Radiologists often need to localise corresponding findings in different images of the breast, such as Magnetic Resonance Images and X-ray mammograms. However, this is a difficult task, as one is a volume and the other a projection image. In addition, the appearance of breast tissue structure can vary significantly between them. Some breast regions are often obscured in an X-ray, due to its projective nature and the superimposition of normal glandular tissue. Automatically determining correspondences between the two modalities could assist radiologists in the detection, diagnosis and surgical planning of breast cancer. This thesis addresses the problems associated with the automatic alignment of 3D and 2D breast images and presents a generic framework for registration that uses the structures within the breast for alignment, rather than surrogates based on the breast outline or nipple position. The proposed algorithm can adapt to incorporate different types of transformation models, in order to capture the breast deformation between modalities. The framework was validated on clinical MRI and X-ray mammography cases using both simple geometrical models, such as the affine, and also more complex ones that are based on biomechanical simulations. The results showed that the proposed framework with the affine transformation model can provide clinically useful accuracy (13.1mm when tested on 113 registration tasks). The biomechanical transformation models provided further improvement when applied on a smaller dataset. Our technique was also tested on determining corresponding findings in multiple X-ray images (i.e. temporal or CC to MLO) for a given subject using the 3D information provided by the MRI. Quantitative results showed that this approach outperforms 2D transformation models that are typically used for this task. The results indicate that this pipeline has the potential to provide a clinically useful tool for radiologists
