Gaussian Differentially Private Human Faces Under a Face Radial Curve Representation

TL;DR

This paper introduces a novel face radial curve representation for 3D human faces and a GDP mechanism that preserves facial shape while ensuring privacy, outperforming traditional methods in noise reduction.

Contribution

The paper extends approximate DP techniques to functional data, proposing a new face representation and a GDP mechanism that better preserves shape with less noise.

Findings

Preserves average face shape effectively.

Injects less noise than traditional methods.

Applicable to general disk-like surfaces.

Abstract

In this paper we consider the problem of releasing a Gaussian Differentially Private (GDP) 3D human face. The human face is a complex structure with many features and inherently tied to one's identity. Protecting this data, in a formally private way, is important yet challenging given the dimensionality of the problem. We extend approximate DP techniques for functional data to the GDP framework. We further propose a novel representation, face radial curves, of a 3D face as a set of functions and then utilize our proposed GDP functional data mechanism. To preserve the shape of the face while injecting noise we rely on tools from shape analysis for our novel representation of the face. We show that our method preserves the shape of the average face and injects less noise than traditional methods for the same privacy budget. Our mechanism consists of two primary components, the first is generally applicable to function value summaries (as are commonly found in nonparametric statistics or functional data analysis) while the second is general to disk-like surfaces and hence more applicable than just to human faces.