D volume, using modern machine learning methods. Previously, supervised learning techniques have not been considered in PET reference region extraction. In this thesis, two new methods are proposed to incorporate expert knowledge and the image models with the data: a hierarchical method and a semi-supervised image segmentation framework. Markov random field (MRF) models are used as a stochastic image model to specify the spatial interactions. The first method uses a Bayesian neural network with a hierarchical Markov random field model. The second method advances the first method by employing a semi-supervised image segmentation framework to combine the fidelity of supervised data with the quantity of unsupervised data. This is realised by a three-level image model structure with probability distributions specifying the interconnections. This has the advantages for the generalisation performance and hence the reduction of bias in PET reference region extraction. An Expectation Maximisation based algorithm is proposed to solve this combined learning problem. The performance of unsupervised, supervised and semi-supervised classification in temporal models and spatio-temporal models are compared, using both simulated and [¹¹C](R)-PK11195 PET data. In conclusion, it shows that the inclusion of expert knowledge greatly reduces the uncertainty in the segmentation with the new semi-supervised framework achieving substantial performance gains over the other methods.