arXiv:2605.07590cs.CV2026-05

通过几何对齐提升点云模型抗扰动能力,无需对抗训练。

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

论文配图:Beyond Defenses: Manifold-Aligned Regularization for Intrinsic 3D Point Cloud Robustness
图 1 · 摘自论文原文
  • 基于流形对齐思想,用内在几何特征增强模型稳定性。
  • 在ModelNet40和ScanObjectNN上分别提升20.02%和8.83%鲁棒性。
  • 适合关注3D点云安全性的研究人员与工业应用开发者。

尽管点云鲁棒性研究取得进展,现有方法多依赖数据增强或防御机制,忽视了对抗脆弱性的几何本质。我们假设3D网络的对抗脆弱性源于模型学习的潜在几何与输入表面内在几何之间的流形错位。沿输入流形的小规模保几何扰动常导致特征空间中剧烈失真,可能引发误分类。本文从几何角度形式化该现象,将经典对抗理论与点云内在结构相联系。受此启发,提出流形对齐点云识别(MAPR)框架,通过在内在扰动下保持预测一致性来正则化潜在几何。MAPR为每个点云引入捕捉局部曲率与扩散结构的内在特征,并施加一致性损失,确保对内在保几何扰动的不变性。不依赖对抗训练或额外数据,在多个数据集上均显著提升鲁棒性,于ModelNet40和ScanObjectNN上分别实现+20.02%和+8.83%的平均鲁棒性提升。

原文摘要 · Abstract (English)

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.

3D点云对抗鲁棒性几何对齐

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