CompletionMamba: Taming State Space Model for Point Cloud Completion.

Point cloud completion aims to reconstruct complete 3D shapes from partial scans. The long-range dependencies between points and shape perception are crucial for this task. While Transformers are effective due to their global processing ability, the quadratic complexity of their attention mechanism makes them unsuitable for long sequences when computational resources are constrained. As an alternative, State Space Models (SSMs) provide a memory-efficient solution for handling long-range dependencies, yet applying them directly to unordered point clouds presents challenges because of their intrinsic causality requirements. Existing methods attempt to address this by sorting points along a single axis. This, however, often overlooks complex causal relationships in 3D space since adjacency relationships based on Euclidean distance between points in the 3D space may not be preserved by this linear arrangement. To overcome this issue, we introduce CompletionMamba, a novel SSM-based network designed to harness SSMs for capturing both global and local dependencies within a point cloud. Initially, the input point cloud is causally structured by rearranging its coordinates. Then, a local SSM framework is proposed that defines neighborhood spaces around each point based on Euclidean distance, enhancing the causal structure. Although local SSM enhances relationships in short and long distance sequences, it still lacks full shape modeling of point cloud. To address this, we propose a novel shape-aware Mamba by integrating the shape code of each 3D shape into the model, enabling shape information propagation to all points. Our experiments show that CompletionMamba achieves state-of-the-art performance on both the MVP and PCN datasets.