Thesis (Ph. D.)--Drexel University, 2007. / Includes abstract and vita. Includes bibliographical references (leaves 93-112).

The number of women diagnosed with the breast cancer continues to rise year on year. Breast cancer is now the most common type of cancer in the UK, with over 55000 cases reported last year. In most cases, mammography is the first step towards diagnosing breast cancer. However, it continues to have many practical limitations as compared to more sophisticated modalities such as MRI. The relatively low cost of mammography, together with the ever increasing risk of women contracting the disease, has led to many developed countries having a breast screening program. These routine breast screens are taken at different points in time and are called temporal mammograms. Currently, a radiologist tends to qualitatively assess temporal mammograms and look for any abnormalities or suspicious regions that might be of a concern. In this thesis, we develop an automatic shape analysis model that can detect and quantify such changes inside the breast. This will not only help in early diagnosis of the disease, which is key to survival, but will potentially aid prognosis and post treatment care. The core to this thesis is the use of Circular Integral Invariants. We explore its multi-scale properties and use it for image smoothing to reduce image noise and enhance features for segmentation. We implement, modify and enhance a segmentation method which previously has been successfully used to acquire breast regions of interest. We applied such Integral Invariants for shape description, to be used for shape matching as well as for subdividing shapes into sub-regions and quantifying the differences between two such shapes. We combine boundary information with the information from inside a shape, thus eccentrically transforming shapes before describing their structure. We develop a novel false positives reduction method based on Integral Invariants scale space. A second aspect of the thesis is the evaluation of and emphasis on the use of breast density maps against the commonly used intensity maps or x-rays. We find density maps sufficient to use in clinical practice. The methods developed in this thesis aim to help clinicians in making diagnostic decision at the point of case. Our shape analysis model is easy to compute, fast and very general in nature that could be deployed in a wide range of applications, beyond mammography.