Spectral Informed Mamba for Robust Point Cloud Processing

Ali Bahri, Moslem Yazdanpanah, Mehrdad Noori, Sahar Dastani, Milad Cheraghalikhani, Gustavo Adolfo Vargas Hakim, David Osowiechi, Farzad Beizaee, Ismail Ben Ayed, Christian Desrosiers; Proceedings of the Computer Vision and Pattern Recognition Conference (CVPR), 2025, pp. 11799-11809

State Space Models (SSMs) have shown significant promise in Natural Language Processing (NLP) and, more recently, computer vision. This paper introduces a new methodology leveraging Mamba and Masked Autoencoder (MAE) networks for point cloud data in both supervised and self-supervised learning. We propose three key contributions to enhance Mamba's capability in processing complex point cloud structures. First, we exploit the spectrum of a graph Laplacian to capture patch connectivity, defining an isometry-invariant traversal order that is robust to viewpoints and better captures shape manifolds than traditional 3D grid-based traversals. Second, we adapt segmentation via a recursive patch partitioning strategy informed by Laplacian spectral components, allowing finer integration and segment analysis. Third, we address token placement in MAE for Mamba by restoring tokens to their original positions, which preserves essential order and improves learning. Extensive experiments demonstrate our approach's improvements in classification, segmentation, and few-shot tasks over state-of-the-art (SOTA) baselines.