Alzheimer’s disease (AD) is the most common form of dementia and is characterised by the deposition of aggregated proteins in neurofibrillary tangles or amyloid plaques within the vascular structure of the brain. Amyloid plaques consist of amyloid-beta (Aβ) in the extracellular spaces of the brain or in the walls of blood vessels, reflecting a failure to eliminate Aβ from the ageing brain. The failure to remove Aβ is potentially reflected in the vessels’ shape: vessel shape can improve or reduce fluid flow and thus drainage, according to tortuosity and other shape factors. Neuropathological studies on post-mortem human tissue have described that the small vessels of aged brains are more tortuous compared to Young brains and tortuosity increases with the presence of Alzheimer pathology[1-4]. There is currently much interest in the diagnosis of AD, especially at the early stages where therapy could be better directed (or even deployed). The central aim of this thesis is to determine whether diagnosis is possible from image data, of brain tissue and MRI scans of the brain. We propose that the capillaries can be analysed as a branching structure, which appears to be a new analysis for medical images. The approach includes new measurements of the branching structure which are enriched by analysis of the vessels’ tortuosity and density. The introduction of measures of shape by compactness and Fourier descriptors further enriches this study. The branching structures are detected by evidence gathering approaches and described by their structure. This allows recognition to be achieved; the structure of those samples derived from patients with AD differs from that for normal subjects. The descriptions can be classified using machine learning techniques, as such, achieving an automated process from image to recognition. We analysed the structure of the blood vessels in a database of brain tissue images collected from control, age-matched and patients with severe AD. The database comprises five subjects of each of the three types imaged in controlled conditions, and five MRI images of a normal brain from the Brain Tissue Resource of Newcastle UK. We show that by automated image analysis we are able to discriminate between brain tissue samples from patients presenting AD and from the normal samples. We also show discriminative capability between posterior and anterior regions of the brain imaged in 3D by MRI. The branching structure is the description that is most suited for classification purposes. On this initial dataset, statistically significant differences (p=0.04) were seen between anterior and posterior and we can achieve 90% correct classification from a combination of these descriptions. We are thus confident that these approaches are well suited to further investigation aiming for a diagnostic tool for clinical use in the assessment of possibility of Alzheimer’s disease.