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

TL;DR

This paper explores a novel link between certified robustness in machine learning and 3D object modeling, proposing an efficient method to compute signed distance functions using randomized smoothing, validated through initial experiments in view synthesis.

Contribution

It introduces a new connection between certified robustness and 3D modeling, and proposes an efficient algorithm to compute SDFs via randomized smoothing in low-dimensional spaces.

Findings

Validated the approach through proof-of-concept experiments in view synthesis.

Established a theoretical link between Maximal Certified Radius and Signed Distance Function.

Proposed an efficient method to compute SDFs using Gaussian smoothing on voxel grids.

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 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.