Image registration is the process of aligning images into a common coordinate system where discrete pixel locations represent the same semantic information. Beside object detection and image segmentation, image registration is the backbone of many image analysis pipelines. However, practical use of automated image registration is limited by accuracy, which remains unsatisfactory except in case of relatively simple problems, e.g. rigid image registration, where only a single linear transformation applied to an image.

In this thesis we present new methods to improve on the existing algorithms for non-rigid image registration, which models local differences between images. Firstly, we formulate a Bayesian model for image registration that overcomes the existing barriers to uncertainty quantification when using a dense, high-dimensional, and diffeomorphic transformation parametrisation, and use stochastic gradient Markov chain Monte Carlo to quantify image registration uncertainty on large, three-dimensional images.

Secondly, we develop a variational Bayesian method for diffeomorphic, non-rigid registration of medical images. This model learns in an unsupervised way a data-specific similarity metric for mono-modal atlas-based image registration, i.e. when all the images in the dataset are aligned to a single target image. The similarity metric is parametrised as a neural network and leads to more accurate results than traditional similarity metrics which are used to initialise the model, e.g. sum of squared differences and local cross-correlation. The proposed approach has little to no impact on image registration speed and transformation smoothness.

Finally, we formulate unsupervised similarity learning as a maximum likelihood estimation problem, with the similarity metric parametrised as an energy-based model. This formulation simplifies the model and enables us to make use of larger datasets in order to further improve unsupervised image registration accuracy also in case of pairwise image registration, i.e. when using any image in the dataset as the target image.