# Gaussian Differentially Private Human Faces Under a Face Radial Curve Representation

arXiv: https://arxiv.org/abs/2409.08301 · HTML: https://mlsanity.com/paper/2409.08301/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 15 of its 54 references that are in the map.
- First posted on arXiv 10 Sep 2024.

## Builds on (most cited first, 15 of 15)

- [Concentrated Differential Privacy: Simplifications, Extensions, and Lower Bounds](https://mlsanity.com/paper/1605.02065/) (2016)
- [Improving the Gaussian Mechanism for Differential Privacy: Analytical Calibration and Optimal Denoising](https://mlsanity.com/paper/1805.06530/) (2018)
- [Differential Privacy Over Riemannian Manifolds](https://mlsanity.com/paper/2111.02516/) (2021)
- [The Bernstein Mechanism: Function Release under Differential Privacy](https://mlsanity.com/paper/1507.04499/) (2015)
- [DeepBlur: A Simple and Effective Method for Natural Image Obfuscation](https://mlsanity.com/paper/2104.02655/) (2021)
- [Fast Disk Conformal Parameterization of Simply-connected Open Surfaces](https://mlsanity.com/paper/1408.6974/) (2014)
- [Differentially private Riemannian optimization](https://mlsanity.com/paper/2205.09494/) (2022)
- [Shape Analysis of Surfaces Using General Elastic Metrics](https://mlsanity.com/paper/1910.02045/) (2019)
- [Parallelizable global conformal parameterization of simply-connected surfaces via partial welding](https://mlsanity.com/paper/1903.12359/) (2019)
- [Shape And Structure Preserving Differential Privacy](https://mlsanity.com/paper/2209.12667/) (2022)
- [Gaussian Differential Privacy on Riemannian Manifolds](https://mlsanity.com/paper/2311.10101/) (2023)
- [A Linear Formulation for Disk Conformal Parameterization of Simply-Connected Open Surfaces](https://mlsanity.com/paper/1508.00396/) (2015)
- [Re-identification of Individuals in Genomic Datasets Using Public Face Images](https://mlsanity.com/paper/2102.08557/) (2021)
- [Aggregated Pairwise Classification of Statistical Shapes](https://mlsanity.com/paper/1901.07593/) (2019)
- [3D Face Parsing via Surface Parameterization and 2D Semantic Segmentation Network](https://mlsanity.com/paper/2206.09221/) (2022)

## Abstract (arXiv)

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.