Spectral Spatial Traversing in Point Clouds: Enhancing Data Analysis with Mamba Networks

Ali Bahri, Moslem Yazdanpanah, Mehrdad Noori, Sahar Dastani, Milad Cheraghalikhani, David OSOWIECHI, Gustavo Adolfo Vargas Hakim, Farzad Beizaee, Ismail Ben Ayed, Christian Desrosiers

Keywords: State Space Models, Masked Autoencoders, 3D Point Clouds, Spectral Spatial Traversing

Abstract:

State Space Models (SSMs) such as Mamba have shown significant promise for sequence modeling in Natural Language Processing (NLP) and, more recently, computer vision. This paper presents a new methodology for both supervised and self-supervised learning using Mamba and Masked Autoencoder networks specifically designed for point cloud data. We propose three main contributions that enhance the capability of Mamba networks to process and understand the complex structure of this type of data. The first strategy exploits the spectrum of a graph Laplacian capturing the local connectivity of patches to define an isometry-invariant traversal order of tokens in the Mamba network. Compared to existing point cloud Mamba architectures, which traverse point patches based on a 3D grid, our approach is more robust to the viewpoint and better captures the shape manifold of the point cloud. The second contribution adapts our approach to segmentation using a recursive patch partitioning strategy informed by spectral components of the Laplacian. This strategy enables a more precise integration and analysis point cloud segments. Our last contribution tackles a significant issue in Masked
Autoencoder (MAE) for Mamba networks by modifying learnable token placement. Instead of adding them at the end, tokens are restored to their original positions, maintaining essential order and improving learning effectiveness. Extensive experiments confirm our method's superiority over State-Of-The-Art (SOTA) baselines, demonstrating marked improvements in classification, segmentation, and few-shot tasks.

Primary Area: unsupervised, self-supervised, semi-supervised, and supervised representation learning

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Submission Number: 8077