OctMamba: Mamba-based octree context entropy model for point cloud geometry compression

• Jointly models spatial, channel, and topological redundancies, moving beyond conventional spatial-only designs. • Embedding Mamba layers locally within specialized subcomponents instead of as a global backbone, enabling structured context modeling. • Achieves efficient long-range modeling with linear complexity, yielding a smaller model and faster decoding while outperforming baselines. Existing learned point cloud compression frameworks face two major limitations: (1) they focus almost exclusively on spatial redundancy and (2) rely on architectures built around local-global transformers or global Mamba blocks. Transformers incur quadratic complexity, while global Mamba lacks the granularity to capture structured correlations across multiple dimensions. We propose OctMamba, the first unified framework to jointly exploit spatial, channel, and topological redundancies, dimensions previously overlooked in point cloud geometry compression. Our approach introduces a new architectural principle: embedding Mamba modules within specialized subcomponents rather than applying them globally, challenging existing design paradigms. OctMamba combines two modules: Spatial-Channel Coupled Grouping Mamba (SCCGM) for spatial-channel fusion and Local Graph CNN-Mamba (LGCM) for topological encoding. This design enables efficient long-range modeling with linear complexity, delivering a smaller model and faster decoding while outperforming transformer-based and global Mamba baselines. On SemanticKITTI, OctMamba reduces bitrate by 60.2% over GPCC (D1 PSNR) and achieves state-of-the-art performance across LiDAR and dynamic human point cloud benchmarks with practical speed and scalability. By introducing multi-dimensional redundancy modeling, OctMamba has the potential to influence future research on efficient point cloud compression. Source code will be released.