3DeformRS: Certifying Spatial Deformations on Point Clouds

TL;DR

This paper introduces 3DeformRS, a novel certification method for assessing the robustness of point cloud DNNs against real-world spatial deformations, demonstrating improved efficiency and larger certification bounds.

Contribution

We developed 3DeformRS, a specialized extension of Randomized Smoothing, to certify point cloud DNNs against parameterized deformations with practical computational costs.

Findings

3DeformRS provides faster certification with larger bounds compared to previous methods.

It scales efficiently with point cloud size and maintains competitive robustness guarantees.

Empirical results show significant improvements in certifying against rotations and other deformations.

Abstract

3D computer vision models are commonly used in security-critical applications such as autonomous driving and surgical robotics. Emerging concerns over the robustness of these models against real-world deformations must be addressed practically and reliably. In this work, we propose 3DeformRS, a method to certify the robustness of point cloud Deep Neural Networks (DNNs) against real-world deformations. We developed 3DeformRS by building upon recent work that generalized Randomized Smoothing (RS) from pixel-intensity perturbations to vector-field deformations. In particular, we specialized RS to certify DNNs against parameterized deformations (e.g. rotation, twisting), while enjoying practical computational costs. We leverage the virtues of 3DeformRS to conduct a comprehensive empirical study on the certified robustness of four representative point cloud DNNs on two datasets and against seven different deformations. Compared to previous approaches for certifying point cloud DNNs, 3DeformRS is fast, scales well with point cloud size, and provides comparable-to-better certificates. For instance, when certifying a plain PointNet against a 3{\deg} z-rotation on 1024-point clouds, 3DeformRS grants a certificate 3x larger and 20x faster than previous work.