PointCert: Point Cloud Classification with Deterministic Certified Robustness Guarantees

Abstract: Point cloud classification is an essential component in many security-critical applications such as autonomous driving and augmented reality. However, point cloud classifiers are vulnerable to adversarially perturbed point clouds. Existing certified defenses against adversarial point clouds suffer from a key limitation: their certified robustness guarantees are probabilistic, i.e., they produce an incorrect certified robustness guarantee with some probability. In this work, we propose a general framework, namely PointCert, that can transform an arbitrary point cloud classifier to be certifiably robust against adversarial point clouds with deterministic guarantees. PointCert certifiably predicts the same label for a point cloud when the number of arbitrarily added, deleted, and/or modified points is less than a threshold. Moreover, we propose multiple methods to optimize the certified robustness guarantees of PointCert in three application scenarios. We systematically evaluate PointCert on ModelNet and ScanObjectNN benchmark datasets. Our results show that PointCert substantially outperforms state-of-the-art certified defenses even though their robustness guarantees are probabilistic.