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Statistical shape characterization using the medial representation

The goal of the research presented in this dissertation is to improve the clinical understanding of processes that affect the shape of anatomical structures. Schizophrenia is an example of such a process: it is known to affect the shape of the hippocampus, but the precise nature of the morphological changes that it causes is not fully understood. This dissertation introduces novel statistical shape characterization methodology that can improve the understanding of shape-altering biological processes by (i) identifying the regions of the affected objects where these processes are most significantly manifested and (ii) expressing the effects of these processes in intuitive geometric terms. The following three new techniques are described and evaluated in this dissertation. (1) In an approach motivated by human form perception, the shape characterization problem is divided into a coarse-to-fine hierarchy of sub-problems that analyze shape at different locations and levels of detail, making it possible to compare the effects of shape altering processes on different object regions. Statistical features are based on the medial (skeletal) object representation, which can be used to decompose objects into simple components called figures and to measure the bending and widening of the figures. Such features make it possible to express shape variability in terms of bending and widening. (2) A new algorithm that identifies regions of biological objects that are most relevant for shape-based classification is developed. In the schizophrenia application, the algorithm is used to find the hippocampus locations most relevant for classification between schizophrenia patients and matched healthy controls. The algorithm fuses shape heuristics with existing feature selection methodology, effectively reducing the inherently combinatorial search space of the latter. (3) Biological objects in 3D and 2D are described using a novel medial representation that models medial loci and boundaries using continuous manifolds. The continuous medial representation is used in the deformable templates framework to segment objects in medical images. The representation allows arbitrary sampling that is needed by the hierarchical shape characterization method.