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Imperceptible 3D Point Cloud Attacks on Lattice-based Barycentric Coordinates

AAAI 2025 · Point clouds › Point cloud classification · approach: Adversarial point cloud attacks · 7 citations (OpenAlex)

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Proposes local parametric constraints that minimize displacement of lattice-based barycentric coordinates (permutohedral lattice partition) to make 3D point cloud adversarial attacks more imperceptible when added to IFGM and C&W.

Problem

Adversarial attacks on 3D point clouds need imperceptibility; existing manifold constraints use a single global parameterization (e.g., sphere) that distorts complex shapes and fails to preserve manifold properties.

Approach

Partition the point cloud with an adaptively subdivided and refined permutohedral lattice and constrain the barycentric coordinates of points within each cell as a local parametric representation, rather than a global sphere/plane mapping.

Key results

• IFGM-LBC reaches 100% ASR on PointNet/ModelNet40 with l2 0.703e-4 and CD 0.356e-2 versus 0.749e-4 l2 for IFGM-MC (prior best manifold-constrained variant).
• On ModelNet40 with PointNet++, IFGM-LBC attains l2 0.339e-4 vs 0.232e-4 for IFGM-MC, so the method does not win every case.
• Under lattice-based barycentric displacement measure, IFGM-LBC achieves the best results in most cases, e.g., on DGCNN ModelNet40 l2 1.332 vs 1.425 for IFGM-MC.

Measured effects reported in the paper

Surprising findings

• On PointNet++ ModelNet40, IFGM-MC has a lower l2 (0.232e-4) than IFGM-LBC (0.339e-4), so the proposed method is not uniformly best.

Limitations

• Gains over the global manifold constraint (IFGM-MC) are not uniform; some metrics favor MC.
• Evaluated only in untargeted setting for white-box attacks on four classifiers; black-box results only in a brief SimBA integration.
• Lattice construction relies on heuristic subdivision thresholds and refinement hyperparameters.

Experimental setup

Datasets: ModelNet40 ShapeNet Part

Benchmarks: ModelNet40 ShapeNet Part

Metrics: ASR Chamfer distance Hausdorff distance l2-norm curvature geometric regularity earth mover's distance barycentric displacement

Baselines: PGD IFGM GeoA3 3d-Adv SI-Adv ITA C&W-MC IFGM-MC SimBA SimBA++

Builds on: C&W attack IFGM manifold constraints (Tang et al. 2024a) permutohedral lattice (Gu et al. 2019) barycentric coordinates (Adams, Baek, Davis 2010)

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