4D Local Modeling Toward Dynamic Global Perception for Ambiguity-free Rotation-Invariant Point Cloud Analysis

Rotation invariance remains a core challenge in point cloud analysis, where existing methods often struggle with structural ambiguities and insufficient global context. Most rotation-invariant (RI) representations are derived from local coordinate systems, which inherently suffer from point-pair ambiguities and fail to capture discriminative features in symmetric or repetitive structures, while discarding informative global pose cues. To overcome these limitations, we propose Ga4DPF, a novel framework that offers a robust, global-aware RI representation by converting rotation-equivariant geometric representations into invariant ones, while concurrently integrating global pose awareness. Specifically, Ga4DPF introduces a learnable steerable transform that equivariantly lifts point clouds into 4D space, facilitating robust local feature construction and mitigating point-pair ambiguities. Concurrently, we model a dynamic global pose reference using the Bingham distribution, which adaptively estimates a consistent global rotation and enhances global feature discriminability. Extensive experiments on multiple benchmark datasets demonstrate that Ga4DPF achieves state-of-the-art performance with high computational efficiency, offering a new paradigm for rotation-invariant point cloud analysis.