Parameters of FGSM and PGD.

Deep convolutional neural networks (DCNNs) are vulnerable to examples with small perturbations. Improving DCNNs’ robustness is of great significance to the safety-critical applications, such as autonomous driving and industry automation. Inspired by the principal way that human eyes recognize objects, i.e., largely relying on the shape features, this paper first designs four learnable edge detectors as layer kernels and proposes a binary edge feature branch (BEFB) to learn the binary edge features, which can be easily integrated into any popular backbone. The four edge detectors can learn the horizontal, vertical, positive diagonal, and negative diagonal edge features, respectively, and the branch is stacked by multiple Sobel layers (using learnable edge detectors as kernels) and one threshold layer. The binary edge features learned by the branch, concatenated with the texture features learned by the backbone, are fed into the fully connected layers for classification. We integrate the proposed branch into VGG16 and ResNet34, respectively, and conduct experiments on multiple datasets. Experimental results demonstrate the BEFB is lightweight and has no side effects on training. And the accuracy of the BEFB-integrated models is better than the original ones when facing white-box attacks and black-box attack. Besides, BEFB-integrated models equipped with the robustness enhancement techniques can achieve better classification accuracy compared to the original models. The work in this paper for the first time shows it is feasible to enhance the robustness of DCNNs through combining both shape-like features and texture features.