Symmetry-based representations of 3D data

The usefulness of the 3D medial axis (MA) is dependent on both the availability of accurate and stable methods for computing individual MA points and on schemes for deriving the local structure and connectivity among these points. We review the leading approaches for computing the 3D MA and the different fields of application for this representation of 3D shapes. We also present the shock scaffold which combines the advantages of exact bisector computations used in computational geometry on the one hand, and the local nature of propagation-based algorithms on the other, but without the computational complexity, connectivity, added dimensionality, and post processing issues commonly found in other approaches