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

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 Dis...

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Bibliographic Details
Published in:arXiv.org 2024-08
Main Authors: Gabriel Pérez S, Pérez, Juan C, Alfarra, Motasem, Zarzar, Jesús, Rojas, Sara, Ghanem, Bernard, Arbeláez, Pablo
Format: Article
Language:English
Subjects:
Algorithms
Deep learning
Image processing
Machine learning
Robustness
Smoothing
Online Access:Get full text
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Summary: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.
ISSN:2331-8422