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In this paper, we prove the uniqueness of the Lp Minkowski problem for q-torsional rigidity with p > 1 and q > 1 in smooth case. Meanwhile, the Lp Brunn-Minkowski inequality and the Lp Hadamard variational formula for q-torsional rigidity are established.

Universal Adversarial Perturbations (UAPs), which is type of image-agnostic adversarial attack, has been deeply investigated for Convolutional Neural Networks due to its high efficiency. On the other hand, as an architecture based on self-attention mechanism, Vision Transformers (ViTs) have boomed and been widely applied to solve various computer vision problems since most recent years. In this letter, we delve into the robustness of ViTs against universal adversarial attack and propose an inheritance attention matrix-based UAPs (IAM-UAP). Specifically, we introduce the inheritance attention weight matrix (IAM), which represents the integration of global information of the input patch sequence. Further, we propose a perturbation optimization objective based on IAM to confuse the global information integration of ViTs. The empirical results confirm the attacking capability of IAM-UAP on ViTs with a moderate attacking rate. In addition, we also disclose that the patch size of ViTs is a latent factor influencing the robustness against the universal attack.

Convolutional neural networks have been successfully applied to detect salient objects in an image. However, how to better use convolutional features for co-saliency detection, which is an emerging branch of saliency detection, is not fully explored. This paper proposes a convolutional neural network based co-saliency detection model, which consists of two key parts including the integration of multi-layer convolutional features extracted from a group of images and the inter-image saliency propagation. Firstly, the input image and its four co-images belonging to the same image category are passed through the VGG16 model, to obtain the multi-layer convolutional features of these images. Secondly, multi-scale synthesized feature maps, which contain both internal features and correlative features, are generated by integrating the multi-layer convolutional features. Thirdly, via the integration of low-level boundary features and high-level semantic features, the multi-scale synthesized feature maps are enhanced and fused together to generate the initial co-saliency map. Finally, an inter-image saliency propagation method is utilized to refine the initial co-saliency map, yielding the final co-saliency map with the improved quality. Experimental results on two public datasets demonstrate that the proposed model achieves the best performance compared to the state-of-the-art co-saliency detection models.

Deep Neural Networks (DNN) has achieved a great success in many tasks in recent years. However, researchers found that DNN is vulnerable to adversarial examples that are maliciously perturbed inputs. The elaborately designed adversarial perturbations can easily confuse the model whereas have no impacts on human perception. To counter adversarial examples, we propose an integrated detection framework for detecting adversarial examples, which involves statistical detector and Gaussian noise injection detector. The statistical detector extracts Subtractive Pixel Adjacency Matrix (SPAM) and uses the second order Markov transition probability matrix to model SPAM so as to highlight the statistical anomaly hidden in an adversarial input. Then an ensemble classifier using SPAM based feature is applied to detect the adversarial input containing large perturbation. The Gaussian noise injection detector first injects an additive Gaussian noise into the input, and then feeds both the original input and its Gaussian noise injected counterpart into a targeted network. By comparing the two outputs difference, the detector is applied to detect adversarial input containing small perturbation: if the difference exceeds a threshold, the input is adversarial; otherwise legitimate. The two detectors are adaptive to different characteristics of adversarial perturbation so that the proposed detection framework is capable of detecting multiple types of adversarial examples. In our work, we test six categories of adversarial examples produced by Fast Gradient Sign Method (FGSM, untargeted), Randomized Fast Gradient Sign Method (R-FGSM, untargeted), Basic Iterative Method (BIM, untargeted), DeepFool (untargeted), Carlini&Wagner Method (CW_UT, untargeted) and CW_T(targeted). Comprehensive empirical results show that the proposed detection framework has achieved a promising performance on ImageNet database.

Albeit Deep neural networks (DNNs) are widely used in computer vision, natural language processing and speech recognition, they have been discovered to be fragile to adversarial attacks. Specifically, in computer vision, an attacker can easily deceive DNNs by contaminating an input image with perturbations imperceptible to humans. As one of the important vision tasks, face verification is also subject to adversarial attack. Thus, in this paper, we focus on defending against the adversarial attack for face verification to mitigate the potential risk. We learn a network via an implementation of stacked residual blocks, namely adversarial perturbations alleviation network (ApaNet), to alleviate latent adversarial perturbations hidden in the input facial image. During the supervised learning of ApaNet, only the Labeled Faces in the Wild (LFW) is used as the training set, and the legitimate examples and corresponding adversarial examples produced by projected gradient descent algorithm compose supervision and inputs respectively. By leveraging the middle and high layer's activation of FaceNet, the discrepancy between an image output by ApaNet and the supervision is calculated as the loss function to optimize ApaNet. Empirical experiment results on the LFW, YouTube Faces DB and CASIA-FaceV5 confirm the effectiveness of the proposed defender against some representative white-box and black-box adversarial attacks. Also, experimental results show the superiority performance of the ApaNet as comparing with several currently available techniques.