Mapper-GIN: Lightweight Structural Graph Abstraction for Corrupted 3D Point Cloud Classification

TL;DR

Mapper-GIN addresses robustness gaps in 3D point-cloud classification by replacing heavy point-encoded backbones with a topology-inspired region-graph abstraction built via Mapper. It converts a cloud into a Mapper region graph using a PCA lens, cubical cover, and density-based clustering, then applies a Graph Isomorphism Network (GIN) over the region graph with a lightweight local encoder. On ModelNet40-C, Mapper-GIN achieves competitive corruption robustness with only about $0.5$M parameters, notably under Noise and Transformation corruptions, illustrating the value of coarse structural signals for robustness. The work highlights the potential of interpretable, region-level graphs as an efficient robustness source and points to future directions for learnable, differentiable Mapper components.

Abstract

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.

Figures (5)

• Figure 1: Mapper graph construction algorithm
• Figure 2: Examples of a clean point cloud and three representative corruptions from the ModelNet40-C dataset, along with their corresponding Mapper graphs. While noise and transformation tend to preserve the overall graph structure, density reduction often disrupts connectivity, leading to noticeable changes in the Mapper graph.
• Figure 3: Mapper-GIN architecture
• Figure 4: Robustness--efficiency tradeoff on ModelNet40-C.
• Figure 5: ModelNet40-C corruptions for an airplane point cloud.