Deep Learning at the Intersection: Certified Robustness as a Tool for 3D Vision
This work addresses the computational inefficiency of certified robustness methods for 3D vision applications, offering a practical tool for researchers in computer vision and machine learning, though it is incremental as it adapts existing techniques to a new domain.
This paper tackles the problem of efficiently computing Signed Distance Functions (SDFs) for 3D vision by linking certified robustness methods to 3D modeling, proposing an algorithm based on randomized smoothing that reduces computational cost, with proof-of-concept experiments in novel view synthesis.
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.