Advances in clinical medical imaging have brought about the routine production of vast numbers of medical images that need to be analysed. As a result an enormous amount of computer vision research effort has been targeted at achieving automated medical image analysis. This has proved to be an elusive goal in many cases. The complexity of the problems encountered has prompted considerable interest in the use of neural networks for such applications. However, many reports of such work have been unsatisfactory in that often only qualitative results are reported, or only few patient cases are used. This thesis presents a study of the use of neural networks and computer vision for medical image analysis which aims to quantitatively investigate and demonstrate the potential of neural networks in such an application. A medical image analysis problem was selected which would facilitate this. The problem chosen was the automatic detection of acoustic neuromas in MR images of the head. Since neural networks excel at statistical pattern recognition tasks a broadly bottom-up approach to the problem was adopted. Neural networks were utilised for `intelligent' tasks which were supported by more conventional image processing operations in order to achieve the objectives set. The prototype system developed as a result of the study achieved a 100% sensitivity and a 99.0% selectivity on a dataset of 50 patient cases.