Existing unsupervised image alignment methods exhibit limited accuracy and high computational complexity. To address these challenges, we propose a dense cross-scale image alignment model. It takes into account the correlations between cross-scale features to decrease the alignment difficulty. Our model supports flexible trade-offs between accuracy and efficiency by adjusting the number of scales utilized. Additionally, we introduce a fully spatial correlation module to further improve accuracy while maintaining low computational costs. We incorporate the just noticeable difference to encourage our model to focus on image regions more sensitive to distortions, eliminating noticeable alignment errors. Extensive quantitative and qualitative experiments demonstrate that our method surpasses state-of-the-art approaches.

Subspace learning has been widely applied for joint feature extraction and dimensionality reduction, demonstrating significant efficacy. Numerous subspace learning methods with diverse assumptions regarding the criteria for the target subspaces have been developed to obtain compact and interpretable data representations. However, when applied to image data, existing methods fail to fully exploit the inherent correlations within the image set. This paper proposes a Robust Discriminative t-Linear Subspace Learning model (RDtSL) to tackle this issue using t-product. The model mainly has four strengths: 1) Taking advantage of t-product, RDtSL learns the projection basis directly from the image set while fully exploiting its internal correlations; 2) Based on its energy preservation module, RDtSL retains the primary energy of samples in the learned subspace, maintaining satisfactory performance even with low subspace dimensions; 3) Class-distinctive features are effectively preserved in the learned representations due to the incorporation of the classification module; 4) Relying on its graph embedding module, RDtSL learns an affinity graph of samples adaptively to enrich the data representations with locality and similarity information. The harmonious balance maintained between the three proposed modules helps RDtSL learn discriminative and informative data representations. We also develop an iterative algorithm to solve RDtSL. Extensive experiments on benchmark databases demonstrate the superiority of the proposed model.

Spread spectrum (SS) watermarking has gained significant attention as it prevents attackers from reading, tampering with, or removing watermarks. Secret key estimation can help with the first two unauthorized operations but cannot remove watermarks. Moreover, existing deep-learning watermark removal methods do not consider the characteristics of SS watermarking, thus leading to unsatisfactory results. In this paper, we design a secret key estimation method that treats secret key estimation as a binary classification problem and updates the estimated key via backpropagation and parameter optimization algorithms. We develop a watermark removal network using quaternion convolutional neural networks (QCNNs) to learn watermark features while capturing the relationship between channels to improve image quality. Based on our estimation method and QCNN-based network, we propose a two-stage watermark removal framework that utilizes information of the secret key to train the network. A loss function is introduced to directly prevent watermark extraction, thereby improving removal performance. Extensive experiments demonstrate the superiority of our methods over the state-of-the-art methods.

The security of spread spectrum (SS) watermarking largely depends on the difficulty of estimating its secret key. Some estimators have been proposed to estimate the secret key in the known-message attack (KMA) scenario. However, the estimation accuracies of existing estimators are not satisfactory when the number of observations is not large enough. Currently, it is still a challenging and open problem to design more effective estimators. In this paper, we propose an equivalent keys (EK)-based estimator to estimate the secret key for both the traditional and more secure SS watermarking methods. Equivalent keys form an equivalent region, which is the intersection of a unit hypersphere and a hypercone. According to the Monte Carlo simulation, we find that the secret key can be estimated by adding up the equivalent keys uniformly sampled from the equivalent region. Thus, the proposed estimator selects equivalent keys from randomly-generated vectors by exploiting the pairs of watermarked signals and their embedded messages. A theoretical analysis is performed for the proposed estimator to evaluate the estimation accuracy. Experimental results verify the theoretical analysis and show the superiority of the proposed estimator over existing estimation methods. Furthermore, this paper also shows the insecurity of the more secure SS watermarking methods in the KMA scenario from a practical perspective for the first time.

Over the past two decades, spread spectrum (SS) embedding has been widely used in digital watermarking due to its competitive performance in robustness and security. However, the robustness of existing secure SS embedding methods, such as natural watermarking (NW) and robust-NW (RNW), is still weak. In this article, we propose a new secure SS embedding method named truncated-RNW (TRNW), which improves the robustness of RNW while maintaining the same security level. The main idea of TRNW is to move RNW-watermarked correlations within an origin-centered sphere onto the spherical surface along the radial direction. Moreover, Hungarian algorithm is used to reduce embedding distortion, and the optimized method is called Hungarian-TRNW (HTRNW). A theoretical analysis and extensive experiments are conducted to validate the effectiveness of the proposed method. The results show that HTRNW achieves the same security level as RNW and a significant improvement over existing representative secure SS embeddings in terms of robustness.