Population based spatio-temporal probabilistic modelling of fMRI data

High-dimensional functional magnetic resonance imaging (fMRI) data is characterized by complex spatial and temporal patterns related to neural activation. Mixture based Bayesian spatio-temporal modelling is able to extract spatiotemporal components representing distinct haemodyamic response and activation patterns. A recent development of such approach to fMRI data analysis is so-called spatially regularized mixture model of hidden process models (SMM-HPM). SMM-HPM can be used to reduce the four-dimensional fMRI data of a pre-determined region of interest (ROI) to a small number of spatio-temporal prototypes, sufficiently representing the spatio-temporal features of the underlying neural activation. Summary statistics derived from these features can be interpreted as quantification of (1) the spatial extent of sub-ROI activation patterns, (2) how fast the brain respond to external stimuli; and (3) the heterogeneity in single ROIs. This thesis aims to extend the single-subject SMM-HPM to a multi-subject SMM-HPM so that such features can be extracted at group-level, which would enable more robust conclusion to be drawn

Learning generative models of mid-level structure in natural images

Natural images arise from complicated processes involving many factors of variation. They reflect the wealth of shapes and appearances of objects in our three-dimensional world, but they are also affected by factors such as distortions due to perspective, occlusions, and illumination, giving rise to structure with regularities at many different levels. Prior knowledge about these regularities and suitable representations that allow efficient reasoning about the properties of a visual scene are important for many image processing and computer vision tasks. This thesis focuses on models of image structure at intermediate levels of complexity as required, for instance, for image inpainting or segmentation. It aims at developing generative, probabilistic models of this kind of structure, and, in particular, at devising strategies for learning such models in a largely unsupervised manner from data. One hallmark of natural images is that they can often be decomposed into regions with very different visual characteristics. The main approach of this thesis is therefore to represent images in terms of regions that are characterized by their shapes and appearances, and an image is then composed from many such regions. We explore approaches to learn about the appearance of regions, to learn about region shapes, and ways to combine several regions to form a full image. To achieve this goal, we make use of some ideas for unsupervised learning developed in the literature on models of low-level image structure and in the “deep learning” literature. These models are used as building blocks of more structured model formulations that incorporate additional prior knowledge of how images are formed. The thesis makes the following contributions: Firstly, we investigate a popular, MRF based prior of natural image structure, the Field-of Experts, with respect to its ability to model image textures, and propose an extended formulation that is considerably more successful at this task. This formulation gives rise to a fully parametric, translation-invariant probabilistic generative model of image textures. We illustrate how this model can be used as a component of a more comprehensive model of images comprising multiple textured regions. Secondly, we develop a model of region shape. This work is an extension of the “Masked Restricted Boltzmann Machine” proposed by Le Roux et al. (2011) and it allows explicit reasoning about the independent shapes and relative depths of occluding objects. We develop an inference and unsupervised learning scheme and demonstrate how this shape model, in combination with the masked RBM gives rise to a good model of natural image patches. Finally, we demonstrate how this model of region shape can be extended to model shapes in large images. The result is a generative model of large images which are formed by composition from many small, partially overlapping and occluding objects