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The ability to cope accurately and fast with Out-Of-Distribution (OOD)samples is crucial in real-world safety demanding applications. In this work wefirst study the interplay between critical points of 3D point clouds and OODsamples. Our findings are that common corruptions and outliers are ofteninterpreted as critical points. We generalize the notion of critical pointsinto importance measures. We show that training a classification network basedonly on less important points dramatically improves robustness, at a cost ofminor performance loss on the clean set. We observe that normalized entropy ishighly informative for corruption analysis. An adaptive threshold based onnormalized entropy is suggested for selecting the set of uncritical points. Ourproposed importance measure is extremely fast to compute. We show it can beused for a variety of applications, such as Explainable AI (XAI), OutlierRemoval, Uncertainty Estimation, Robust Classification and Adversarial Defense.We reach SOTA results on the two latter tasks. Code is available at:https://github.com/yossilevii100/critical_points2

Critical Points ++: An Agile Point Cloud Importance Measure for Robust Classification, Adversarial Defense and Explainable AI