A spherical-aware network for point cloud completion to enable high-precision sphere fitting from small-angle data

Abstract High-precision sphere fitting with small spherical central angles remains a formidable challenge in precision measurement. In practical spherical surface measurements, factors such as occlusion often lead to point clouds corresponding to spheres with small spherical central angles, making accurate fitting difficult. To address this, we propose an improved AdaPoinTr model, termed Spherical-Aware Deformable PoinTr (SAdaPoinTr), which facilitates high-precision fitting by leveraging point cloud completion. The improvements integrate two key mechanisms: (1) standard position encodings (e.g. linear transformations from Cartesian coordinates or simple MLP mappings) in existing models often fail to effectively capture the rotational symmetry inherent in 3D space and the unique geometric distribution of curved surfaces. This limitation is particularly critical for spherical data, which demands precise perception of curvature and directional variations. To overcome this, we introduce a spherical position encoding (SPE) mechanism. SPE explicitly incorporates spherical coordinate information into the encoding process, significantly enhancing the network’s ability to represent local spherical geometric structures within point clouds. (2) At the encoder stage, a novel spherical attention mechanism is introduced. This mechanism enhances attention computation by balancing feature similarity and geometric proximity, incorporating spherical geodesic distances between points as geometric constraints, and dynamically adjusting attention weights. Experimental results demonstrate that, even when completing point clouds of spheres with small spherical central angles with over 90% missing data, the proposed SAdaPoinTr method achieves over 50% improvement in fitting accuracy compared to the baseline AdaPoinTr network.