Three-Dimensional Medial Shape Representation Incorporating Object Variability

Abstract

The paper presents a novel processing scheme for the automatic computation of a medial shape model which is representative for an object population with shape variability. The sensitivity of medial descriptions to object variations and small boundary perturbations are fundamental problems of any skeletonization technique. These problems are approached with the computation of a model with common medial branching topology and grid sampling. This model is then used for a medial shape description of individual objects via a constrained model fit. The process starts from parametric 3D boundary representations with existing point-to-point homology between objects. The Voronoi diagram of each sampled object boundary is grouped into medial sheets and simplified by a pruning algorithm using a volumetric contribution criterion. Medial sheets are combined to form a common medial branching topology. Finally, the medial sheets are sampled and represented as meshes of medial primitives. We present new results on populations of up to 184 biological objects. For these objects, the common medial branching topology is described by a small number of sheets. Despite the coarse medial sampling, a close approximation of individual objects is achieved.