  Explaining the decisions of models is becoming pervasive in the image
processing domain, whether it is by using post-hoc methods or by creating
inherently interpretable models. While the widespread use of surrogate
explainers is a welcome addition to inspect and understand black-box models,
assessing the robustness and reliability of the explanations is key for their
success. Additionally, whilst existing work in the explainability field
proposes various strategies to address this problem, the challenges of working
with data in the wild is often overlooked. For instance, in image
classification, distortions to images can not only affect the predictions
assigned by the model, but also the explanation. Given a clean and a distorted
version of an image, even if the prediction probabilities are similar, the
explanation may still be different. In this paper we propose a methodology to
evaluate the effect of distortions in explanations by embedding perceptual
distances that tailor the neighbourhoods used to training surrogate explainers.
We also show that by operating in this way, we can make the explanations more
robust to distortions. We generate explanations for images in the Imagenet-C
dataset and demonstrate how using a perceptual distances in the surrogate
explainer creates more coherent explanations for the distorted and reference
images.
