Metastasised breast cancer kills. There is no known cure, there are no known preventative measures, there are no drugs available with proven capacity to abate its effects. Early identification and excision of a malignancy prior to metastasis is the only method currently available for reducing the mortality due to breast disease. Automated analysis of mammograms has been proposed as a tool to aid radiologists detect breast disease earlier and with greater efficiency and success. This thesis addresses some of the major difficulties associated with the automated analysis of mammograms, in particular the difficulties caused by the high-frequency, relatively insignificant curvi-linear structures (CLS) comprising the blood vessels, milk-ducts and fibrous tissues. Previous attempts at automation have been overlooked these structures and the resultant complexity of that oversight has been handled inappropriately. We develop a model-based analysis of the CLS features, from the very anatomy of the breast, through mammography and digitisation to the image intensities. The model immediately dictates an algorithm for extracting a high-level feature description of the CLS features. This high-level feature description allows a systematic treatment of these image features prior to searching for instances of breast disease. We demonstrate a procedure for implementing such prior treatment by 'removing' the CLS features from the images. Furthermore, we develop a model of the expected appearance of mammographic densities in the CLS-removed image, which leads directly to an algorithm for their identification. Unfortunately the model also extracts many regions of the image that are not significant mammographic densities, and this therefore requires a subsequent segmentation stage. Unlike previous attempts which apply neural networks to this task, and therefore incorporate inherent insignificance as a consequence of insufficient data availability describing the significant mammographic densities, we illustrate the application of a new statistical method (novelty analysis) for achieving a statistically significant segmentation of the mammographic densities from the plethora of candidates identified at the previous stage. We demonstrate the ability of the CLS feature description to identify instances of radial-scar in mammograms, and note the suitability of the CLS and density descriptions for assessment of bilateral and temporal asymmetry. Some additional potential applications of these feature descriptions in arenas other than mammogram analysis are also noted.