  Unsupervised non-rigid point cloud shape correspondence underpins a multitude
of 3D vision tasks, yet itself is non-trivial given the exponential complexity
stemming from inter-point degree-of-freedom, i.e., pose transformations. Based
on the assumption of local rigidity, one solution for reducing complexity is to
decompose the overall shape into independent local regions using Local
Reference Frames (LRFs) that are invariant to SE(3) transformations. However,
the focus solely on local structure neglects global geometric contexts,
resulting in less distinctive LRFs that lack crucial semantic information
necessary for effective matching. Furthermore, such complexity introduces
out-of-distribution geometric contexts during inference, thus complicating
generalization. To this end, we introduce 1) EquiShape, a novel structure
tailored to learn pair-wise LRFs with global structural cues for both spatial
and semantic consistency, and 2) LRF-Refine, an optimization strategy generally
applicable to LRF-based methods, aimed at addressing the generalization
challenges. Specifically, for EquiShape, we employ cross-talk within separate
equivariant graph neural networks (Cross-GVP) to build long-range dependencies
to compensate for the lack of semantic information in local structure modeling,
deducing pair-wise independent SE(3)-equivariant LRF vectors for each point.
For LRF-Refine, the optimization adjusts LRFs within specific contexts and
knowledge, enhancing the geometric and semantic generalizability of point
features. Our overall framework surpasses the state-of-the-art methods by a
large margin on three benchmarks. Code and models will be publicly available.
