This thesis presents a novel set of image analysis tools developed for the purpose of assisting radiologists with the task of detecting and characterizing breast lesions in image data acquired using magnetic resonance imaging (MRI). MRI is increasingly being used in the clinical setting as an adjunct to x-ray mammography (which is, itself, the basis of breast cancer screening programs worldwide) and ultrasound. Of these imaging modalities, MRI has the highest sensitivity to invasive cancer and to multifocal disease. MRI is the most reliable method for assessing tumour size and extent compared to the gold standard histopathology. It also shows great promise for the improved screening of younger women (with denser, more radio opaque breasts) and, potentially, for women at high risk. Breast MRI presently has two major shortcomings. First, although its sensitivity is high its specificity is relatively poor; i.e. the method detects many false positives. Second, the method involves acquiring several high-resolution image volumes before, during and after the injection of a contrast agent. The large volume of data makes the task of interpretation by the radiologist both complex and time-consuming. These shortcomings have motivated the research and development of the computer-aided detection systems designed to improve the efficiency and accuracy of interpretation by the radiologist. Whilst such systems have helped to improve the sensitivity/specificity of interpretation, it is the premise of this thesis that further gains are possible through automated image analysis. However, the automated analysis of breast MRI presents several technical challenges. This thesis investigates several of these, noise filtering, parametric modelling of contrast enhancement, segmentation of suspicious tissue and quantitative characterisation and classification of suspicious lesions. In relation to noise filtering, a new denoising algorithm for dynamic contrast-enhanced (DCE-MRI) data is presented, called the Dynamic Non-Local Means (DNLM). The DCE-MR image data is inherently contaminated by Rician noise and, additionally, the limited acquisition time per volume and the use of fat-suppression diminishes the signal-to-noise ratio. The DNLM algorithm, specifically designed for the DCE-MRI, is able to attenuate this noise by exploiting the redundancy of the information between the different temporal volumes, while taking into account the contrast enhancement of the tissue. Empirical results show that the algorithm more effectively attenuates noise in the DCE-MRI data than any of the previously proposed algorithms. In relation to parametric modelling of contrast enhancement, a new empiric model of contrast enhancement has been developed that is parsimonious in form. The proposed model serves as the basis for the segmentation and feature extraction algorithms presented in the thesis. In contrast to pharmacokinetic models, the proposed model does not rely on measured parameters or constants relating to the type or density of the tissue. It also does not assume a particular relationship between the observed changes in signal intensity and the concentration of the contrast agent. Empirical results demonstrate that the proposed model fits real data better than either the Tofts or Brix models and equally as well as the more complicated Hayton model. In relation to the automatic segmentation of suspicious lesions, a novel method is presented, based on seeded region growing and merging, using criteria based on both the original image MR values and the fitted parameters of the proposed model of contrast enhancement. Empirical results demonstrate the efficacy of the method, both as a tool to assist the clinician with the task of locating suspicious tissue and for extracting quantitative features. Finally, in relation to the quantitative characterisation and classification of suspicious lesions, a novel classifier (i.e. a set of features together with a classification method) is presented. Features were extracted from noise-filtered and segmented-image volumes and were based both on well-known features and several new ones (principally, on the proposed model of contrast enhancement). Empirical results, based on routine clinical breast MRI data, show that the resulting classifier performs better than other such classifiers reported in the literature. Therefore, this thesis demonstrates that improvements in both sensitivity and specificity are possible through automated image analysis.