Geometric statistically based methods for the segmentation and registration of medical imagery

Medical image analysis aims at developing techniques to extract information from medical images. Among its many sub-fields, image registration and segmentation are two important topics. In this report, we present four pieces of work, addressing different problems as well as coupling them into a unified framework of shape based image segmentation. Specifically: 1. We link the image registration with the point set registration, and propose a globally optimal diffeomorphic registration technique for point set registration. 2. We propose an image segmentation technique which incorporates the robust statistics of the image and the multiple contour evolution. Therefore, the method is able to simultaneously extract multiple targets from the image. 3. By combining the image registration, statistical learning, and image segmentation, we perform a shape based method which not only utilizes the image information but also the shape knowledge. 4. A multi-scale shape representation based on the wavelet transformation is proposed. In particular, the shape is represented by wavelet coefficients in a hierarchical way in order to decompose the shape variance in multiple scales. Furthermore, the statistical shape learning and shape based segmentation is performed under such multi-scale shape representation framework.Ph.D.Committee Chair: Tannenbaum, Allen; Committee Co-Chair: Giddens, Don; Committee Member: Hu, Xiaoping; Committee Member: Stillman, Arthur; Committee Member: Yezzi, Anthon