  The linear and non-flexible nature of deep convolutional models makes them
vulnerable to carefully crafted adversarial perturbations. To tackle this
problem, we propose a non-linear radial basis convolutional feature mapping by
learning a Mahalanobis-like distance function. Our method then maps the
convolutional features onto a linearly well-separated manifold, which prevents
small adversarial perturbations from forcing a sample to cross the decision
boundary. We test the proposed method on three publicly available image
classification and segmentation datasets namely, MNIST, ISBI ISIC 2017 skin
lesion segmentation, and NIH Chest X-Ray-14. We evaluate the robustness of our
method to different gradient (targeted and untargeted) and non-gradient based
attacks and compare it to several non-gradient masking defense strategies. Our
results demonstrate that the proposed method can increase the resilience of
deep convolutional neural networks to adversarial perturbations without
accuracy drop on clean data.
