Automatic and robust computation of 3D medial models incorporating object variability

Abstract. This paper presents a novel processing scheme for the automatic and robust computation of a medial shape model which represents 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 skeleton of each sampled object boundary is partitioned into non-branching medial sheets and simplified by a novel pruning algorithm using a volumetric contribution criterion. Using the surface homology, medial sheets are combined to form a common medial branching topology. Finally, the medial sheets are sampled and represented as meshes of medial primitives. Results on populations of up to 184 biological objects clearly demonstrate that the common medial branching topology can be described by a small number of medial sheets and that even a coarse sampling leads to a close approximation of individual objects.