Combined Boundary-Medial Shape Description of Variable Biological Objects

This dissertation describes a novel shape description scheme that incorporates variability of an object population into the generation of a characteristic 3D shape model. Knowledge about the biological variability of anatomical objects is essential for statistical shape analysis and discrimination between healthy and pathological structures. The proposed shape representation is based on a fine-scale spherical harmonics (SPHARM) description and a coarse-scale m-rep description. The SPHARM description describes the boundary as a weighted series of spherical harmonics. The correspondence on the boundary is defined by a first-order ellipsoid normalized parameterization. The medial m-rep description is composed of a net of medial primitives with fixed graph properties. A m-rep model is computed automatically from the shape space of a training population of SPHARM objects. Pruned 3D Voronoi skeletons are used to determine a common medial branching topology in a stable way. An intrinsic coordinate system and an implicit correspondence between objects are defined on the medial manifold. My novel representation scheme describes shape and shape changes in a meaningful and intuitive manner. Several experimental studies of shape asymmetry and shape similarity in biological structures demonstrate the power of the new representation to describe global and local form. The clinical importance of shape measurements is shown in the presented applications. The contributions made in this dissertation include the development of a novel automatic pruning scheme for 3D Voronoi skeletons. My experiments showed that only a small number of skeletal sheets are necessary to describe families of even quite complex objects. This work is also the first to compute a common medial branching topology of an object population, which deals with the sensitivity of the branching topology to small shape variations. The sensitivity of the medial descriptions to small boundary perturbations, a fundamental problem of any skeletonization technique, is approached with a new sampling technique.

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