  Recently, state space model (SSM) has gained great attention due to its
promising performance, linear complexity, and long sequence modeling ability in
both language and image domains. However, it is non-trivial to extend SSM to
the point cloud field, because of the causality requirement of SSM and the
disorder and irregularity nature of point clouds. In this paper, we propose a
novel SSM-based point cloud processing backbone, named Point Mamba, with a
causality-aware ordering mechanism. To construct the causal dependency
relationship, we design an octree-based ordering strategy on raw irregular
points, globally sorting points in a z-order sequence and also retaining their
spatial proximity. Our method achieves state-of-the-art performance compared
with transformer-based counterparts, with 93.4% accuracy and 75.7 mIOU
respectively on the ModelNet40 classification dataset and ScanNet semantic
segmentation dataset. Furthermore, our Point Mamba has linear complexity, which
is more efficient than transformer-based methods. Our method demonstrates the
great potential that SSM can serve as a generic backbone in point cloud
understanding. Codes are released at https://github.com/IRMVLab/Point-Mamba.
