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Curvature-Invariant Adversarial Attacks for 3D Point Clouds
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Proposes the Curvature-Invariant Method (CIM), which regularizes back-propagated gradients for 3D point cloud adversarial attacks using local principal-curvature directions and normal direction to improve imperceptibility.
Problem
Adversarial attacks on 3D point cloud classifiers produce noticeable outliers and distort local surface geometry, giving low imperceptibility; prior curvature-based objectives are hard to balance and ignore direction-dependent perceptibility.
Approach
Instead of adding geometry distances to the attack loss, decompose each point's gradient into principal-curvature tangent directions and normal, drop the gradient along the large-curvature direction, and keep only the negative normal component, with a curvature-ratio threshold gamma selecting the direction.
Key results
- Achieves average white-box ASR of 95.6% across PointNet, PointNet++, PointConv and DGCNN on ModelNet40, the highest among compared attacks.
- Improves Hausdorff distance by 7.2% and Gaussian curvature difference by 14.5% over baselines on average.
- Against defenses (SOR, SRS, DUP-Net) on PointNet-generated examples, averages 77.5% attack success rate versus 75.7% for SI-PC.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use CIM instead of SI-PC | PointNet attack · ModelNet40 | ASR (%): 94.2 -> 96.3 | Helped |
| Use CIM instead of SI-PC | PointNet attack · ModelNet40 | DH (10−2): 3.45 -> 3.29 | Helped |
| Use CIM instead of GeoA | PointNet++ attack · ModelNet40 | DG (10−4): 7.38 -> 6.68 | Helped |
| Use CIM instead of SI-PC | PointConv attack · ModelNet40 | ASR (%): 93.2 -> 94.8 | Helped |
| Use CIM instead of SI-PC | DGCNN attack · ModelNet40 | DG (10−4): 7.97 -> 6.96 | Helped |
| Use CIM instead of SI-PC | PointNet attack against defended models · ModelNet40 | ASR (%): 75.7 -> 77.5 | Helped |
| Add tangent-plane and normal-direction gradient regularization (ablation) | CIM · ModelNet40, PointNet | DH (10−2): 3.65 -> 3.29 | Helped |
| Add tangent-plane regularization (ablation) | CIM with normal regularization · ModelNet40, PointNet | DH (10−2): 3.63 -> 3.29 | Helped |
| Add normal-direction regularization (ablation) | CIM with tangent regularization · ModelNet40, PointNet | DH (10−2): 3.36 -> 3.29 | Helped |
| Add normal-direction regularization (ablation) | CIM with tangent regularization · ModelNet40, PointNet | DG (10−4): 4.24 -> 4.18 | Helped |
Surprising findings
- Constraining the normal-direction gradient alone does not improve imperceptibility; the gain comes mainly from tangent-plane regularization.
Limitations
- Evaluated only on ModelNet40 with L-infinity budget and a single source model setting for defenses.
- Hyper-parameter gamma (set to 0.3) must be chosen and its sensitivity is not broadly studied.
Experimental setup
Datasets: ModelNet40
Benchmarks: ModelNet40
Metrics: attack success rate MSE Hausdorff distance Gaussian curvature difference
Baselines: 3d-ADV GeoA SI-PC
Builds on: C&W attack SI-PC GeoA 3d-ADV
Closest papers by meaning
- Hide in Thicket: Generating Imperceptible and Rational Adversarial Perturbations on 3D Point Clouds (CVPR 2024 · similarity 0.92)
- Manifold Constraints for Imperceptible Adversarial Attacks on Point Clouds (AAAI 2024 · similarity 0.91)
- Explicitly Perceiving and Preserving the Local Geometric Structures for 3D Point Cloud Attack (AAAI 2024 · similarity 0.90)
- Imperceptible 3D Point Cloud Attacks on Lattice-based Barycentric Coordinates (AAAI 2025 · similarity 0.89)
- Toward Availability Attacks in 3D Point Clouds (ICML 2024 · similarity 0.86)
- Improving Robustness of 3D Point Cloud Recognition from a Fourier Perspective (NeurIPS 2024 · similarity 0.86)
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