Proper Shape Representation of Single Figure and Multi-Figure Anatomical Objects

Qiong Han: Proper Shape Representation of Single Figure and Multi-Figure Anatomical Objects (Under the direction of Stephen M. Pizer) Extracting anatomic objects from medical images is an important process in various medical applications. This extraction, called image segmentation, is often realized by deformable models. Among deformable model methods, medial deformable models have the unique advantage of representing not only the object boundary surfaces but also the object interior volume. Based on one medial deformable model called the m-rep, the main goal of this dissertation is to provide proper shape representations of simple anatomical objects of one part and complex anatomical objects of multiple parts in a population. This dissertation focuses on several challenges in the existing medially based deformable model method: 1. how to derive a proper continuous form by interpolating a discrete medial shape representation; 2. how to represent complex objects with several parts and do statistical analysis on them; 3. how to avoid local shape defects, such as folding or creasing, in shapes represented by the deformable model. The proposed methods in this dissertation address these challenges in more detail: 1. An interpolation method for a discrete medial shape model is proposed to guarantee the legality of the interpolated shape. This method is based on the integration of medial shape operators. 2. A medially based representation with hierarchy is proposed to represent complex objects with multiple parts by explicitly modeling interrelations between object parts and modeling smooth transitions between each pair of connected parts. A hierarchical statistical analysis is also proposed for these complex objects.