The content presents a novel framework, EquiShape, designed for unsupervised non-rigid point cloud shape correspondence. The key insights are:
To address the exponential complexity arising from inter-point pose transformations, EquiShape employs Cross-GVP, which learns pair-wise independent SE(3)-equivariant LRFs for each point. This enables the descriptors to be decoupled from inter-point pose transformations while integrating sufficient global geometric contexts.
To address the inherent challenges posed by out-of-distribution geometric contexts, exacerbated by extensive shape variations, EquiShape incorporates LRF-Refine, an optimization strategy that adjusts the LRF vectors to specific inputs under the guidance of model constraints, thereby substantially improving the geometric and semantic generalizability of point features.
The authors demonstrate that EquiShape significantly outperforms existing state-of-the-art methods on various non-rigid shape matching benchmarks, including human and animal datasets. The proposed framework marks a novel approach in the field of non-rigid shape matching by incorporating equivariant networks.
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by Ling Wang,Ru... at arxiv.org 04-02-2024
https://arxiv.org/pdf/2404.00959.pdfDeeper Inquiries