Probabilistic Graphical Models for Medical Image Segmentation

Abstract

Image segmentation constitutes one of the elementary tasks in computer vision. Various variations exists, one of them being the segmentation of layers that entail a natural ordering constraint. One instance of that problem class are the cell layers in the human retina. In this thesis we study a segmentation approach for this problem class, that applies the machinery of probabilistic graphical models. Linked to probabilistic graphical models is the task of inference, that is, given an input scan of the retina, how to obtain an individual prediction or, if possible, a distribution over potential segmentations of that scan. In general, exact inference is unfeasible which is why we study an approximative approach based on variational inference, that allows to efficiently approximate the full posterior distribution. A distinguishing feature of our approach is the incorporation of a prior shape model, which is not restricted to local information. We evaluate our approach for different data sets, including pathological scans, and demonstrate how global shape information yields state-of-the-art segmentation results. Moreover, since we approximatively infer the full posterior distribution, we are able to assess the quality of our prediction as well as rate the scan in terms of its abnormality. Motivated by our problem we also investigate non-parametric density estimation with a log-concavity constraint. This class of density functions is restricted to the convex hull of the empirical data, which naturally leads to shape distributions that comply with the ordering constraint of retina layers, by not assigning any probability mass to invalid shape configurations. We investigate a prominent approach from the literature, show its extensions from 2-D to N-D and apply it to retina boundary data.