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 pointpair 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. The source code