Medial models incorporating shape variability for 3D shape analysis

Knowledge about the biological variability of anatomical objects is essential for statistical shape analysis and discrimination between healthy and pathological structures. This paper describes a novel approach that incorporates variability of an object population into the generation of a characteristic 3D shape model. The proposed shape representation is based on a fine-scale spherical harmonics (SPHARM) boundary description and a coarse-scale sampled medial description. The medial description is composed of a net of medial samples (m-rep) with fixed graph properties. The medial model is computed automatically from a predefined shape space using pruned 3D Voronoi skeletons to determine the stable medial branching topology. An intrinsic coordinate system and an implicit correspondence between shapes is defined on the medial manifold. Our novel representation describes shape and shape changes in a natural and intuitive fashion. Several experimental studies of biological structures regarding shape asymmetry and similarity clearly demonstrate the meaningful represesentation of local and global form.