The focus of my thesis is to build upon the method of Shells and Spheres developed in our laboratory. The method as previously implemented extracts medial points based on the divergence of the direction function to the nearest boundary as it changes across medial ridges, and reports the angle between the directions from the medial point to two respective boundary points. The direction function is determined by analyzing the mean and variance of intensity within pairs of adjacent spherical (circular in 2D) regions in the image. My thesis research has involved improving the search method for determining the distance function and identifying medial points, and then clustering those medial points to extract features including scale, orientation and medial dimensionality. These are then analyzed to detect local geometric shapes. I have implemented the methods in N dimensions in the Insight Toolkit (ITK). In 3D, the method yields three fundamental dimensionalities of local shape: the sphere, the cylinder, and the slab, which, along with scale, are invariant to translation and rotation. Tests are performed on simple geometric objects including the hollow sphere (slab), torus (cylinder) and sphere. The results confirm the capability of the system to successfully identify the described medial shape features, and lay the foundation for ongoing research in identifying more complex anatomical objects in medical images.
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