Coverage Axis: Inner Point Selection for 3D Shape Skeletonization

Abstract

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.

Polygrammar: Grammar for Digital Polymer Representation and Generation

“…All the experimental results are conducted using a consistent parameter setting. We choose to use the simplified medial axis obtained from [Dou et al 2022] as the initial start of medial skeletal diagram construction to strike a balance between computational speed and skeleton accuracy. Note that our approach is not strictly tied to this choice, but can readily accommodate other variants of medial axis representations as inputs.…”

“…Baselines. For comparison, we include five types of baselines: (1) MATFP [Wang et al 2022a], a state-of-the-art technique for computing the medial axis transform while preserving features; (2) LS Skeleton [Baerentzen and Rotenberg 2021], a curve skeletonization approach grounded in local separators; (3) Coverage Axis (CA) [Dou et al 2022], a shape skeletonization method that simplifies from MAT; (4) Point2Skeleton (P2S) [Lin et al 2021], a deep learningbased method for constructing medial meshes from point clouds;…”

“…Erosion Thickness [Yan et al 2016] computes the simplified medial axis by introducing a burning process over the medial axis but is unable to reconstruct the original shape exactly. Coverage Axis [Dou et al 2022] aims to encompass all mesh surface points while minimizing the number of internal medial spheres. MATFP [Wang et al 2022a] computes MAT using a restricted power diagram while ensuring the preservation of both external mesh surface features and internal medial axis features.…”

“…The excessive complexity hinders the application of medial axis to shape generation and interactive shape editing, which require a more compact skeleton but a complete representation. Numerous research efforts have been dedicated to simplifying the discrete part of the skeletal representation to enhance its manageability and visual cleanliness [Dou et al 2022;Li et al 2015;Lin et al 2021;Tagliasacchi et al 2016]. However, despite these advancements, the simplified skeleton is still bounded by excessively many elements with compromised reconstruction accuracy, resulting in degraded quality of the skeleton and a loss of geometric detail.…”

Variational Pruning of Medial Axes of Planar Shapes

“…Finally, a group of recent methods (mostly in 3D) aim to simultaneously simplify the discrete representation of an approximate MA while removing the spurious branches [FTB13,LWS*15,DLX*22]. These methods are typically guided by a combination of measures that concern both the saliency of shape features and the sampling density of MA.…”