Gabriel Perez S.

Gabriel Pérez S., Juan C. Pérez, Motasem Alfarra et al.

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° z-rotation on 1024-point clouds, 3DeformRS grants a certificate 3x larger and 20x faster than previous work.

Gabriel Pérez S, Juan C. Pérez, Motasem Alfarra et al.

This paper presents preliminary work on a novel connection between certified robustness in machine learning and the modeling of 3D objects. We highlight an intriguing link between the Maximal Certified Radius (MCR) of a classifier representing a space's occupancy and the space's Signed Distance Function (SDF). Leveraging this relationship, we propose to use the certification method of randomized smoothing (RS) to compute SDFs. Since RS' high computational cost prevents its practical usage as a way to compute SDFs, we propose an algorithm to efficiently run RS in low-dimensional applications, such as 3D space, by expressing RS' fundamental operations as Gaussian smoothing on pre-computed voxel grids. Our approach offers an innovative and practical tool to compute SDFs, validated through proof-of-concept experiments in novel view synthesis. This paper bridges two previously disparate areas of machine learning, opening new avenues for further exploration and potential cross-domain advancements.