Robust 3D point cloud classification is often pursued by scaling up backbones or relying on specialized data augmentation. We instead ask whether structural abstraction alone can improve robustness, and study a simple topology-inspired decomposition based on the Mapper algorithm. We propose Mapper-GIN, a lightweight pipeline that partitions a point cloud into overlapping regions using Mapper (PCA lens, cubical cover, and followed by density-based clustering), constructs a region graph from their overlaps, and performs graph classification with a Graph Isomorphism Network. On the corruption benchmark ModelNet40-C, Mapper-GIN achieves competitive and stable accuracy under Noise and Transformation corruptions with only 0.5M parameters. In contrast to prior approaches that require heavier architectures or additional mechanisms to gain robustness, Mapper-GIN attains strong corruption robustness through simple region-level graph abstraction and GIN message passing. Overall, our results suggest that region-graph structure offers an efficient and interpretable source of robustness for 3D visual recognition.

翻译：鲁棒的三维点云分类通常通过扩展主干网络规模或依赖专门的数据增强技术来实现。我们则探讨仅通过结构抽象是否也能提升鲁棒性，并研究了一种基于Mapper算法的简单拓扑分解方法。我们提出了Mapper-GIN，一种轻量级处理流程：首先使用Mapper算法（采用PCA透镜、立方体覆盖及基于密度的聚类）将点云分割为重叠区域，然后根据区域重叠关系构建区域图，最后通过图同构网络进行图分类。在损坏基准数据集ModelNet40-C上，Mapper-GIN仅用0.5M参数量，便在噪声和变换损坏条件下取得了具有竞争力且稳定的分类精度。与先前需要更复杂架构或额外机制以获得鲁棒性的方法相比，Mapper-GIN通过简单的区域级图抽象和GIN消息传递即可实现强大的损坏鲁棒性。总体而言，我们的研究结果表明，区域图结构为三维视觉识别提供了一种高效且可解释的鲁棒性来源。