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

TL;DR

Mapper-GIN introduces a lightweight, topology-inspired graph abstraction method for 3D point cloud classification that enhances robustness against corruptions without heavy architectures.

Contribution

It proposes Mapper-GIN, a simple, efficient pipeline using Mapper-based region graphs and GIN for robust 3D point cloud classification, emphasizing structural abstraction.

Findings

Achieves competitive accuracy on ModelNet40-C under noise and transformations.

Uses only 0.5M parameters, demonstrating efficiency.

Attains robustness through simple graph abstraction and message passing.

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.