Certified L2-Norm Robustness of 3D Point Cloud Recognition in the Frequency Domain

• URL: http://arxiv.org/abs/2511.07029v1
• Date: Mon, 10 Nov 2025 12:24:35 GMT
• Title: Certified L2-Norm Robustness of 3D Point Cloud Recognition in the Frequency Domain
• Authors: Liang Zhou, Qiming Wang, Tianze Chen,
• Abstract summary: 3D point cloud classification is a fundamental task in safety-critical applications such as autonomous driving, robotics, and augmented reality.<n>Existing certified defenses limit point-wise perturbations but overlook subtle geometric distortions that preserve individual points yet alter the overall structure.<n>We propose FreqCert, a novel certification framework that shifts robustness analysis to the frequency domain, enabling structured certification against global L2-bounded perturbations.
• Score: 5.537678998880092
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 3D point cloud classification is a fundamental task in safety-critical applications such as autonomous driving, robotics, and augmented reality. However, recent studies reveal that point cloud classifiers are vulnerable to structured adversarial perturbations and geometric corruptions, posing risks to their deployment in safety-critical scenarios. Existing certified defenses limit point-wise perturbations but overlook subtle geometric distortions that preserve individual points yet alter the overall structure, potentially leading to misclassification. In this work, we propose FreqCert, a novel certification framework that departs from conventional spatial domain defenses by shifting robustness analysis to the frequency domain, enabling structured certification against global L2-bounded perturbations. FreqCert first transforms the input point cloud via the graph Fourier transform (GFT), then applies structured frequency-aware subsampling to generate multiple sub-point clouds. Each sub-cloud is independently classified by a standard model, and the final prediction is obtained through majority voting, where sub-clouds are constructed based on spectral similarity rather than spatial proximity, making the partitioning more stable under L2 perturbations and better aligned with the object's intrinsic structure. We derive a closed-form lower bound on the certified L2 robustness radius and prove its tightness under minimal and interpretable assumptions, establishing a theoretical foundation for frequency domain certification. Extensive experiments on the ModelNet40 and ScanObjectNN datasets demonstrate that FreqCert consistently achieves higher certified accuracy and empirical accuracy under strong perturbations. Our results suggest that spectral representations provide an effective pathway toward certifiable robustness in 3D point cloud recognition.

Related papers

• PWAVEP: Purifying Imperceptible Adversarial Perturbations in 3D Point Clouds via Spectral Graph Wavelets [8.051098153943704]
  adversarial attacks on 3D point clouds present significant challenges for defenders.<n>We propose a plug-and-play and non-invasive defense mechanism in the spectral domain.<n>We show that the proposed PWAVEP achieves superior accuracy and robustness compared to existing approaches.
  arXiv  Detail & Related papers  (2026-02-03T10:00:04Z)
• Adaptive Dual-Weighted Gravitational Point Cloud Denoising Method [10.397999108705962]
  This paper proposes an adaptive dual-weight gravitational-based point cloud denoising method.<n>It achieves consistent improvements in F1, PSNR, and Chamfer Distance across various noise conditions.<n>It also reduces the single-frame processing time, thereby validating its high accuracy, robustness, and real-time performance in multi-noise scenarios.
  arXiv  Detail & Related papers  (2025-12-11T07:49:28Z)
• 3D-ANC: Adaptive Neural Collapse for Robust 3D Point Cloud Recognition [21.95358957900039]
  We present 3D-ANC, a novel approach that capitalizes on the Neural Collapse (NC) mechanism to orchestrate discriminative feature learning.<n>We show that 3D-ANC significantly improves the robustness of models with various structures on two datasets.
  arXiv  Detail & Related papers  (2025-11-10T12:37:00Z)
• Adaptive Dual Uncertainty Optimization: Boosting Monocular 3D Object Detection under Test-Time Shifts [80.32933059529135]
  Test-Time Adaptation (TTA) methods have emerged to adapt to target distributions during inference.<n>We propose Dual Uncertainty Optimization (DUO), the first TTA framework designed to jointly minimize both uncertainties for robust M3OD.<n>In parallel, we design a semantic-aware normal field constraint that preserves geometric coherence in regions with clear semantic cues.
  arXiv  Detail & Related papers  (2025-08-28T07:09:21Z)
• LDRFusion: A LiDAR-Dominant multimodal refinement framework for 3D object detection [5.820124526272312]
  Existing LiDAR-Camera fusion methods have achieved strong results in 3D object detection.<n>We propose LDRFusion, a novel Lidar-dominant two-stage refinement framework for multi-sensor fusion.<n>Our framework consistently achieves strong performance across multiple categories and difficulty levels.
  arXiv  Detail & Related papers  (2025-07-22T04:35:52Z)
• Overlap-Aware Feature Learning for Robust Unsupervised Domain Adaptation for 3D Semantic Segmentation [9.578322021478426]
  3D point cloud semantic segmentation (PCSS) is a cornerstone for environmental perception in robotic systems and autonomous driving.<n>Existing methods critically overlook the inherent vulnerability to real-world perturbations (e.g., snow, fog, rain) and adversarial distortions.<n>This work first identifies two intrinsic limitations that undermine current PCSS-UDA robustness.<n>We propose a tripartite framework consisting of: 1) a robustness evaluation model quantifying resilience against adversarial attack/corruption types through robustness metrics; 2) an invertible attention alignment module (IAAM) enabling bidirectional domain mapping while preserving discriminative structure via attention-guided overlap suppression; and
  arXiv  Detail & Related papers  (2025-04-02T12:16:23Z)
• Reliability-Adaptive Consistency Regularization for Weakly-Supervised Point Cloud Segmentation [80.07161039753043]
  Weakly-supervised point cloud segmentation with extremely limited labels is desirable to alleviate the expensive costs of collecting densely annotated 3D points. This paper explores applying the consistency regularization that is commonly used in weakly-supervised learning, for its point cloud counterpart with multiple data-specific augmentations. We propose a novel Reliability-Adaptive Consistency Network (RAC-Net) to use both prediction confidence and model uncertainty to measure the reliability of pseudo labels.
  arXiv  Detail & Related papers  (2023-03-09T10:41:57Z)
• PointCert: Point Cloud Classification with Deterministic Certified Robustness Guarantees [63.85677512968049]
  Point cloud classification is an essential component in many security-critical applications such as autonomous driving and augmented reality. Existing certified defenses against adversarial point clouds suffer from a key limitation: their certified robustness guarantees are probabilistic. We propose a general framework, namely PointCert, that can transform an arbitrary point cloud classifier to be certifiably robust against adversarial point clouds.
  arXiv  Detail & Related papers  (2023-03-03T14:32:48Z)
• Ada3Diff: Defending against 3D Adversarial Point Clouds via Adaptive Diffusion [70.60038549155485]
  Deep 3D point cloud models are sensitive to adversarial attacks, which poses threats to safety-critical applications such as autonomous driving. This paper introduces a novel distortion-aware defense framework that can rebuild the pristine data distribution with a tailored intensity estimator and a diffusion model.
  arXiv  Detail & Related papers  (2022-11-29T14:32:43Z)
• PointCAT: Contrastive Adversarial Training for Robust Point Cloud Recognition [111.55944556661626]
  We propose Point-Cloud Contrastive Adversarial Training (PointCAT) to boost the robustness of point cloud recognition models. We leverage a supervised contrastive loss to facilitate the alignment and uniformity of the hypersphere features extracted by the recognition model. To provide the more challenging corrupted point clouds, we adversarially train a noise generator along with the recognition model from the scratch.
  arXiv  Detail & Related papers  (2022-09-16T08:33:04Z)
• Deep Point Cloud Reconstruction [74.694733918351]
  Point cloud obtained from 3D scanning is often sparse, noisy, and irregular. To cope with these issues, recent studies have been separately conducted to densify, denoise, and complete inaccurate point cloud. We propose a deep point cloud reconstruction network consisting of two stages: 1) a 3D sparse stacked-hourglass network as for the initial densification and denoising, 2) a refinement via transformers converting the discrete voxels into 3D points.
  arXiv  Detail & Related papers  (2021-11-23T07:53:28Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.