Sampled medial loci for 3D shape representation

The medial axis transform is valuable for shape representation as it is complete and captures part structure. However, its exact computation for arbitrary 3D models is not feasible. We introduce a novel algorithm to approximate the medial axis of a polyhedron with a dense set of medial points, with a guarantee that each medial point is within a specified tolerance from the medial axis. Given this discrete approximation to the medial axis, we use Damon's work on radial geometry (Damon, 2005 [1]) to design a numerical method that recovers surface curvature of the object boundary from the medial axis transform alone. We also show that the number of medial sheets comprising this representation may be significantly reduced without substantially compromising the quality of the reconstruction, to create a more useful part-based representation.

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