mlsanityData to 7 Oct 2026

Robustness Certification for Point Cloud Models

arXiv 2103.16652 ↗First posted 30 Mar 2021cs.LG cs.AI cs.CVcited by 16

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Abstract (arXiv)

The use of deep 3D point cloud models in safety-critical applications, such as autonomous driving, dictates the need to certify the robustness of these models to real-world transformations. This is technically challenging, as it requires a scalable verifier tailored to point cloud models that handles a wide range of semantic 3D transformations. In this work, we address this challenge and introduce 3DCertify, the first verifier able to certify the robustness of point cloud models. 3DCertify is based on two key insights: (i) a generic relaxation based on first-order Taylor approximations, applicable to any differentiable transformation, and (ii) a precise relaxation for global feature pooling, which is more complex than pointwise activations (e.g., ReLU or sigmoid) but commonly employed in point cloud models. We demonstrate the effectiveness of 3DCertify by performing an extensive evaluation on a wide range of 3D transformations (e.g., rotation, twisting) for both classification and part segmentation tasks. For example, we can certify robustness against rotations by ±60deg for 95.7% of point clouds, and our max pool relaxation increases certification by up to 15.6%.

Key facts. Cited by 16 papers in the map (data through 7 Oct 2026). Builds on 45 of its 74 references that are in the map. First posted on arXiv 30 Mar 2021.

Builds on

45 of 74 references.

References · 45

  1. 2014Explaining and Harnessing Adversarial Examplescited by 7,287
  2. 2017Towards Deep Learning Models Resistant to Adversarial Attackscited by 6,326
  3. 2016PointNet: Deep Learning on Point Sets for 3D Classification and Segmentationcited by 5,223
  4. 2017PointNet++: Deep Hierarchical Feature Learning on Point Sets in a Metric Spacecited by 4,384
  5. 2015ShapeNet: An Information-Rich 3D Model Repositorycited by 2,880
  6. 2018Dynamic Graph CNN for Learning on Point Cloudscited by 2,220
  7. 2019Certified Adversarial Robustness via Randomized Smoothingcited by 1,324
  8. 2018Obfuscated Gradients Give a False Sense of Security: Circumventing Defenses to Adversarial Examplescited by 1,259
  9. 2017Reluplex: An Efficient SMT Solver for Verifying Deep Neural Networkscited by 739
  10. 2020Fast is better than free: Revisiting adversarial trainingcited by 723
  11. 2016Multi-View 3D Object Detection Network for Autonomous Drivingcited by 721
  12. 2017Frustum PointNets for 3D Object Detection from RGB-D Datacited by 640
33 more
  1. 2017Provable defenses against adversarial examples via the convex outer adversarial polytopecited by 564
  2. 2020On Adaptive Attacks to Adversarial Example Defensescited by 547
  3. 2018Certified Robustness to Adversarial Examples with Differential Privacycited by 462
  4. 2018Efficient Neural Network Robustness Certification with General Activation Functionscited by 439
  5. 2016Target-driven Visual Navigation in Indoor Scenes using Deep Reinforcement Learningcited by 351
  6. 2019Provably Robust Deep Learning via Adversarially Trained Smoothed Classifierscited by 328
  7. 2020Deep Continuous Fusion for Multi-Sensor 3D Object Detectioncited by 263
  8. 2018Towards Fast Computation of Certified Robustness for ReLU Networkscited by 254
  9. 2019Towards Stable and Efficient Training of Verifiably Robust Neural Networkscited by 204
  10. 2018Formal Security Analysis of Neural Networks using Symbolic Intervalscited by 185
  11. 2018Semidefinite relaxations for certifying robustness to adversarial examplescited by 178
  12. 2018Efficient Formal Safety Analysis of Neural Networkscited by 165
  13. 2021Deep Parametric Continuous Convolutional Neural Networkscited by 161
  14. 2018Generating 3D Adversarial Point Cloudscited by 144
  15. 2018Scaling provable adversarial defensescited by 141
  16. 2019A Convex Relaxation Barrier to Tight Robustness Verification of Neural Networkscited by 124
  17. 2019Extending Adversarial Attacks and Defenses to Deep 3D Point Cloud Classifierscited by 92
  18. 20203D Point Cloud Processing and Learning for Autonomous Drivingcited by 68
  19. 2019Adversarial Attack and Defense on Point Setscited by 63
  20. 2019Adversarial Objects Against LiDAR-Based Autonomous Driving Systemscited by 62
  21. 2020A Rotation-Invariant Framework for Deep Point Cloud Analysiscited by 62
  22. 2019Robustness of 3D Deep Learning in an Adversarial Settingcited by 55
  23. 2020Certified Defense to Image Transformations via Randomized Smoothingcited by 51
  24. 2018CNN-Cert: An Efficient Framework for Certifying Robustness of Convolutional Neural Networkscited by 50
  25. 2021PointGuard: Provably Robust 3D Point Cloud Classificationcited by 49
  26. 2020On Isometry Robustness of Deep 3D Point Cloud Models under Adversarial Attackscited by 46
  27. 2020ShapeAdv: Generating Shape-Aware Adversarial 3D Point Cloudscited by 20
  28. 2017Towards Practical Verification of Machine Learning: The Case of Computer Vision Systemscited by 19
  29. 2020Defense-PointNet: Protecting PointNet Against Adversarial Attackscited by 13
  30. 2020Efficient Certification of Spatial Robustnesscited by 11
  31. 2020Geometric Adversarial Attacks and Defenses on 3D Point Cloudscited by 11
  32. 2020On Adversarial Robustness of 3D Point Cloud Classification under Adaptive Attackscited by 10
  33. 2019Geometry-Aware Generation of Adversarial Point Cloudscited by 6

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Cited by year

Citing papers per year: 2021: 2; 2022: 7; 2023: 3; 2024: 2; 2025: 2.

16 papers.

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  1. 2021Scalable Certified Segmentation via Randomized Smoothingcited by 35
  2. 2022Frame Mining: a Free Lunch for Learning Robotic Manipulation from 3D Point Cloudscited by 31
  3. 2022TPC: Transformation-Specific Smoothing for Point Cloud Modelscited by 10
  4. 20223DeformRS: Certifying Spatial Deformations on Point Cloudscited by 10
  5. 2022Invariance-Aware Randomized Smoothing Certificatescited by 7
  6. 2023PointCert: Point Cloud Classification with Deterministic Certified Robustness Guaranteescited by 6
  7. 20223DVerifier: Efficient Robustness Verification for 3D Point Cloud Modelscited by 5
  8. 2023Precise and Generalized Robustness Certification for Neural Networkscited by 4
  9. 2022Robustness Certification of Visual Perception Models via Camera Motion Smoothingcited by 3
  10. 2023Pixel-wise Smoothing for Certified Robustness against Camera Motion Perturbationscited by 2
  11. 2021Certifiers Make Neural Networks Vulnerable to Availability Attackscited by 1
  12. 2022Tightening Robustness Verification of MaxPool-based Neural Networks via Minimizing the Over-Approximation Zonecited by 1
4 more
  1. 2024Towards General Robustness Verification of MaxPool-based Convolutional Neural Networks via Tightening Linear Approximationcited by 0
  2. 2024Improving Adversarial Robustness for 3D Point Cloud Recognition at Test-Time through Purified Self-Trainingcited by 0
  3. 2025Hi-ALPS -- An Experimental Robustness Quantification of Six LiDAR-based Object Detection Systems for Autonomous Drivingcited by 0
  4. 2025Certified L2-Norm Robustness of 3D Point Cloud Recognition in the Frequency Domaincited by 0