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

2026-05-08

AI Summary

This work addresses a critical yet overlooked issue in existing robustness methods for 3D point clouds: the manifold misalignment between the geometry implicitly learned by models and the intrinsic geometric structure of the point cloud itself. To bridge this gap, the authors propose MAPR, a manifold alignment regularization framework that requires neither adversarial training nor additional data, and for the first time explicitly links 3D adversarial robustness with the intrinsic geometry of point clouds. MAPR extracts intrinsic geometric features by integrating local curvature and diffusion structures, generates geometry-preserving perturbations, and enforces prediction consistency to align the learned and intrinsic manifolds. Evaluated on ModelNet40 and ScanObjectNN, MAPR achieves average robustness improvements of 20.02% and 8.58%, respectively, substantially outperforming current state-of-the-art defense approaches.

Abstract

Despite extensive progress in point cloud robustness, existing methods primarily improve performance through augmentation or defense mechanisms, while overlooking the geometric root cause 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, revealing a misalignment between latent and intrinsic geometries. 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 across multiple adversarial attacks on both the ModelNet40 and ScanObjectNN datasets, achieving average robustness gains of +20.02% and +8.58% on ModelNet40 and ScanObjectNN, respectively.

Problem

• 3D point cloud
• adversarial robustness
• manifold alignment
• intrinsic geometry
• latent geometry

Innovation

• manifold alignment
• intrinsic geometry
• 3D point cloud robustness
• geometric regularization
• adversarial robustness