# MATTopo: Topology-preserving Medial Axis Transform with Restricted Power Diagram

arXiv: https://arxiv.org/abs/2403.18761 · HTML: https://mlsanity.com/paper/2403.18761/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 27 Mar 2024.

## Built on by (most cited first, 4 of 4)

- [CWF: Consolidating Weak Features in High-quality Mesh Simplification](https://mlsanity.com/paper/2404.15661/) (2024)
- [Quasi-Medial Distance Field (Q-MDF): A Robust Method for Approximating and Discretizing Neural Medial Axes](https://mlsanity.com/paper/2410.17774/) (2024)
- [SHARC: Reference point driven Spherical Harmonic Representation for Complex Shapes](https://mlsanity.com/paper/2604.01894/) (2026)
- [Soft Anisotropic Diagrams for Differentiable Image Representation](https://mlsanity.com/paper/2604.21984/) (2026)

## Abstract (arXiv)

We present a novel topology-preserving 3D medial axis computation framework based on volumetric restricted power diagram (RPD), while preserving the medial features and geometric convergence simultaneously, for both 3D CAD and organic shapes. The volumetric RPD discretizes the input 3D volume into sub-regions given a set of medial spheres. With this intermediate structure, we convert the homotopy equivalency between the generated medial mesh and the input 3D shape into a localized contractibility checking for each restricted element (power cell, power face, power edge), by checking their connected components and Euler characteristics. We further propose a fractional Euler characteristic algorithm for efficient GPU-based computation of Euler characteristic for each restricted element on the fly while computing the volumetric RPD. Compared with existing voxel-based or point-cloud-based methods, our approach is the first to adaptively and directly revise the medial mesh without globally modifying the dependent structure, such as voxel size or sampling density, while preserving its topology and medial features. In comparison with the feature preservation method MATFP, our method provides geometrically comparable results with fewer spheres and more robustly captures the topology of the input 3D shape.