Assembly Fuzzy Representation on Hypergraph for Open-Set 3D Object Retrieval

The lack of object-level labels presents a significant challenge for 3D object retrieval in the open-set environment. However, part-level shapes of objects often share commonalities across categories but remain underexploited in existing retrieval methods. In this paper, we introduce the Hypergraph-Based Assembly Fuzzy Representation (HAFR) framework, which navigates the intricacies of open-set 3D object retrieval through a bottom-up lens of Part Assembly . To tackle the challenge of assembly isomorphism and unification, we propose the Hypergraph Isomorphism Convolution (HIConv) for smoothing and adopt the Isomorphic Assembly Embed-ding (IAE) module to generate assembly embeddings with geometric-semantic consistency. To address the challenge of open-set category generalization, our method employs high-order correlations and fuzzy representation to mitigate distribution skew through the Structure Fuzzy Reconstruction (SFR) module, by constructing a leveraged hypergraph based on local certainty and global uncertainty correlations. We construct three open-set retrieval datasets for 3D objects with part-level annotations: OP-SHNP, OP-INTRA, and OP-COSEG. Extensive experiments and ablation studies on these three benchmarks show our method outperforms current state-of-the-art methods.