MambaGCN: Synergistic Integration of Graph Convolutional Networks and State Space Models for Point Cloud Processing

Abstract

Graph Neural Networks have emerged as a formidable tool for analyzing point clouds, leveraging their capacity to aggregate local features across multiple spatial scales via layered structures. However, a significant challenge lies in effectively and selectively integrating these multi-scale features to maximize overall performance. To tackle this integration challenge, we design a novel model, MambaGCN, which employs a state space model to dynamically adjust the feature weights across spatial scales during aggregation, enabling more refined feature integration while ensuring computational efficiency. Unlike transformers with their quadratic complexity, MambaGCN achieves linear complexity, substantially reducing GPU memory usage and computational cost. Moreover, we have enhanced the architectural depth by designing a density-based farthest point sampling algorithm, which allows us to selectively downsample the input data to achieve varying levels of point density. This innovation facilitates the seamless concatenation of multiple MambaGCN layers, significantly deepening the structure of the network and enhancing its ability to tackle complex point cloud tasks effectively. Through these strategic developments, MambaGCN has demonstrated outstanding performance in tasks such as point cloud classification and part segmentation, affirming its robustness and efficiency in processing point cloud data.