Shape Spaces via Medial Axis Transforms for Segmentation of Complex Geometry in 3D Voxel Data

In this paper we construct a shape space of medial ball representations from given shape training data using methods of Computational Geometry and Statistics. The ultimate goal is to employ the shape space as prior information in supervised segmentation algorithms for complex geometries in 3D voxel data. For this purpose, a novel representation of the shape space (i.e., medial ball representation) is worked out and its implications on the whole segmentation pipeline are studied. Such algorithms have wide applications for industrial processes and medical imaging, when data are recorded under varying illumination conditions, are corrupted with high noise or are occluded.