What is it about?
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.
Photo by Bernard Hermant on Unsplash
Why is it important?
As a more general skeletal representation, medial axis transform (MAT) [Blu*67] is able to encode arbitrary shapes with curve-like and mesh-like structures. The maximal balls defined in the volume together with their locii complete the representation of the shape. That being said, the MAT is difficult to use which mainly manifests in two aspects. First, the MAT is notoriously sensitive to boundary noise, i.e., small perturbations on the boundary surface will result in dramatic changes on the medial axis. Second, the computation of the MAT usually relies on stringent requirements of the input geometry, such as the watertightness and manifoldness of the surface. In this paper, we propose Coverage Axis, a novel and simple formulation to generate skeletal representations for 3D shapes. Our goal is to give a compact approximation of the MAT, while this approximation should inherit good geometric and topological properties of the MAT but overcome its aforementioned drawbacks.
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This page is a summary of: Coverage Axis: Inner Point Selection for 3D Shape Skeletonization, Computer Graphics Forum, May 2022, Wiley, DOI: 10.1111/cgf.14484.
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