  In this paper, we present a simple yet effective formulation called Coverage
Axis for 3D shape skeletonization. Inspired by the set cover problem, our key
idea is to cover all the surface points using as few inside medial balls as
possible. This formulation inherently induces a compact and expressive
approximation of the Medial Axis Transform (MAT) of a given shape. Different
from previous methods that rely on local approximation error, our method allows
a global consideration of the overall shape structure, leading to an efficient
high-level abstraction and superior robustness to noise. Another appealing
aspect of our method is its capability to handle more generalized input such as
point clouds and poor-quality meshes. Extensive comparisons and evaluations
demonstrate the remarkable effectiveness of our method for generating compact
and expressive skeletal representation to approximate the MAT.
