  Due to the pervasiveness of image capturing devices in every-day life, images
of individuals are routinely captured. Although this has enabled many benefits,
it also infringes on personal privacy. A promising direction in research on
obfuscation of facial images has been the work in the k-same family of methods
which employ the concept of k-anonymity from database privacy. However, there
are a number of deficiencies of k-anonymity that carry over to the k-same
methods, detracting from their usefulness in practice. In this paper, we first
outline several of these deficiencies and discuss their implications in the
context of facial obfuscation. We then develop a framework through which we
obtain a formal differentially private guarantee for the obfuscation of facial
images in generative machine learning models. Our approach provides a provable
privacy guarantee that is not susceptible to the outlined deficiencies of
k-same obfuscation and produces photo-realistic obfuscated output. In addition,
we demonstrate through experimental comparisons that our approach can achieve
comparable utility to k-same obfuscation in terms of preservation of useful
features in the images. Furthermore, we propose a method to achieve
differential privacy for any image (i.e., without restriction to facial images)
through the direct modification of pixel intensities. Although the addition of
noise to pixel intensities does not provide the high visual quality obtained
via generative machine learning models, it offers greater versatility by
eliminating the need for a trained model. We demonstrate that our proposed use
of the exponential mechanism in this context is able to provide superior visual
quality to pixel-space obfuscation using the Laplace mechanism.
