Structure-First Point Cloud Learning with Mapper Region Graphs

Jeongbin You; Donggun Kim; Sejun Park; Seungsang Oh

cs.CVFeb 5, 2026

Structure-First Point Cloud Learning with Mapper Region Graphs

Authors: Jeongbin You, Donggun Kim, Sejun Park, Seungsang Oh

Organizations: Department of Mathematics Korea University

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 & tables

Figure 1: Structure-first point cloud learning with Mapper-GNN. (a) Mapper-GNN first constructs an overlapping region graph, while existing methods directly learn point-level features. (b) Mean corruption accuracy (mCA) versus parameter count on ModelNet40-C.

Figure 3: Mapper with a 1D lens; our model uses 3D identity/PCA lenses and a cubical cover.

Figure 4: Corrupted point clouds and their Mapper graphs.

Model	Params $\downarrow$	mCA $\uparrow$	DEN	NOI	TRA
PointNet	3.47M	72.84	68.52	73.37	76.64
PointNet++	1.47M	78.38	69.04	84.32	81.80
DGCNN	1.81M	77.07	68.92	76.34	85.95
RSCNN	1.29M	73.17	64.44	77.37	77.71
PCT	2.74M	77.93	69.27	79.17	85.36
SimpleView	0.80M	66.27	52.78	74.33	71.68

Table 1: Comparison on ModelNet40-C

Model	Add-G	Add-L	Drop-G	Drop-L	Jitter	Rotate	Scale
PointNet	$13.83$	$48.68$	$63.66$	$49.78$	$60.51$	$45.13$	$55.65$
PointNet++	$\mathbf{70.86}$	$62.17$	$\mathbf{78.20}$	$\underline{67.66}$	$71.48$	$64.34$	$70.61$
DGCNN	$30.90$	$64.65$	$74.17$	$67.65$	$73.77$	$72.32$	$71.46$
RSCNN	$58.03$	$60.32$	$73.65$	$50.13$	$70.30$	$65.67$	$65.56$
PCT	$36.85$	$61.75$	$73.00$	$66.33$	$72.77$	$69.24$	$67.61$
SimpleView	$54.94$	$45.80$	$33.29$	$36.41$	$56.13$	$44.38$	$47.04$

Table 2: Per-corruption accuracy on ModelNet-C

Model	Scale	Jitter	Rotate	Drop-G	Drop-L	Add-G	Add-L	Retention
PointNet++	62.2	29.4	54.4	57.1	54.2	43.1	40.5	67.2
DGCNN	56.3	32.9	55.0	52.3	53.8	27.9	41.1	70.9
PointNeXt-S ( $C=64$ )	63.5	29.0	56.5	54.3	56.6	48.5	45.0	67.7
Point Transformer	53.1	30.1	57.7	31.7	45.7	24.8	27.3	60.0
Mapper-GNN	54.8	33.9	50.4	59.6	57.7	38.3	34.0	71.6

Table 3: Classification robustness on ScanObjectNN-C

Model	5-way			10-way			Retention	N=512	N=256	N=128
Model	1-shot	2-shot	3-shot	1-shot	2-shot	3-shot	Retention	N=512	N=256	N=128
PointNet	35.40 / 33.63	54.10 / 53.11	64.10 / 60.39	33.40 / 30.44	45.30 / 41.62	52.60 / 49.26	94.01	87.38	85.84	77.27
PointNet++	46.60 / 44.15	58.10 / 55.67	64.10 / 59.41	37.80 / 35.14	47.05 / 43.24	54.05 / 49.25	93.20	85.92	61.93	23.14
DGCNN	56.70 / 54.93	70.60 / 67.62	75.50 / 72.28	45.65 / 43.19	59.15 / 54.97	65.70 / 62.36	95.14	84.26	60.79	24.21
RSCNN	43.40 / 40.68	47.90 / 47.42	57.50 / 54.08	28.45 / 27.52	35.95 / 35.67	43.75 / 42.83	96.77	80.33	65.47	32.77
PCT	52.70 / 49.75	66.70 / 64.69	72.70 / 69.25	46.00 / 42.12	57.15 / 52.74	63.90 / 60.81	94.28	85.17	67.29	22.72

Table 4: Extreme few-shot classification results on clean ModelNet40 and ModelNet40-C. Each entry reports cOA / mCA (clean overall accuracy / mean corruption accuracy) and the results are averaged over 20 episodes. The last three columns indicate clean-test accuracy under reduced input point count, where ‘–’ denotes unavailable results.

Figure 5: Representation stability under corruption: (a) linear CKA between clean and corrupted features. (b) UMAP of clean and density-s5 corrupted class samples.

Figure 6: Region attribution under clean and corruption inputs.

Config	cOA	mCA
None	88.00	77.45
+ GNN residual propagation	88.36	77.97
+ Layer aggregation	88.59	78.87
+ Base-to-graph residual fusion	88.71	79.13

Table 5: Incremental ablation study

Encoder	Lens	Params	Density	Noise	Trans.	mCA
GIN	Identity	0.87M	$\mathbf{74.1}$	78.2	80.5	77.6
	PCA 3	0.87M	71.2	82.3	81.2	78.2
GCN	Identity †	$\mathbf{0.60M}$	72.2	83.7	81.5	79.1
	PCA 3	$\mathbf{0.60M}$	71.6	83.7	$\mathbf{82.3}$	79.2
GAT	Identity	1.40M	73.0	$\mathbf{84.1}$	81.3	79.4
	PCA 3	1.40M	72.9	83.8	82.2	$\mathbf{79.6}$

Table 6: Ablation study of Mapper-based variants on ModelNet40-C. † denotes the representative configuration used in the main comparison.

Cover $n$	Overlap $=0.2$		Overlap $=0.3$		Overlap $=0.4$
	cOA	mCA	cOA	mCA	cOA	mCA
4	88.70	77.98	88.83	77.45	88.91	76.85
6	88.63	79.30	88.74	79.13 †	89.10	78.74
8	87.74	78.58	88.88	79.40	88.95	79.63

Table 7: Effect of Mapper cover resolution and overlap ratio. † denotes the default setting

(n,\mathrm{overlap})=(6,0.3)

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Beyond Defenses: Manifold-Aligned Regularization for Intrinsic 3D Point Cloud Robustness

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Point Clouds Regularization LLM Defense Mechanisms

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Despite extensive progress in point cloud robustness, existing methods primarily rely on augmentation strategies or defense mechanisms while overlooking the geometric nature of adversarial fragility. We hypothesize that adversarial vulnerability in 3D networks arises from a manifold misalignment between the latent geometry learned by the model and the intrinsic geometry of the underlying surface. Small, geometry-preserving perturbations along the input manifold often induce disproportionate distortions in feature space, potentially leading to misclassifications. We formalize this phenomenon by developing a geometric interpretation of 3D robustness that links classical adversarial theory to the intrinsic structure of point clouds. Motivated by this analysis, we introduce Manifold-Aligned Point Recognition (MAPR), a framework that regularizes the latent geometry by aligning predictions across intrinsic perturbations. MAPR augments each point cloud with intrinsic features capturing local curvature and diffusion structure, and applies a consistency loss that preserves invariance to intrinsic, geometry-preserving perturbations. Without relying on adversarial training or additional data, MAPR consistently improves robustness under multiple adversarial attacks across several datasets, achieving average robustness gains of +20.02 and +8.83 percentage points over vanilla models on ModelNet40 and ScanObjectNN, respectively.

Abstract

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