# OctMesh: A Unified Octree-Hierarchical Framework for Lossless Triangle Mesh Compression

arXiv: https://arxiv.org/abs/2610.04281 · HTML: https://mlsanity.com/paper/2610.04281/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 25 of its 61 references that are in the map.
- First posted on arXiv 3 Oct 2026.

## Builds on (most cited first, 25 of 25)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Swin Transformer: Hierarchical Vision Transformer using Shifted Windows](https://mlsanity.com/paper/2103.14030/) (2021)
- [Graph Attention Networks](https://mlsanity.com/paper/1710.10903/) (2017)
- [Fast Graph Representation Learning with PyTorch Geometric](https://mlsanity.com/paper/1903.02428/) (2019)
- [4D Spatio-Temporal ConvNets: Minkowski Convolutional Neural Networks](https://mlsanity.com/paper/1904.08755/) (2019)
- [Perceiver: General Perception with Iterative Attention](https://mlsanity.com/paper/2103.03206/) (2021)
- [Variational image compression with a scale hyperprior](https://mlsanity.com/paper/1802.01436/) (2018)
- [Joint Autoregressive and Hierarchical Priors for Learned Image Compression](https://mlsanity.com/paper/1809.02736/) (2018)
- [PolyGen: An Autoregressive Generative Model of 3D Meshes](https://mlsanity.com/paper/2002.10880/) (2020)
- [MeshGPT: Generating Triangle Meshes with Decoder-Only Transformers](https://mlsanity.com/paper/2311.15475/) (2023)
- [Checkerboard Context Model for Efficient Learned Image Compression](https://mlsanity.com/paper/2103.15306/) (2021)
- [MeshXL: Neural Coordinate Field for Generative 3D Foundation Models](https://mlsanity.com/paper/2405.20853/) (2024)
- [Practical Full Resolution Learned Lossless Image Compression](https://mlsanity.com/paper/1811.12817/) (2018)
- [Multiscale Point Cloud Geometry Compression](https://mlsanity.com/paper/2011.03799/) (2020)
- [OctSqueeze: Octree-Structured Entropy Model for LiDAR Compression](https://mlsanity.com/paper/2005.07178/) (2020)
- [Sparse Tensor-based Multiscale Representation for Point Cloud Geometry Compression](https://mlsanity.com/paper/2111.10633/) (2021)
- [VoxelContext-Net: An Octree based Framework for Point Cloud Compression](https://mlsanity.com/paper/2105.02158/) (2021)
- [OctAttention: Octree-Based Large-Scale Contexts Model for Point Cloud Compression](https://mlsanity.com/paper/2202.06028/) (2022)
- [Learning-based lossless compression of 3D point cloud geometry](https://mlsanity.com/paper/2011.14700/) (2020)
- [Deep Lossy Plus Residual Coding for Lossless and Near-lossless Image Compression](https://mlsanity.com/paper/2209.04847/) (2022)
- [Neural Progressive Meshes](https://mlsanity.com/paper/2308.05741/) (2023)
- [Geometric Prior Based Deep Human Point Cloud Geometry Compression](https://mlsanity.com/paper/2305.01309/) (2023)
- [UVG-VPC: Voxelized Point Cloud Dataset for Visual Volumetric Video-based Coding](https://mlsanity.com/paper/2504.05888/) (2025)
- [Mesh Compression with Quantized Neural Displacement Fields](https://mlsanity.com/paper/2504.01027/) (2025)
- [DALD-PCAC: Density-Adaptive Learning Descriptor for Point Cloud Lossless Attribute Compression](https://mlsanity.com/paper/2601.12261/) (2026)

## Abstract (arXiv)

Lossless triangle mesh compression must preserve both vertex positions and connectivity. Octrees support learned point cloud geometry coding and progressive refinement, but extending them to meshes requires a compatible connectivity representation. Unlike the eight occupancy decisions of a voxel, a parent edge can develop into varied child connections, making edge refinement difficult to model with a compact prediction prior. We propose OctMesh, a learned framework that codes geometry and connectivity on a shared octree hierarchy. Its key observation is that octree pooling produces parents with either one child or two to eight children. Child edges are then grouped by their endpoint parents' types and whether the endpoints share a parent. Each candidate group contains children from just one parent or two connected parents. The resulting four categories define small, fixed-shape prediction tasks: connections uniquely determined by the parent graph are inherited without bits, while three neural predictors estimate probabilities for the remaining candidates. These probabilities guide arithmetic coding of the actual edge symbols. Binarized predictions of within-parent connections provide context for predicting connections between different parents. A graph-aware parent feature extractor combines local geometry, parent connectivity and global shape. The connectivity models use dedicated weights at coarse levels and share weights at fine levels. Residual edges and a finest-level face-selection payload complete the reconstruction. On 256 frames from eight MPEG V-DMC test sequences, OctMesh losslessly recovers the finest-level vertex-coordinate, edge and unoriented face sets at an average of 7.033 bits per face, 12.8% below V-Mesh. The same hierarchical representation supports nine levels of progressive vertex-and-edge refinement.