# Hierarchical Neural Surfaces for 3D Mesh Compression

arXiv: https://arxiv.org/abs/2512.15985 · HTML: https://mlsanity.com/paper/2512.15985/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 16 of its 39 references that are in the map.
- First posted on arXiv 17 Dec 2025.

## Builds on (most cited first, 16 of 16)

- [SGDR: Stochastic Gradient Descent with Warm Restarts](https://mlsanity.com/paper/1608.03983/) (2016)
- [DeepSDF: Learning Continuous Signed Distance Functions for Shape Representation](https://mlsanity.com/paper/1901.05103/) (2019)
- [Implicit Neural Representations with Periodic Activation Functions](https://mlsanity.com/paper/2006.09661/) (2020)
- [On the Spectral Bias of Neural Networks](https://mlsanity.com/paper/1806.08734/) (2018)
- [Neural Geometric Level of Detail: Real-time Rendering with Implicit 3D Shapes](https://mlsanity.com/paper/2101.10994/) (2021)
- [WIRE: Wavelet Implicit Neural Representations](https://mlsanity.com/paper/2301.05187/) (2023)
- [Thingi10K: A Dataset of 10,000 3D-Printing Models](https://mlsanity.com/paper/1605.04797/) (2016)
- [Implicit Neural Representations for Image Compression](https://mlsanity.com/paper/2112.04267/) (2021)
- [VideoINR: Learning Video Implicit Neural Representation for Continuous Space-Time Super-Resolution](https://mlsanity.com/paper/2206.04647/) (2022)
- [HNeRV: A Hybrid Neural Representation for Videos](https://mlsanity.com/paper/2304.02633/) (2023)
- [ACORN: Adaptive Coordinate Networks for Neural Scene Representation](https://mlsanity.com/paper/2105.02788/) (2021)
- [Geometry-Consistent Neural Shape Representation with Implicit Displacement Fields](https://mlsanity.com/paper/2106.05187/) (2021)
- [Neural Geometry Processing via Spherical Neural Surfaces](https://mlsanity.com/paper/2407.07755/) (2024)
- [Neural Convolutional Surfaces](https://mlsanity.com/paper/2204.02289/) (2022)
- [CoFie: Learning Compact Neural Surface Representations with Coordinate Fields](https://mlsanity.com/paper/2406.03417/) (2024)
- [Mesh Compression with Quantized Neural Displacement Fields](https://mlsanity.com/paper/2504.01027/) (2025)

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

- [GenSP: Consistent Spherical Parameterization via Learning Shape Generative Models](https://mlsanity.com/paper/2607.00492/) (2026)

## Abstract (arXiv)

Implicit Neural Representations (INRs) have been demonstrated to achieve state-of-the-art compression of a broad range of modalities such as images, videos, 3D surfaces, and audio. Most studies have focused on building neural counterparts of traditional implicit representations of 3D geometries, such as signed distance functions. However, the triangle mesh-based representation of geometry remains the most widely used representation in the industry, while building INRs capable of generating them has been sparsely studied. In this paper, we present a method for building compact INRs of zero-genus 3D manifolds. Our method relies on creating a spherical parameterization of a given 3D mesh - mapping the surface of a mesh to that of a unit sphere - then constructing an INR that encodes the displacement vector field defined continuously on its surface that regenerates the original shape. The compactness of our representation can be attributed to its hierarchical structure, wherein it first recovers the coarse structure of the encoded surface before adding high-frequency details to it. Once the INR is computed, 3D meshes of arbitrary resolution/connectivity can be decoded from it. The decoding can be performed in real time while achieving a state-of-the-art trade-off between reconstruction quality and the size of the compressed representations.