  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.
