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

2026-10-03

AI Summary

This study addresses the challenge of jointly modeling geometry and topology in lossless triangle mesh compression by proposing a shared octree hierarchical framework. The method decomposes dynamic connectivity into four categories of static prediction tasks based on parent node types, and introduces a graph-aware feature extractor that fuses local geometric, topological, and global shape information. Combined with graph neural networks employing coarse-level-specific and fine-level-shared weights to drive arithmetic coding, this approach achieves an average bitrate of 7.033 bits/face on the MPEG V-DMC benchmark, representing a 12.8% reduction over V-Mesh. Furthermore, it supports nine levels of progressive refinement while ensuring strictly lossless reconstruction.

Abstract

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.

Problem

• triangle mesh compression
• lossless compression
• octree hierarchy
• connectivity representation
• edge refinement

Innovation

• Lossless mesh compression
• Octree hierarchy
• Connectivity prediction
• Arithmetic coding
• Progressive refinement