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We introduce the distance transform for surfaces in 3D images, i.e., the distance transform where every voxel in the surface is labelled with its geodesic distance to the closest voxel on the border of the surface. Then, the distance transform is used to identify the set of centres of maximal geodesic discs in the surface. The centres of maximal geodesic discs can be used to give a compact representation of any surface. In particular, they can provide a useful representation of the surface skeleton of solid volume objects.

Detecting Centres of Maximal Geodesic Discs on the Distance Transform of Surfaces in 3D Images