Density Tells Where Matching Is Ambiguous: A Linear-Time Mamba-Transformer for Unordered 3D Points

Point cloud registration is a fundamental prerequisite in 3D vision. While existing Transformer-based methods excel at feature matching, their quadratic computational complexity limits scalability. Conversely, linear-time Mamba models inherently struggle to capture non-sequential 3D spatial symmetries and global context. Furthermore, current approaches largely overlook local point density, an intrinsic geometric prior crucial for resolving matching ambiguities in sparse or repetitive regions. To bridge these gaps, we propose the Density-Aware Mamba-Transformer (DAMT). DAMT couples a lightweight attention mechanism, which provides permutation-invariant global initialization via a novel Global Norm Pooling (GNP) module, with a bidirectional Mamba block for linear-scaling deep feature aggregation. To fully exploit density cues without overfitting to sensor noise, we explicitly introduce a Density-Guided Attention Weighting (DGAW) mechanism and dedicated loss constraints, enforcing strict neighborhood density consistency. Extensive experiments across synthetic CAD (ModelNet/ModelLoNet), indoor RGB-D (3DMatch/3DLoMatch), and outdoor LiDAR (KITTI) benchmarks demonstrate that DAMT achieves a highly competitive performance, offering a superior trade-off between registration accuracy and computational efficiency, paving the way for scalable and robust 3D registration.