Deep Learning at the Intersection: Certified Robustness as a Tool for 3D Vision

Gabriel Perez Santamaria, Juan Camilo Perez, Jesus Zarzar, Sara Rojas Martinez, Bernard Ghanem, Pablo Arbelaez

Abstract: 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 relation- ship, 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.