Spectral Informed Mamba for Robust Point Cloud Processing

2025-03-06

AI Summary

To address viewpoint sensitivity and insufficient structural modeling robustness in point cloud processing, this paper proposes an isometry-invariant learning framework integrating the Mamba state-space model with a masked autoencoder (MAE). Methodologically: (i) an isometry-invariant traversal sequence is designed via graph Laplacian spectrum analysis to enable topology-aware point cloud serialization; (ii) a spectral clustering-guided recursive partitioning strategy is introduced to strengthen joint local-global structural modeling; (iii) a token in-place reconstruction mechanism is incorporated into the MAE to tightly couple geometric priors with state-space dynamics. This work presents the first systematic adaptation of the Mamba architecture to intrinsic point cloud geometry. Experiments demonstrate consistent state-of-the-art performance across classification, segmentation, and few-shot learning tasks. Moreover, the method exhibits显著 enhanced robustness under viewpoint transformations, sparse sampling, and local deformations.

Technology Category

• Machine Learning: Learning with Manifolds
• Intelligent Robots: State Estimation
• Computer Vision: Representation Learning for Vision

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs
• User Modeling, Personalization and Recommendation: Accountability, Transparency, and Ethics for personalization

Abstract

State space models 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 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 Masked Autoencoder for Mamba by restoring tokens to their original positions, which preserves essential order and improves learning. Extensive experiments demonstrate the improvements of our approach in classification, segmentation, and few-shot tasks over state-of-the-art baselines.

Problem

• Enhance Mamba for robust point cloud processing using spectral graph Laplacian.
• Improve segmentation via recursive patch partitioning with Laplacian spectral components.
• Optimize token placement in Masked Autoencoder for better learning and order preservation.

Innovation

• Graph Laplacian spectrum for robust point cloud traversal
• Recursive patch partitioning using Laplacian spectral components
• Token restoration in Masked Autoencoder for Mamba