3D Voronoi Skeletons and Their Usage for the Characterization and Recognition of 3D Organ Shape

The paper describes a procedure for the generation of the Blum skeleton (medial axis) of large, complex, digitized 3D objects. The proposed algorithm is a 3D generalization of the Voronoi skeleton concept, which is already in routine use for 2D shapes. A specific algorithm for the generation of 3D Voronoi diagrams of very large point sets (containing several 100,000 generating points) is described. The pitfalls and drawbacks of pruning procedures are discussed, and a topologically correct regularization algorithm is given for the necessary regularization of the resulting Voronoi diagram. The performance of the developed procedures is illustrated on synthetic objects as well as on large, complex anatomical data, e.g., the segmented white matter of a human brain extracted from MR data.

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