PICG-U: Robust underwater MBES point cloud registration via reliability-aware pose-invariant geometry

Multibeam echo sounder (MBES) point cloud registration is challenged by sonar noise, strip-wise sparse sampling, local geometric degeneration, and low-overlap observations. Unlike RGB-D or LiDAR point clouds, MBES point clouds exhibit substantial variations in local geometric reliability, making it difficult for existing general-purpose registration methods to establish stable cross-frame correspondences. To address these challenges, we propose PICG-U, a reliability-aware pose-invariant geometric framework for robust underwater MBES point cloud registration. PICG-U first jointly encodes pose-invariant geometric relations, including point-pair distances and normal-angle relations, with local reliability cues, including surface variation and sampling sparsity, to adaptively suppress unreliable neighborhoods. It then constructs a hierarchical distance-angle spatial structure embedding to model long-range geometric consistency at the coarse level. Furthermore, we introduce an overlap-guided sparse cross-frame interaction mechanism that constrains feature propagation within potentially overlapping regions, thereby reducing mismatches caused by non-overlapping regions and repetitive seabed structures. Experiments on the public DotsonEast dataset and the self-collected LQL-MBES dataset demonstrate that PICG-U outperforms representative state-of-the-art registration methods, especially under low-overlap and locally degraded conditions, validating the effectiveness of reliability-aware pose-invariant geometry for robust underwater MBES registration.