# Medial Meshes for Volume Approximation

arXiv: https://arxiv.org/abs/1308.3917 · HTML: https://mlsanity.com/paper/1308.3917/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 19 Aug 2013.

## Built on by (most cited first, 1 of 1)

- [Coverage Axis++: Efficient Inner Point Selection for 3D Shape Skeletonization](https://mlsanity.com/paper/2401.12946/) (2024)

## Abstract (arXiv)

Volume approximation is an important problem found in many applications of computer graphics, vision, and image processing. The problem is about computing an accurate and compact approximate representation of 3D volumes using some simple primitives. In this study, we propose a new volume representation, called medial meshes, and present an efficient method for its computation. Specifically, we use the union of a novel type of simple volume primitives, which are spheres and the convex hulls of two or three spheres, to approximate a given 3D shape. We compute such a volume approximation based on a new method for medial axis simplification guided by Hausdorff errors. We further demonstrate the superior efficiency and accuracy of our method over existing methods for medial axis simplification.