Existing latent-representation-based watermarking methods for diffusion models typically embed watermark information directly into the original latent representations through mapping or modulation. However, such approaches largely overlook the stable signal relationships inherent in latent representations, and they fail to systematically investigate their impact on watermarking performance and generative quality. Through empirical analysis, we observe that the relative relationships between symmetric frequency coefficient pairs of latent representations exhibit greater stability under image manipulations and throughout the reverse diffusion process. Motivated by this observation, we propose Fourier Differential Watermarking (FDW), a training-free watermarking framework for latent diffusion models that achieves a balanced trade-off among robustness, embedding capacity, and generation quality. In the Fourier domain of latent noise, FDW enforces Hermitian symmetry and embeds watermark bits via thresholded differential encoding over symmetric frequency coefficient pairs. To further enhance reliability, we integrate Low-Density Parity-Check (LDPC) error correction and AES-CTR–based pseudorandom encryption, ensuring that embedded codewords remain consistent with the Gaussian prior of the latent space. This design preserves embedding capacity while maintaining watermark traceability and high-fidelity image generation. We conducted comprehensive experiments on the MS-COCO and Stable Diffusion Prompts datasets. The results demonstrate that, under competitive embedding capacities, FDW consistently achieves superior watermark extraction performance across most attack scenarios while preserving acceptable generation diversity and image quality.

Quantization-table-modification (QTM) is widely utilized in current studies of reversible data hiding (RDH) for JPEG images. However, the performance of existing QTM-based methods is far from optimal due to the uniform quantization step division and imperfect distortion modeling. In this letter, by incorporating Syndrome-Trellis-Code (STC) into QTM, a novel hybrid JPEG images RDH method is proposed. Firstly, instead of the uniformly dividing strategy conducted in previous works, by adaptively dividing the quantization steps, a hybrid embedding mechanism combining binary and ternary embedding is proposed. Then, the corresponding capacity-distortion model is established, by which the spatial domain distortion is estimated. Finally, based on the derived capacity-distortion model, for performance optimization, STC is utilized to minimize the cover modification. In this way, JPEG images RDH can be effectively conducted so that the visual quality of the marked image is well maintained. Experimental results demonstrate that the proposed method significantly outperforms some state-of-the-art works in terms of visual quality.

Reversible data hiding (RDH) for JPEG images remains relatively underexplored, with key challenges lying in coefficient selection and modification strategies. Existing methods select coefficients for embedding through block-wise or frequency-band-based operations, resulting in coarse-grained decisions that constrain embedding performance. In this paper, a novel RDH scheme for JPEG images based on gap-driven histograms generation with coefficient-wise selection is proposed. First, a multi-metric weighted complexity and coefficient-wise selection approach is proposed, integrating four local feature criteria to assess each coefficient individually, enabling more precise per-coefficient selection. Then, a gap-driven adaptive multi-histogram generation strategy is introduced, leveraging gap pairs to minimize shifting distortion by segmenting histograms via bisection and avoiding modifications to high-magnitude coefficients. Experimental results confirm that the proposed method achieves improved visual quality and more efficient file size control compared to existing state-of-the-art approaches.

Deepfake technology poses a serious threat to society by synthesizing a victims facial features and attributes to carry out deception. Traditional active defense methods against deepfake attacks are typically designed for specific models, and protected images often lose their anti-forgery capability after compression or reconstruction, severely limiting their practical applicability. This paper proposes a Meta-Learning-based active defense Scheme against deep facial forgery attacks (MLPDS), which effectively safeguards facial images against diverse deepfake attacks in real-world scenarios. Our approach adopts a general paradigminjecting noise into the original image to construct a cross-model defense algorithm against deepfake attacks. Specifically, by leveraging a meta-learning strategy, we integrate perturbations generated by multiple deepfake models, enabling robust protection against a variety of forgery models. Furthermore, to maintain the high fidelity of the images, we propose a symmetric gradient quantization strategy based on the arctan function to minimize the perceptual discrepancy between the perturbed and original images. Finally, an end-to-end optimization network is employed to generate universal perturbations tailored to specific images, supported by a pixel-level error metric that constrains deviations from the original content. Since no retraining is required to protect newly encountered images, this approach significantly improves the efficiency and practicality of real-time anti-deepfake defense. Experiments show that the proposed MLPDS algorithm can effectively resist attacks from multiple forgery models, outperforming state-of-the-art defense methods and significantly reducing image distortion with an average PSNR gain of approximately 7 dB, which fully meets the practical desire for efficient and reliable deepfake defense.

The development of the internet has greatly facilitated the transmission of images over social networks, while also triggering serious copyright issues. Deep robust watermarking serves as a crucial technique for image copyright protection. However, the image distortions caused by Social Network Transmission Operations (SNTOs) make existing deep robust watermarking methods fragile in real-world social network scenarios. To address this, we propose a Curriculum Learning-based Deep Robust Watermarking method, called CL-DRW, to generate watermarks that can be resilient to SNTOs. Specifically, we develop a watermarking model constructed with an invertible neural network and present a multi-stage training framework based on curriculum learning to train it effectively. We incrementally introduce noise attacks based on their disruptive impact on the watermark, from weak to strong, thereby enabling our model to build robustness against SNTOs gradually. Additionally, we design an SNTOs simulation noise layer, which is built upon a transformer-based deep network and incorporates differentiable JPEG, to simulate the black-box distortions caused by SNTOs. Extensive experiments indicate that our proposed CL-DRW outperforms state-of-the-art deep watermarking methods in terms of robustness against real-world social network transmission operations. Source code is available at https://github.com/yingshuai-zhao/CL-DRW.

The reversibility of robust reversible watermarking (RRW) strictly depends on the premise that the watermarked image has not been attacked. However, in practical applications, multimedia content often suffers from various attacks, and existing RRW technologies completely lose their reversible recovery capabilities. Therefore, this paper proposes a self-recovery robust watermarking (SRRW) algorithm, which provides a new ability to recover the watermarked and attacked image more closely to the original image while the watermark maintains strong robustness to those common signal processing operations and geometric attacks. First, the watermark information is inserted into low-order Zernike moments of a cover image by using quantization watermarking technique so that the watermark is resistant to those additive noise- like operations ( like JPEG compression and Gaussian noises) and invariant to geometric transforms ( like rotation and scaling). Then, the scaled difference vectors between the cover vectors and its quantized watermarked vectors are luminously and ingeniously computed as the distortion compensation information added back to the quantized watermarked vectors for restoration of the cover image. Finally, at the receiver side, based on the watermark bits extracted from the watermarked image or its distorted versions, those Zernike moments embedded data can be restored by the known scaling factor of the difference vector. Furthermore, a self-recovery image resembling the original image more closely can be reconstructed. Experimental results show that the proposed SRRW scheme can effectively restore those distorted images due to the 128-bit watermark embedding, JPEG compression with the quality factor 60 or JPEG2000 compression with the compression ratio 9, while providing strong robustness performance to various kinds of attacks. Compared with the attacked watermarked images, the restored images show PSNR improvements of 1.66 dB, 3.53 dB, and 1.72 dB under JPEG compression ($Q = 90$), JPEG2000 compression ($R = 3$), and AWGN ($\sigma = 0.0001$), respectively.

In reversible data hiding (RDH) based on prediction-error-expansion (PEE), the embedding distortion is lower for bit “0” than for bit “1”. To favor bit “0”, a binary matrix embedding (BME)-based data transformation strategy is introduced. In this strategy, the transformed data replaces the original, and embedding is performed via two-dimensional (2D) mappings. However, the mappings are restricted to at most two modification directions by BME, limiting flexibility and increasing distortion. Moreover, the embedded data distribution is altered by data transformation, rendering traditional mapping selection models inapplicable. To address the above problems, a multivariate matrix embedding (MME)-based 2D PEE framework is proposed in this paper. First, a piecewise data transformation strategy is introduced to enable embedding via generalized mappings with three modification directions. Then, the corresponding capacity-distortion model is established to optimize mapping selection. Finally, adaptive costs are refined based on mapping patterns to minimize the embedding distortion. Experimental results demonstrate that the proposed method achieves superior marked image quality over some state-of-the-art methods.

Reversible data hiding (RDH) for JPEG images, particularly those focusing on DCT coefficient modification, has garnered significant attention in recent years. Existing methods primarily select coefficients valued$\pm 1$for expansion embedding to avoid significant file size increases caused by modifying zero-valued DCT coefficients. However, zero-valued coefficients, which constitute the majority of DCT coefficients, are more suitable for data embedding to reduce the shift distortion. To efficiently utilize zero-valued coefficients for high-capacity embedding while controlling the file size increment, this paper introduces a novel JPEG RDH method based on ternary matrix embedding, where ternary syndrome trellis codes (STC) is employed on selected zero-valued coefficients to minimize the expansion embedding distortion, and other non-zero-valued coefficients are shifted for reversibility. Furthermore, a novel DCT coefficients measurement strategy is proposed for coefficient selection to further reduce the shift distortion. Extensive experimental validations demonstrate the superiority of the proposed method in various evaluation criteria. Notably, the proposed method achieves more than twice the embedding capacity of some state-of-the-art methods at the same PSNR while maintaining file size increment within acceptable bounds.

Transferable adversarial examples (AEs) have attracted considerable attention due to their ability to expose vulnerabilities in black-box deep neural networks (DNNs). However, achieving superior transferability for targeted attacks remains a challenge. In this article, inspired by the observation that AEs with smaller intra-class distances and larger inter-class distances tend to exhibit higher transferability, we propose a novel targeted attack based on Feature Contrastive Optimization (FCO). This attack enhances adversarial transferability by minimizing intra-class distances and maximizing inter-class distances. Specifically, we first define positive samples (belonging to the target class) and negative samples (belonging to non-target classes) that correspond to targeted AEs. Subsequently, leveraging these defined positive and negative samples, we propose two metrics—Intra-class Compactness (IC) and Inter-class Separability (IS)—to construct a novel Feature Contrastive (FC) loss. By integrating this plug-and-play FC loss into standard adversarial objectives, the generated AEs are encouraged to better align with the target class distribution while diverging from those of non-target classes. Extensive experiments on the ImageNet-compatible dataset demonstrate that our approach consistently improves targeted transferability across a broad range of DNN architectures.

The widespread emergence of Deepfake content has made it increasingly important to distinguish real and fake faces. Although many methods focus on detecting Deepfake content, only a few address the protection of real faces against forgery. Therefore, this paper proposes a proactive Deepfake detection scheme named FALU, which combines the uniqueness of facial identity features with the robustness of average hashing. The method first divides the input image into facial and non-facial regions, extracts identity-related features from the facial region, encodes them using average hashing, and embeds the result as a watermark into the non-facial region. During detection, the watermark is extracted from the non-facial region and compared with a newly generated hash code from the facial region. High correlation indicates authenticity, while low correlation suggests Deepfake forgery. To facilitate efficient and reliable watermark embedding, FALU integrates the symmetric sampling structure of U-Net with Mamba-like linear attention mechanism, proposing a lightweight encoder network. This scheme ensures the persistent presence of secret information before and after manipulation, thereby enhancing face source detection and tampering identification. Experimental results demonstrate that the proposed scheme effectively counters traditional Deepfake techniques and shows significant potential for preserving personal privacy.

The images transmitted by IoT devices, particularly those used for surveillance or sensor data, are vulnerable to malicious screenshots and unauthorized access, leading to potential privacy breaches. To address this, we propose a multi-stage Singular Value Decomposition (SVD)-based robust data-hiding scheme for JPEG images aimed at mitigating screenshot attacks. The method exploits the decorrelation properties of the Discrete Cosine Transform (DCT) to preprocess the carrier image, facilitating the selection of specific frequency coefficients. These coefficients undergo a dual-stage SVD transformation, where dimensionality reduction reduces the impact of noise from non-critical image regions. Additionally, we optimize Grad-CAM heatmap generation to better align with human visual perception, enabling the identification of stable and reliable feature regions for embedding secret information. This approach ensures that the visual integrity of the carrier image is maintained while preserving the legibility of the embedded information, even under attack.Our method enhances both the visual fidelity of the carrier image and the robustness of the embedded information. Experimental results demonstrate that the proposed scheme outperforms existing methods, achieving at least a 5% improvement in confidential information extraction accuracy and a data extraction rate exceeding 95% across screenshot angles ranging from -40∘ to 40∘. Extensive evaluations confirm the superior performance, efficiency, and security of our method in mitigating screenshot attacks, showcasing its broad applicability to various image formats and resilience to distortions.

With the rapid advancement of the Internet of Things (IoT), massive volumes of multimedia data are continuously generated by distributed sensing devices and edge nodes. Efficient and accurate image retrieval from such data has become a key component in enabling advanced IoT applications. However, the constraints of edge computing—including limited bandwidth, low power budgets, and heterogeneous hardware—pose significant challenges to conventional image retrieval schemes. To address these issues, this paper proposes a lightweight and effective Content-Based Image Retrieval (CBIR) framework optimized for cloud-enabled IoT environments. Specifically, this paper introduces a new multi-feature construction scheme that integrates the Color Granular Descriptor (CGD) for fine-grained color characterization, the Double-Radius Local Binary Pattern (DR-LBP) for enhanced local texture extraction, and the Lower-Order Polar Harmonic Fourier Moments (LPHFMs) for capturing global shape features with strong rotational and scale invariance. The proposed scheme achieves high retrieval precision with low computational cost, making it well-suited for deployment in resource-constrained IoT environments. Extensive evaluations conducted on widely used benchmark datasets—including Corel-1K, Corel-5K, Corel-10K, Oxford105K, and GHIM-10K—demonstrate the superior performance and robustness of the proposed method, validating its practical applicability to IoT scenarios.

Perceptual image hashing has emerged as a crucial forensic tool within the Internet of Things (IoT) ecosystem. Traditional perceptual hashing algorithms predominantly rely on global image features to generate hash codes, which limit their ability to represent key features of images effectively. This paper introduces a Perceptual Region Recognition Network (PRRN) to accurately identify key feature regions in images based on their texture distribution characteristics, thereby generating image perceptual hashing codes that reflect the key content of the images. At the same time, a perceptual hashing feature extraction module, which integrates a Residual Network (ResNet) and a Weighted Feature Fusion Network (WFFN), is built to extract deep semantic features of the object image. Where, ResNet is leveraged to extract high-level semantic features, while WFFN ensures the preservation of low-level local features. Furthermore, skip connections are employed to achieve content enhancements for intricate details of critical image regions. Additionally, the Mean Squared Error (MSE) loss is incorporated to enhance the accuracy of key region localization, further improving the sensitivity of image perceptual hash codes and accelerating the network’s convergence speed. Extensive experimental evaluations demonstrate that the proposed PRRN-based perceptual image hashing scheme significantly outperforms other state-of-the-art methods in terms of image feature representation capability. Specifically, it achieves an average improvement of over 1.2 in attack-resistant capability for images compared with other counterparts, making it a promising candidate for practical applications in the IoT environment.

Existing deep learning-based reversible data hiding (RDH) predictors are affected by the difference of pixel complexity, which leads to the reduction of prediction accuracy. Therefore, this letter proposes an optimization framework tailored for RDH predictors, which integrates the local complexity of pixels into the predictor's regression optimization process. By analyzing the image's texture features, the framework adaptively determines the optimal prediction coefficients, thereby improving prediction accuracy. Notably, this optimization framework is versatile and can be applied to optimize other deep learning-based RDH predictors. Additionally, recognizing the critical role of interpolation strategies in RDH pixel prediction, we introduce a multi-scale fusion-enhanced interpolation network specifically designed for RDH, which integrates features across different scales to provide accurate reference pixels for subsequent predictions. Finally, experimental results demonstrate that the proposed method outperforms several advanced RDH predictors in terms of both prediction accuracy and embedding performance.

Prediction-error expansion (PEE) is the most efficient approach in reversible data hiding (RDH). However, in PEE, to ensure the reversibility, significant distortion is introduced since many pixels are shifted without embedded data. Based on this consideration, a novel double-layered RDH framework called S+PEE is proposed in this paper. Unlike the conventional PEE, by S+PEE, shifted pixels can also be utilized for carrying secret data. The secret data is embedded in the first embedding layer with steganography and a specifically designed PEE-like mechanism. Then, to ensure the reversibility, the irreversible modifications introduced by the first embedding layer are recorded and embedded in the second embedding layer. Moreover, the corresponding capacity-distortion model is established to minimize the embedding impact, so that the marked image quality can be optimized. Experimental results demonstrate that the proposed method can provide high marked image quality, and it outperforms some state-of-the-art methods.

Detecting double JPEG compression with the same quantization matrix is a crucial yet challenging task in image forensics. Existing methods often fail to accurately identify and fully exploit the differences between singly and doubly compressed images, resulting in unsatisfactory detection performance, especially for cases with low quality factors (QFs). To address this issue, a novel method is proposed to extract highly discriminative features for performance enhancement. First, we design a new error block classification method that categorizes error blocks into stable error blocks, rounding error blocks (REBs), and truncation error blocks (TEBs). This classification method enables more accurate identification of TEBs, which are the most discriminative blocks in error images for cases with low QFs. Then, based on the theoretical analysis of REBs and TEBs, an intrinsic variable that directly leads to the differences between two classes of images is derived, providing more essential characteristics for the detection. Finally, a number of 25-dimensional highly discriminative features are extracted from REBs, TEBs, and flat blocks. Experimental results demonstrate that the proposed method outperforms several state-of-the-art works, especially on images with low QFs.

In this paper, we propose a robust image steganography method utilizing color conversion, leveraging de-colorization and colorization models to achieve covert transmission of secret information. The motivation is to use color conversion of the stego image to conceal steganographic behavior. For the sender, secret information is embedded into the color cover image using a robust embedding algorithm based on quaternion exponent moments. The stego images are then de-colorized to obtain grayscale images, which can be transmitted over public channels. For the receiver, a corresponding colorization network is designed to reconstruct the stego image and extract the secret information. Additionally, an attack module using Gaussian noise is implemented to enhance the robustness of the proposed steganography. Given a color image, its grayscale version can be chosen from various options, making it difficult for attackers to detect steganographic activity as long as the generated grayscale image appears normal and meaningful. Extensive simulation results demonstrate the feasibility and scalability of the proposed steganography method.

Aiming to mitigate image distortion caused by steganography algorithms at high-capacity information embedding and enhance the steganalysis resistance capability of generated stego images, this paper proposes a high-capacity differential steganography algorithm for color images based on multiple adversarial networks. Instead of directly modifying the pixels of the cover image, the algorithm embeds the secret information into the differential plane generated by the two most similar channels of the cover image. Consequently, the distortion of the stego image is minimized while embedding a secret image of the same size. At the same time, the fidelity of the stego and extracted secret images is continually improved through adversarial training between the generator and discriminator in the proposed steganography network. Furthermore, multiple steganalysis networks are parallelly utilized to enhance the steganalysis resistance capability of stego images. In addition, the Lion optimizer is utilized for the first time to improve the convergence speed of the proposed steganographic network. Experimental results show that the comprehensive performance of the proposed algorithm outperforms other state-of-the-art steganography algorithms significantly.

In the reversible data hiding (RDH) community, both prediction and mapping strategies are vital for reducing distortion. With high prediction performance, small prediction errors can be generated to reduce the embedding distortion. Besides, the efficient mapping strategy can improve the practicality. In this paper, we propose a new RDH method for color images by using convolution neural networks (CNNs) for prediction and an efficient 3D mapping strategy for embedding. At first, each color image is elaborately divided into three isolated image sets so that the proposed deep prediction network (DPN) can exploit more neighboring pixels in the current channel and the correlation between three channels. Then, an efficient 3D mapping strategy is luminously designed by using the symmetry of the 3D prediction error histogram (PEH). The symmetry of 3D PEH has been analyzed in statistical and experimental ways. Based on the proposed deep prediction network and efficient 3D mapping strategy (DPEM), we construct an efficient RDH method for color images. The performance of the proposed DPN is evaluated by comparing it with several predictors on different image datasets. The embedding performance has been demonstrated by hiding information in color images, e.g., the average PSNR value of the Kodak dataset is 63.63 dB with an embedding capacity of 50,000 bits. Furthermore, the experimental results on the ImageNet and PASCAL VOC2012 datasets have shown the proposed RDH method is superior to several state-of-the-art RDH methods. With the introduction of deep learning, the development of the RDH method for color images can be promoted.

Transferable adversarial examples have received increasing attention for their utility in spoofing multiple models, but existing attacks still perform poorly in terms of transferability. In light of this, a novel attack method called Spatio-Temporal Context-Based Enhanced Momentum Iteration (STCEMI) is proposed for transferability enhancement. First, two spatially and temporally oriented context exploitation strategies are devised, respectively. On the one hand, the blended image is obtained by summing a randomly scrambled version of the original image with itself, and the correction of spatial context momentum to the gradient of the current position is achieved by utilizing the blended image to optimize the perturbation. On the other hand, with the short-time context obtained from single-step iteration along the backward and forward gradient directions, the gradient of the current iteration can be corrected by the temporal context momentum. Second, considering the complementarity of spatial and temporal contexts, two strategies are naturally integrated to construct the spatio-temporal context-based attack, STCEMI, with the objective of achieving stronger transferability. The results of extensive experiments demonstrate that the adversarial images generated by STCEMI achieve the highest cross-model attack success rate across multiple mainstream normally trained and adversarially trained models.

With accelerating development of artificial intelligence, neural network models have been applied in many fields. The structure designing and training for models consume vast manpower and computing resources, which are the core interests of related research institutions and enterprises. However, the high-value attributes of neural network models also attract the attention of pirates, who may steal them for illegal profits and also slightly modify model parameters to escape model piracy detection. In order to solve the problem, in this work, we propose a robust and secure model hashing method based on dynamic branch reorganization and multi-feature fusion. Detailedly, we dynamically adjust the branches in our model hashing network to extract the robust features of all kinds of model parameters for generating the hash sequence. Besides, we integrate the encryption and the feature matrix generation to a unified stage in the hash generation for resisting possible encryption escape attack. Thus, the pirated models, even with some modifications, can be correctly detected through calculating hash distances. Experimental results demonstrate the effectiveness and superiority of our model hashing method with respect to pirated model detection, non-pirated model discrimination and security.

Traditional gradient descent (GD) has been fully investigated for convex or L-smoothness functions, and it is widely utilized in current neural network optimization. The classical descent lemma ensures that for a function with L-smoothness, the GD trajectory converges stably towards the minimum when the learning rate is below 2 / L. This convergence is marked by a consistent reduction in the loss function throughout the iterations. However, recent experimental studies have demonstrated that even when the L-smoothness condition is not met, or if the learning rate is increased leading to oscillations in the loss function during iterations, the GD trajectory still exhibits convergence over the long run. This phenomenon is referred to as the unstable convergence regime of GD. In this paper, we present a theoretical perspective to offer a qualitative analysis of this phenomenon. The unstable convergence is in fact an inherent property of GD for general twice differentiable functions. Specifically, the forwardinvariance of GD is established, i.e., it ensures that any point within a local region will always remain within this region under GD iteration. Then, based on the forward-invariance, for the initialization outside an open set containing the local minimum, the loss function will oscillate at the first several iterations and then become monotonely decreasing after the GD trajectory jumped into the open set. This work theoretically clarifies the unstable convergence phenomenon of GD discussed in previous experimental works. The unstable convergence of GD mainly depends on the selection of the initialization, and it is actually inevitable due to the complex nature of loss function.

Recently, matrix embedding (ME), a well-known steganographic technique, has been employed in reversible data hiding (RDH) for the first time, improving the performance of single histogram modification (SHM) methods. In this letter, the ME-based RDH strategy is extended from SHM to the more effective multiple histograms modification (MHM) to further improve the reversible embedding performance. The capacity-distortion model is first established in the novel scenario. Then, some theoretical results for payload partition and expansion-bins-determination are given. Finally, based on the derived theoretical investigations, an efficient RDH method with low computational complexity is proposed. Experimental results show that the proposed method can achieve better visual quality compared to some state-of-the-art methods.

This letter proposes a high-performance image steganography scheme based on dual-adversarial networks to enhance the performance of secret message hiding. According to the characteristics of generative adversarial networks, a dual-adversarial steganography scheme is devised to improve both the visual quality and the steganalysis resistance capability of the stego image. In the first adversarial block, the U-net structure is employed to reconstruct the original image as the generated image, and the adversarial noise is imperceptibly embedded into the generated image to produce the adversarial image that is most suitable for data hiding. In the second adversarial block, secret messages are undetectably embedded into the adversarial image under the confrontation of multiple steganalysis networks. Moreover, a multiple-channel attention module is introduced to enhance the performance of the adversarial image and accelerate the convergence speed of the proposed dual-adversarial networks. Additionally, the MSE loss is employed to minimize the divergence between the original and the adversarial image. Experimental results indicate that the average PSNR of the adversarial images reach 41 dB, and the detection probability is 2.79% lower than that of other advanced schemes. The proposed scheme outperforms its counterparts in terms of performance.

Advancements in computer vision and deep learning have led to difficulty in distinguishing Deepfake and real videos. In particular, forgery audios are also generated to accompany fake videos and make them more realistic, which makes Deepfake detection more difficult. Existing Deepfake detection methods that use multimodal information ignore the representation gap between different modalities, resulting in limited performance. To address this problem, in this paper, a novel Deepfake detection method utilizing multimodal contrastive learning (MCL) is proposed to better explore intra-modal and cross-modal forgery clues. To reduce the cross-modal gap and explore multimodal forgery artifacts, a cross-modal contrastive learning strategy is designed to learn a compositional embedding from multimodal information, which facilitates pulling together representations across uni-modalities and multi-modalities. Moreover, to supplement the intra-frame forgery clues mining ability of the video network, the frame knowledge is distilled to the video network without adding additional computation. Specifically, to mine intra-modal clues, three modality features are first extracted from audio, frame and video, respectively. Secondly, the audio and frame features are separately composed with the video feature to derive two cross-modal representations. Subsequently, these cross-modal features are contrastive with the intra-modal features to reduce cross-modal gap. By jointly pulling together the unimodal and multimodal features through MCL, a more effective representation that contains intra-modal and cross-modal forgery artifacts can be learned. Finally, a noise-based feature augmentation (NFA) module is proposed to adaptively perturb the audio-visual feature and further improve generalization performance. Extensive experiments demonstrate that the proposed framework outperforms SOTA methods.

Aiming at the problem of most Robust Reversible Data Hiding (RRDH) schemes failing to anti geometric deformation attacks, a new RRDH algorithm based on Polar Harmonic Fourier Moments (PHFMs) is presented in this paper, thereby enhancing both the robustness of the embedded data and perceptual quality of the data-embedded image. Firstly, by leveraging the anti-geometric transformation and high-fidelity features of PHFMs, the image is transformed into its frequency domain for RRDH. Then, a quantitation index modulation (QIM) algorithm is designed to embed secret data into the integer part of PHFMs coefficients. By minimizing the differences between the secret-data-embedded image and the original image, the amount of compensation data is reduced. Meanwhile, a two-dimensional RDH scheme is further adopted to embed the compensation data, thus reducing the distortion of the full data-embedded image. Finally, the robustness of the embedded data and the fidelity of the full data-embedded image are both improved. The combination of PHFMs transformation and two-dimensional RDH enables the proposed RRDH algorithm to achieve high visual quality and strong resistance capability against geometric transformation attacks. Extensive experimental results demonstrate that the proposed RRDH algorithm outperforms other state-of-the-art techniques.

Over the past few years, deep generative models have significantly evolved, enabling the synthesis of realistic content and also bringing security concerns of illegal misuse. Therefore, active protection for generative models has been proposed recently, aiming to generate samples with hidden messages for future identification while preserving the original generating performance. However, existing active protection methods are specifically designed for generative adversarial networks (GANs), restricted to handling unconditional image generation. We observe that they get limited identification performance and visual quality when handling audio-driven video generation conditioned on target audio and source input to drive video generation with consistent context, e.g., identity and movement, between frame sequences. To address this issue, we introduce a simple yet effective activeProtection framework forAudio-DrivenVideoGeneration, named PADVG. To be specific, we present a novel frame-shared embedding module in which messages to hide are first transformed into frame-shared message coefficients. Then, these coefficients are assembled with the intermediate feature maps of video generators at multiple feature levels to generate the embedded video frames. Besides, PADVG further considers two visual consistent losses: (i) intra-frame loss is utilized to keep the visual consistency with different hidden messages; (ii) inter-frame loss is used to preserve the visual consistency across different video frames. Moreover, we also propose an auxiliary denoising training strategy through perturbing the assembled features by learnable pixel-level noise to improve identification performance, while enhancing robustness against real-world disturbances. Extensive experiments demonstrate that our proposed PADVG for audio-driven video generation can effectively identify the generated videos and achieve high visual quality.

Talking head, driving a source image to generate a talking video using other modality information, has made great progress in recent years. However, there are two main issues: 1) These methods are designed to utilize a single modality of information. 2) Most methods cannot control head pose. To address these problems, we propose a novel framework that can utilize multi-modal information to generate a talking head video, while achieving arbitrary head pose control by a movement sequence. Specifically, first, to extend driving information to multiple modalities, multi-modal information is encoded to a unified semantic latent space to generate expression parameters. Secondly, to disentangle attributes, the 3D Morphable Model (3DMM) is utilized to obtain identity information from the source image, and translation and rotation information from the target image. Thirdly, to control head pose and mouth shape, the source image is warped by a motion field generated by the expression parameter, translation parameter, and angle parameter. Finally, all the above parameters are utilized to render a landmark map, and the warped source image is combined with the landmark map to generate a delicate talking head video. Our experimental results demonstrate that our proposed method is capable of achieving state-of-the-art performance in terms of visual quality, lip-audio synchronization, and head pose control.

In this paper, we study the problem of end-to-end multi-person pose estimation. State-of-the-art solutions adopt the DETR-like framework, and mainly develop the complex decoder, e.g., regarding pose estimation as keypoint box detection and combining with human detection in ED-Pose [38], hierarchically predicting with pose decoder and joint (keypoint) decoder in PETR [27].We present a simple yet effective transformer approach, named Group Pose. We simply regard K-keypoint pose estimation as predicting a set of N × K keypoint positions, each from a keypoint query, as well as representing each pose with an instance query for scoring N pose predictions.Motivated by the intuition that the interaction, among across-instance queries of different types, is not directly helpful, we make a simple modification to decoder self-attention. We replace single self-attention over all the N × (K + 1) queries with two subsequent group self-attentions: (i) N within-instance self-attention, with each over K keypoint queries and one instance query, and (ii) (K +1) same-type across-instance self-attention, each over N queries of the same type. The resulting decoder removes the interaction among across-instance type-different queries, easing the optimization and thus improving the performance. Experimental results on MS COCO and Crowd-Pose show that our approach without human box supervision is superior to previous methods with complex decoders, and even is slightly better than ED-Pose that uses human box supervision. Paddle1and PyTorch2codes are available.

Abstract In this paper, we propose a human visual system (HVS) guided reversible data hiding method based on multiple histograms modification. The proposed method utilizes the texture features of an image to adaptively modify the pixels, for a lower HVS quality distortion. The HVS quality is taken as the optimization objective and a new expansion-bin-selection strategy is given to solve the optimization. For the same HVS quality distortion, the proposed method can embed more secret bits and give higher priority for the modifications in texture regions. Besides, a better optimization rule is proposed to accelerate the speed and then consider more available solutions. In this way, a trade-off between the embedding performance and time complexity can be achieved. Experimental results show that the proposed method can achieve a better HVS quality than the conventional methods.

Advancements in computer vision and deep learning have made it difficult to distinguish deepfake visual media. While existing detection frameworks have achieved significant performance on challenging deepfake datasets, these approaches consider only a single perspective. More importantly, in urban scenes, neither complex scenarios can be covered by a single view nor can the correlation between multiple datasets of information be well utilized. In this article, to mine the new view for deepfake detection and utilize the correlation of multi-view information contained in images, we propose a novel triple complementary streams detector (TCSD). First, a novel depth estimator is designed to extract depth information (DI), which has not been used in previous methods. Then, to supplement depth information for obtaining comprehensive forgery clues, we consider the incoherence between image foreground and background information (FBI) and the inconsistency between local and global information (LGI). In addition, we designed an attention-based multi-scale feature extraction (MsFE) module to extract more complementary features from DI, FBI, and LGI. Finally, two attention-based feature fusion modules are proposed to adaptively fuse information. Extensive experiment results show that the proposed approach achieves state-of-the-art performance on detecting deepfakes.

Prediction-error expansion (PEE) is the most popular reversible data hiding (RDH) technique due to its efficient capacity-distortion tradeoff. With the generated prediction-error histogram (PEH) and adaptively selected expansion bins, the image redundancy is well exploited by PEE. However, for the most widely used rhombus predictor, the rounding operation which groups different prediction-errors into one value is completely unnecessary. The embedding can be extended to a general case by removing the rounding operation, and more histogram bins can be derived for expansion with a new mapping mechanism. Therefore, in this article, instead of pixel prediction-error, we propose to compute the pixel residuals without the rounding operation, and a new embedding mechanism based on pixel-residual histogram (PRH) modification is devised. In PRH, four bins correspond to one bin in PEH. Then, different from the one-to-one mapping between the prediction-error and pixel modification, a four-to-one mapping between the pixel-residual and pixel modification is established, and the performance is optimized by adaptively selecting four expansion bin pairs for embedding. Since more modification selections are considered, better performance can be obtained. Moreover, the proposed scheme is extended to the two-dimensional (2D) histogram and multiple histograms based embedding, and the performance is further enhanced. The superiority of the proposed method is experimentally verified by comparing it with some state-of-the-art works.

Digital watermarking is an effective way to protect the copyright of digital medium. However, most existing video watermarking algorithms cannot resist both spatial and temporal attacks as they cannot utilize the temporal and spatial video redundancy simultaneously. In this paper, based on spatial domain intra-frame difference, a new robust video watermarking algorithm is proposed. Firstly, the frame sequences of the to-be-marked digital video are grouped based on the time period. Then, by a spatial domain image watermarking algorithm, all frames within each group are embedded with one-bit data, and the watermark is finally embedded. Extensive experiments are conducted, and these results verify that the proposed algorithm is more robust than some other video watermarking methods under the same impact on the video quality.

Reversible data hiding (RDH) is a research hotspot nowadays. By RDH, after data extraction, the cover image can be restored without information loss. Among numerous existing RDH techniques, multiple histograms modification (MHM) is a general reversible embedding framework, and it is experimentally verified better than the traditional single histogram based methods. However, the expansion-bins-determination process for MHM is conducted through naive exhaustive search, which is time consuming. Based on this consideration, a fast expansion-bins-determination method for MHM is proposed in this paper. Specifically, to determine the optimal expansion bins, instead of solving the optimization problem of discrete variables, we consider a general form of this problem with differentiable objective function and real variables, so that advanced analysis tools such as Lagrange multiplier can be utilized. By the proposed approach, compared with the original MHM, the expansion bins can be determined quickly with only a tiny performance loss, and thus the practicality of MHM is improved.

The problem of general distortion model for reversible data hiding (RDH) is investigated in this letter. Unlike previous RDH schemes that regard the cover image as a memory-less sequence and assign the same distortion for each pixel, in this work, the modification distortion is adaptively defined for each pixel for visual performance enhancement. The situation is totally different compared with the traditional RDH approaches, and the classical histogram based methods can not be utilized. To deal with this new and challenging problem, we then propose a two-steps embedding framework. Considering binary image as cover, firstly, some pixels are selected and losslessly compressed as the reconstruction information for image recovery. Then, with the adaptively defined distortion and by utilizing matrix embedding, the secret message and the reconstruction information are embedded into the cover. In this way, reversible embedding is realized while the total distortion is minimized. By comparing with some previous RDH schemes for binary covers, experimental results show that better visual performance is achieved by the proposed method.

Reversible data hiding (RDH) is a hot research topic, and many related techniques are proposed, but only a few are devised for color images. Most current RDH schemes, including those for color images, follow a well-developed framework: histogram-based embedding, which consists of two main steps, i.e., prediction-error histogram (PEH) generation by a pixel predictor and PEH modification through exploring efficient reversible mappings. The reversible mappings employed in these RDH approaches for color images, on the other hand, are empirically designed ignoring the specific image content, resulting in limited embedding performance. To address this issue, a novel RDH method for color images based on adaptive mapping selection is proposed in this paper. First, to leverage high inter-channel correlation of color images, a three-dimensional (3D) PEH is generated. Then, an effective reversible mapping selection mechanism is proposed, in which 3D mappings are adjusted in an ordered iterative manner according to PEH frequency ranking so that the embedding performance is optimized. By the proposed approach, the optimal reversible mapping can be acquired with low computing complexity and better embedding performance, and its efficiency is experimentally validated in comparison to various state-of-the-art studies.

In image forensics, quantization step estimation plays a crucial role in revealing the JPEG compression history. This study focuses on the estimation for images that have been JPEG compressed and re-saved in lossless formats. Several effective methods have been developed, whereas the performance on small sized images still needs to be improved. In this paper, a novel JPEG quantization step estimation method with low complexity and high efficiency is proposed. First, for a given decompressed image, as the special shape of its DCT coefficients distribution is highly related to the quantization step, a function of the candidate step taking a similar shape is designed. Then, the quantization step is determined as the candidate leading to the maximum response of the designed function on the probability density function of DCT coefficients. The relation between the maximum response and the quantization step is verified mathematically, which provides a theoretical basis for the proposed method. In addition, to further improve the estimation performance, two fine adjustment procedures are adopted. Experimental results demonstrate that the proposed method outperforms some state-of-the-art works, especially on small sized images.

Detecting double JPEG compression with the same quantization matrix is a challenging task in image forensics. To address this problem, in this paper, a novel method is proposed by leveraging the component convergence during repeated JPEG compressions. Firstly, an in-depth analysis of the pipeline in successive JPEG compressions is conducted, and it reveals that the rounding/truncation errors as well as JPEG coefficients tend to converge after multiple recompressions. Based on this fact, the backward quantization error (BQE) is defined, and we find that the ratio of non-zero BQE for single compression is larger than that for double compression. Moreover, to exploit the convergence property of JPEG coefficients, a multi-threshold strategy is designed for capturing the statistics of the number of different JPEG coefficients between two sequential compressions. Finally, the statistical features of the dual components are concatenated into a 15-D vector to detect double JPEG compression. Experimental results demonstrate the efficiency of the proposed method, which outperforms some state-of-the-art schemes.

As a specific data hiding technique, reversible data hiding (RDH) has recently received extensive attention. By this technique, both the embedded data and the original cover image can be exactly extracted from the marked image. In our previous work, a general expansion-shifting model for RDH is proposed by introducing the so-called reversible embedding function (REF). With REF, RDH can be designed and the corresponding rate-distortion formulations can be established, providing an approach to optimize the reversible embedding performance. In this paper, by extending our previous work, optimal REF for one-dimensional histogram is investigated, and all optimal REF are derived in this case when the maximum modification to the cover pixel is limited as a small value. Moreover, based on the derived optimal REF for one-dimensional histogram and multiple histograms modification, a practical RDH scheme is presented and it is experimental verified better than some state-of-the-art algorithms in terms of capacity-distortion performance.

Reversible data hiding (RDH) for JPEG images has attracted extensive attentions in recent years. However, since DCT is a de-correlation operation, it is difficult for JPEG images to employ the image redundancy for RDH design like uncompressed images. In this paper, considering better utilizing the special properties of quantized DCT coefficients, a new RDH scheme for JPEG images based on multiple two-dimensional (2D) histograms modification is proposed. Firstly, by combining every two nonzero alternating current (AC) coefficients of adjacent DCT blocks in each band as a pair, a new coefficients pairing strategy is proposed for a sharper 2D histogram. Then, with a classification process, multiple 1D and 2D histograms are generated, in which the 2D histograms are selected for data embedding and the bins in 1D histograms are shifted for reversibility. Finally, to further enhance the embedding performance, the 2D mappings are adaptively determined for different 2D histograms through a formulated rate-distortion model. Experimental results demonstrate the superiority of the proposed scheme both in visual quality and file size preservation.

In recent years, high-dimensional histogram modification based reversible data hiding for images has drawn much attention among researchers. Pairwise prediction-error expansion (pairwise PEE) achieves great performance by exploiting the correlations among prediction-errors, in which a two-dimensional (2D) prediction-error histogram (PEH) is generated, and then modified based on a specific 2D modification mapping for reversible embedding. However, the used 2D mapping is fixed and heuristically designed without considering the image content, so the embedding performance of pairwise PEE can be further improved. To this end, the adaptive pairwise PEE (APPEE) is proposed in this paper to adaptively design the 2D mapping according to the distribution of 2D PEH, such that a better embedding performance is derived. To further improve the embedding performance, the proposed APPEE is extended from one single 2D PEH to multiple 2D PEHs generated based on different local complexities, in which multiple content-based 2D mappings are designed adaptively and individually for each 2D PEH. Experimental results show that the APPEE for either one single 2D PEH or multiple 2D PEHs significantly outperforms the conventional pairwise PEE. Simultaneously, the superiority of the proposed method is also experimentally verified compared with some other state-of-the-art works.

Most current reversible data hiding (RDH) techniques are designed for uncompressed images. However, JPEG images are more commonly used in our daily lives. Up to now, several RDH methods for JPEG images have been proposed, yet few of them investigated the adaptive data embedding as the lack of accurate measurement for the embedding distortion. To realize adaptive embedding and optimize the embedding performance, in this article, a novel RDH scheme for JPEG images based on multiple histogram modification (MHM) and rate-distortion optimization is proposed. Firstly, with selected coefficients, the RDH for JPEG images is generalized into a MHM embedding framework. Then, by estimating the embedding distortion, the rate-distortion model is formulated, so that the expansion bins can be adaptively determined for different histograms and images. Finally, to optimize the embedding performance in real time, a greedy algorithm with low computation complexity is proposed to derive the nearly optimal embedding efficiently. Experiments show that the proposed method can yield better embedding performance compared with state-of-the-art methods in terms of both visual quality and file size preservation.

Batch steganography is a technique that hides information into multiple covers. To achieve a better performance on the security of data hiding, we propose a novel strategy of batch steganography using a generative network. In this method, the approaches of cover selection, payload allocation, and distortion evaluation are considered in the round. We define a quality metric to evaluate the distortion between the cover image and the stego. When training the generation function, we define an objective function containing two parts: the entropy loss and the steganalytic loss. While the entropy loss is used to represent the gap between the payload inside stego images and the entire embedding capacity, the steganalytic loss is used to assess the data embedding impact using the proposed quality metric. With back-propagation, we minimize the objective function to obtain an optimal solution. Accordingly, different payloads can be allocated to different images, and the ± 1 modification probability for pixels in each cover can be calculated. Finally, we embed information into the selected images by STC. Experimental results show that the proposed method achieves a better undetectability against modern steganalytic tools.

Reconstructing the image processing chain and the parameters used in each step would provide important forensic clues. Many methods have been designed to estimate the primary quality factor of double compressed JPEG images. However, it is still a challenge to address such problem in the presence of resizing. In this paper, we concentrate on this topic by theoretically analysing the Welch Power Spectral Density (PSD) of the DC coefficients histogram of the counter-resized image. According to the analysis, We find that: i) the most prominent peak of PSD not only dependents on the first quality factor, but also relates to the second one, ii) the peak location nonlinearly maps to the quality factor in the first compression. A simple yet efficient method is proposed to estimate the primary quality factor based on the nonlinear mapping and geometric fitting. Experimental results demonstrate the proposed method provides superior performances.

Recently, a method based on multiple histograms modification (MHM) is proposed for reversible data hiding (RDH), in which a sequence of prediction-error histograms are generated and two expansion bins are selected in each histogram for expansion embedding. However, although efficient, it only chooses a single pair of expansion bins which limits the embedding capacity. On the other hand, the exhaustive expansion-bin-selection procedure in MHM takes huge computation time, so that it cannot be extended for high capacity RDH. In order to overcome the aforementioned drawbacks, an optimal RDH scheme based on MHM for high capacity embedding is proposed in this paper. First, to improve the embedding capacity, instead of a single pair of expansion bins, multiple pairs of expansion bins are utilized for each histogram, and the multiple-expansion-bin-selection for optimal embedding is formulated as an optimization problem. Then, unlike the exhaustive searching way used in MHM, a computationally efficient algorithm is proposed to solve the optimization problem, so that the optimal expansion bins can be adaptively determined to optimize the embedding performance. By the proposed approach, high embedding capacity can be achieved with good marked image quality, and the experimental results show that it is better than the original MHM and some other state-of-the-art methods.

Robustness is the most important factor that limits the practical application of reversible watermarking. To deal with this issue, several robust reversible watermarking (RRW) techniques have been proposed. Among them, the two-stage RRW framework proposed by Coltuc et al. is a promising one. In the first state of this framework, a robust watermark is embedded into the cover image to provide robustness, and then in the second stage, the information enabling revert the robust embedding is reversibly embedded into the already marked image to guarantee the reversibility. However, because of using the same area for these two embedding stages, the robustness in the first stage is seriously weakened by the reversible embedding. As a result, this elegant method is not effective as expected. Based on this consideration, this paper proposes an independent embedding domain (ED)-based two-stage RRW. The cover image is first transformed into two independent EDs, and then the robust and reversible watermarks are embedded into each domain separately. The carrier derived from the first embedding stage that carrying the robust watermark will not change after the reversible embedding, and thus, the robustness of the first stage is well preserved. By the proposed method, the embedding performance of the original two-stage RRW is significantly enhanced. Moreover, the proposed method is experimentally verified better than some other state-of-the-art RRW methods.

Pixel-value-ordering (PVO) is an efficient technique of reversible data hiding (RDH). By PVO, the maximum and minimum in each cover image block are first predicted and then modified to embed data. Actually, many PVO-based methods are essentially based on high-dimensional histogram modification. For these methods, a two-dimensional (2D) prediction-error histogram (PEH) is first generated and then modified based on a 2D mapping. However, these methods have two drawbacks. On one hand, the generated 2D PEH is irregular so that it is difficult to design suitable histogram modification strategy. On the other hand, the employed 2D mapping is empirically designed, and thus the embedding performance is far from optimal. Based on these considerations, a new PVO-based RDH scheme is proposed in this paper. By considering both pixel value orders and pixel locations, a new predictor is proposed so that the generated 2D PEH is regular in shape and suitable for reversible embedding. Moreover, instead of manually designing 2D mappings, to optimize the embedding performance, a self-learning mechanism is proposed to adaptively select the 2D mapping according to the image content. With the new predictor and the self-learning mechanism for 2D mapping selection, the proposed method works well with a good marked image quality, e.g., the PSNR of the image Lena is as high as 61.53 dB for an embedding capacity of 10 000 bits. Besides, compared with some state-of-the-art RDH methods, the superiority of the proposed method is experimentally verified.

Steganography detection based on Rich Model features is a hot research direction in steganalysis. However, rich model features usually result a large computation cost. To reduce the dimension of steganalysis features and improve the efficiency of steganalysis algorithm, differing from previous works that normally proposed new feature extraction algorithm, this paper proposes a general steganalysis feature selection method based on decision rough set α-positive region reduction. First, it is pointed out that decision rough set α-positive region reduction is suitable for steganalysis feature selection. Second, a quantization method of attribute separability is proposed to measure the separability of steganalysis feature components. Third, steganalysis feature components selection algorithm based on decision rough set α-positive region reduction is given; thus, stego images can be detected by the selected feature. The proposed method can significantly reduce the feature dimensions and maintain detection accuracy. Based on the BOSSbase-1.01 image database of 10000 images, a series of feature selection experiments are carried on two kinds of typical rich model features (35263-D J+SRM feature and 17000-D GFR feature). The results show that even though these two kinds of features are reduced to approximately 8000-D, the detection performance of steganalysis algorithms based on the selected features are also maintained with that of original features, which will remarkably improve the efficiency of feature extraction and stego image detection.

Pairwise prediction-error expansion (pairwise PEE) is a recent technique for the high-dimensional reversible data hiding. However, in the absence of adaptive embedding, its potential has not been fully exploited. In this paper, we propose the adaptive pixel pairing (APP) and the adaptive mapping selection for the enhancement of pairwise PEE. Our motivation is twofold: building a sharper 2D histogram and designing the effective 2D mapping for it. In APP, we consider to increase the similarity between pixels in a pair, by excluding the rough pixels from pairing and only putting the smooth pixels into pairs. In this way, the pixels in a pair have a larger possibility of being equal, and thus the resulted 2D prediction-error histogram (PEH) has lower entropy. Next, the adaptive mapping selection mechanism is introduced to properly determine the optimal modification, based on “whether it fits for the resulted PEH” rather than heuristic experience. The experimental results show that the proposed method has a significant improvement over the pairwise PEE.

We address the problem of data-driven image manipulation detection in the presence of an attacker with limited knowledge about the detector. Specifically, we assume that the attacker knows the architecture of the detector, the training data, and the class of features V the detector can rely on. In order to get an advantage in his race of arms with the attacker, the analyst designs the detector by relying on a subset of features chosen at random in V. Given its ignorance about the exact feature set, the adversary attacks a version of the detector based on the entire feature set. In this way, the effectiveness of the attack diminishes since there is no guarantee that attacking a detector working in the full feature space will result in a successful attack against the reduced-feature detector. We theoretically prove that, thanks to random feature selection, the security of the detector significantly increases at the expense of a negligible loss of performance in the absence of attacks. We also provide an experimental validation of the proposed procedure by focusing on the detection of two specific kinds of image manipulations, namely adaptive histogram equalization and median filtering. The experiments confirm the gain in security at the expense of a negligible loss of performance in the absence of attacks.

Reversible data hiding (RDH) is desirable in applications where both the hidden message and the cover image need to be recovered without loss. Among many RDH approaches is prediction-error expansion (PEE), containing two steps: i) prediction of a target pixel value, and ii) embedding according to the value of the prediction error. In general, higher prediction performance leads to larger embedding capacity and/or lower signal distortion. Leveraging on recent advances in graph signal processing (GSP), we pose pixel prediction as a graph-signal restoration problem, and design non-local graph-based prediction schemes where the appropriate edge weights of the underlying graph are computed using a similar patch searched in a semi-local neighborhood. Specifically, for each candidate patch, we first examine eigenvalues of its structure tensor to estimate its local smoothness. If sufficiently smooth, we pose a maximum a posteriori (MAP) problem using either a quadratic Laplacian regularizer or a graph total variation (GTV) term as signal prior. While the MAP problem using the first prior has a closed-form solution, we design an efficient algorithm for the second prior using alternating direction method of multipliers (ADMM) with nested proximal gradient descent. Finally, hidden message will be embedded into the image according to the resulting prediction errors. Experimental results show that with better quality GSP-based prediction, at low capacity the visual quality of the embedded image exceeds state-of-the-art methods noticeably.

Pairwise prediction-error expansion (pairwise PEE) is an improvement of the conventional PEE and it can provide excellent performance for reversible data hiding (RDH). Unlike PEE in which the prediction-errors are modified individually, the correlation among prediction-errors is exploited in pairwise PEE by jointly modifying each prediction-error pair. In this paper, the idea of pairwise PEE is developed and a new RDH scheme is proposed. A three-dimensional prediction-error histogram (3D-PEH) is generated by counting every non-overlapped prediction-error triple. Then, data embedding is conducted by modifying the 3D-PEH with a specifically designed reversible mapping. By using 3D-PEH and the proposed reversible mapping, the inter-correlation of prediction-errors is better exploited, and the performance of PEE is significantly enhanced. Moreover, the superiority of our method over pairwise PEE and some other state-of-the-art RDH methods is also experimentally verified. The proposed method is an effective extension of PEE towards the direction of high-dimensional histogram modification.

Prediction-error expansion (PEE) is an efficient technique for reversible data hiding (RDH). Instead of expanding the highest histogram bins in conventional PEE, in this paper, to better utilize the image redundancy, we propose a new PEE-based RDH scheme with an advisable expansion strategy utilizing referential prediction-errors. For each pixel, we first calculate its prediction-error and use its neighbor prediction-error as a reference. The correlation of the prediction-error and its reference is exploited to adaptively select bins for expansion embedding. In addition, to further enhance the reversible embedding performance, we apply the pixel selection technique in our scheme such that the pixels located in smooth image areas are priorly embedded. Experimental results show that the proposed scheme outperforms conventional PEE and it is better than some state-of-the-art RDH works as well.

Prediction-error expansion (PEE)-based reversible data hiding schemes consist of two steps. First, a sharp prediction-error (PE) histogram is generated by utilizing pixel prediction strategies. Second, secret messages are reversibly embedded into the prediction-errors through expanding and shifting the PE histogram. Previous PEE methods treat the two steps independently while they either focus on pixel prediction to obtain a sharp PE histogram, or aim at histogram modification to enhance the embedding performance for a given PE histogram. This paper propose a pixel prediction method based on the minimum rate criterion for reversible data hiding, which establishes the consistency between the two steps in essence. And correspondingly, a novel optimized histograms modification scheme is presented to approximate the optimal embedding performance on the generated PE sequence. Experiments demonstrate that the proposed method outperforms the previous state-of-art counterparts significantly in terms of both the prediction accuracy and the final embedding performance.

In this paper, we propose a scheme to detect the copy-move forgery in an image, mainly by extracting the keypoints for comparison. The main difference to the traditional methods is that the proposed scheme first segments the test image into semantically independent patches prior to keypoint extraction. As a result, the copy-move regions can be detected by matching between these patches. The matching process consists of two stages. In the first stage, we find the suspicious pairs of patches that may contain copy-move forgery regions, and we roughly estimate an affine transform matrix. In the second stage, an Expectation-Maximization-based algorithm is designed to refine the estimated matrix and to confirm the existence of copy-move forgery. Experimental results prove the good performance of the proposed scheme via comparing it with the state-of-the-art schemes on the public databases.

To identify whether an image has been JPEG compressed is an important issue in forensic practice. The state-of-the-art methods fail to identify high-quality compressed images, which are common on the Internet. In this paper, we provide a novel quantization noise-based solution to reveal the traces of JPEG compression. Based on the analysis of noises in multiple-cycle JPEG compression, we define a quantity called forward quantization noise. We analytically derive that a decompressed JPEG image has a lower variance of forward quantization noise than its uncompressed counterpart. With the conclusion, we develop a simple yet very effective detection algorithm to identify decompressed JPEG images. We show that our method outperforms the state-of-the-art methods by a large margin especially for high-quality compressed images through extensive experiments on various sources of images. We also demonstrate that the proposed method is robust to small image size and chroma subsampling. The proposed algorithm can be applied in some practical applications, such as Internet image classification and forgery detection.

Most of the recently proposed steganographic schemes are based on minimizing an additive distortion function defined as the sum of embedding costs for individual pixels. In such an approach, mutual embedding impacts are often ignored. In this paper, we present an approach that can exploit the interactions among embedding changes in order to reduce the risk of detection by steganalysis. It employs a novel strategy, called clustering modification directions (CMDs), based on the assumption that when embedding modifications in heavily textured regions are locally heading toward the same direction, the steganographic security might be improved. To implement the strategy, a cover image is decomposed into several subimages, in which message segments are embedded with well-known schemes using additive distortion functions. The costs of pixels are updated dynamically to take mutual embedding impacts into account. Specifically, when neighboring pixels are changed toward a positive/negative direction, the cost of the considered pixel is biased toward the same direction. Experimental results show that our proposed CMD strategy, incorporated into existing steganographic schemes, can effectively overcome the challenges posed by the modern steganalyzers with high-dimensional features.

Prediction-error expansion (PEE) is the most successful reversible data hiding (RDH) technique, and existing PEE-based RDH methods are mainly based on the modification of one- or two-dimensional prediction-error histogram (PEH). The two-dimensional PEH-based methods perform generally better than those based on one-dimensional PEH; however, their performance is still unsatisfactory since the PEH modification manner is fixed and independent of image content. In this paper, we propose a new RDH method based on PEE for multiple histograms. Unlike the previous methods, we consider in this paper a sequence of histograms and devise a new embedding mechanism based on multiple histograms modification (MHM). A complexity measurement is computed for each pixel according to its context, and the pixels with a given complexity are collected together to generate a PEH. By varying the complexity to cover the whole image, a sequence of histograms can be generated. Then, two expansion bins are selected in each generated histogram and data embedding is realized based on MHM. Here, the expansion bins are adaptively selected considering the image content such that the embedding distortion is minimized. With such selected expansion bins, the proposed MHM-based RDH method works well. Experimental results show that the proposed method outperforms the conventional PEE and its miscellaneous extensions including both one- or two-dimensional PEH-based ones.

In this paper, we present a statistical analysis of JPEG noises, including the quantization noise and the rounding noise during a JPEG compression cycle. The JPEG noises in the first compression cycle have been well studied; however, so far less attention has been paid on the statistical model of JPEG noises in higher compression cycles. Our analysis reveals that the noise distributions in higher compression cycles are different from those in the first compression cycle, and they are dependent on the quantization parameters used between two successive cycles. To demonstrate the benefits from the analysis, we apply the statistical model in JPEG quantization step estimation. We construct a sufficient statistic by exploiting the derived noise distributions, and justify that the statistic has several special properties to reveal the ground-truth quantization step. Experimental results demonstrate that the proposed estimator can uncover JPEG compression history with a satisfactory performance.

Recently, a recursive code construction (RCC) approaching the rate-distortion bound of reversible data hiding (RDH) was proposed. However, to estimate the rate-distortion bound or execute RCC, one should first estimate the optimal transition probability matrix (OTPM). By previous methods, OTPM can be effectively estimated only for some specific distortion metrics, such as square error distortion or L1-Norm. In this paper, we proposed a unified framework of estimating the OTPM for general distortion metrics, with which we can calculate the rate-distortion bound of RDH for general cases and extend RCC to improve state-of-the-art RDH schemes based on any distortion metrics.

In this paper, referred to the general framework of histogram-shifting-based reversible data hiding, some valuable related works based on two-dimensional pixel-intensity-histogram modification are first introduced. In these schemes, all pixels are classified into two categories, which are embedded with data or shifted for reversibility, respectively. From this point of view, novel embedding schemes are proposed with more applicable pixel partition and more redundant information utilized. Moreover, pixel selection is conducted such that smooth pixels are priorly embedded to further exploit the image redundancy. The experimental results show the superiority of the proposed methods over some state-of-the-art works in terms of capacity-distortion performance.

Compression of encrypted data has attracted considerable research interests nowadays due to distributed processing and cloud computing. In this work, we propose a novel lossy compression scheme for encrypted gray-scale images. The original image is first divided into non-overlapping blocks. Then, it is encrypted by a modulo-256 addition and block permutation. In compression phase, the spatial correlation and quantization are exploited to reduce the compression ratio. At the decoder side, context-adaptive interpolation with an image-dependent threshold is used to make image reconstruction precise. Experimental results show that the proposed scheme achieves better performance compared to the previous work.

A well defined cost function is crucial to steganography under the scenario of minimizing embedding distortion. In this paper, we present a new cost function for spatial image steganography. The proposed cost function is designed by using a high-pass filter to locate the less predictable parts in an image, and then using two low-pass filters to make the low cost values more clustered. Experiments show that the steganographic method with the proposed cost function makes the embedding changes more concentrated in texture regions, and thus achieves a better performance on resisting the state-of-the-art steganalysis over prior works, including HUGO, WOW, and S-UNIWARD.

In this paper, based on two-dimensional difference- histogram modification, a novel reversible data hiding (RDH) scheme is proposed by using difference-pair-mapping (DPM). First, by considering each pixel-pair and its context, a sequence consisting of pairs of difference values is computed. Then, a two-dimensional difference-histogram is generated by counting the frequency of the resulting difference-pairs. Finally, reversible data embedding is implemented according to a specifically designed DPM. Here, the DPM is an injective mapping defined on difference-pairs. It is a natural extension of expansion embedding and shifting techniques used in current histogram-based RDH methods. By the proposed approach, compared with the conventional one-dimensional difference-histogram and one-dimensional prediction-error-histogram-based RDH methods, the image redundancy can be better exploited and an improved embedding performance is achieved. Moreover, a pixel-pair-selection strategy is also adopted to priorly use the pixel-pairs located in smooth image regions to embed data. This can further enhance the embedding performance. Experimental results demonstrate that the proposed scheme outperforms some state-of-the-art RDH works.

Histogram shifting (HS) is a useful technique of reversible data hiding (RDH). With HS-based RDH, high capacity and low distortion can be achieved efficiently. In this paper, we revisit the HS technique and present a general framework to construct HS-based RDH. By the proposed framework, one can get a RDH algorithm by simply designing the so-called shifting and embedding functions. Moreover, by taking specific shifting and embedding functions, we show that several RDH algorithms reported in the literature are special cases of this general construction. In addition, two novel and efficient RDH algorithms are also introduced to further demonstrate the universality and applicability of our framework. It is expected that more efficient RDH algorithms can be devised according to the proposed framework by carefully designing the shifting and embedding functions.

In prediction-error expansion (PEE) based reversible data hiding, better exploiting image redundancy usually leads to a superior performance. However, the correlations among prediction-errors are not considered and utilized in current PEE based methods. Specifically, in PEE, the prediction-errors are modified individually in data embedding. In this paper, to better exploit these correlations, instead of utilizing prediction-errors individually, we propose to consider every two adjacent prediction-errors jointly to generate a sequence consisting of prediction-error pairs. Then, based on the sequence and the resulting 2D prediction-error histogram, a more efficient embedding strategy, namely, pairwise PEE, can be designed to achieve an improved performance. The superiority of our method is verified through extensive experiments.

State-of-the-art schemes for reversible data hiding (RDH) usually consist of two steps: first construct a host sequence with a sharp histogram via prediction errors, and then embed messages by modifying the histogram with methods, such as difference expansion and histogram shift. In this paper, we focus on the second stage, and propose a histogram modification method for RDH, which embeds the message by recursively utilizing the decompression and compression processes of an entropy coder. We prove that, for independent identically distributed (i.i.d.) gray-scale host signals, the proposed method asymptotically approaches the rate-distortion bound of RDH as long as perfect compression can be realized, i.e., the entropy coder can approach entropy. Therefore, this method establishes the equivalency between reversible data hiding and lossless data compression. Experiments show that this coding method can be used to improve the performance of previous RDH schemes and the improvements are more significant for larger images.

Least significant bit (LSB) matching is a well-known steganographic method with advantages of high payload, good visual/statistical imperceptibility and extreme ease of implementation. However, by utilizing the distortion of one-dimensional histogram or the generated additive embedding noise, some steganalyzers can perceive the existence of covert communication to some extent. Due to this, we extend the LSB matching steganography by minimizing the distortion of first order statistics (i.e., one-dimensional histogram) and adaptively embedding data into noise regions. With these extensions, our method significantly improves the stego-security. The experimental results also prove its superiority over some state-of-the-art steganographic methods against various steganalyzers.

The steganalysis of least significant bit (LSB) matching steganography has been well realized by many highly sensitive detectors so far, but few of them can analyze further to higher levels. Most of current steganalysis methods still stay in the low-level stage that can only detect the existence of secret message. In this paper, we focus on higher level steganalysis and an improved method for payload location of LSB matching is proposed. Our work is based on the combination and improvement of previous techniques including message length estimation and payload location. The proposed method first solves a regression problem to estimate the embedding rate utilizing steganalysis features. Then, the embedding payload can be located via optimal cover estimation and improved residuals calculation, in which the embedding rate achieved above is a crucial parameter. By this approach, the payload location method can be applied to practical use needless of any prior knowledge. Experimental results show that the proposed method outperforms the state-of-the-art work with a higher accuracy for payload location of LSB matching.

This paper presents a new reversible watermarking algorithm for color image. The traditional technique is to embed data into each color channel independently. Considering that the color channels correlate with each other, we propose a reversible watermarking algorithm based on prediction-error expansion that can enhance the prediction accuracy in one color channel through exploiting the gradient information from the other channels. In doing so, the magnitude of the prediction-error is decreased generally, and consequently, the distortion to the host image is diminished. Experimental results demonstrate that the proposed algorithm outperforms the traditional methods that independently embed watermark into each channel.

Discriminating computer generated graphics from photographic images is a challenging problem of digital forensics. An important approach to this issue is to explore usual image statistics. In this way, when the statistical distributions (i.e., histograms) of some types of residual images are established, previous works usually apply operations on these histograms or compute statistical quantities to extract features. However, as the histograms are fundamental resources and can present most image information, the histograms themselves can be directly used as features and we do not need further manipulations on them. Based on this consideration, we simply take several highest histogram bins of the difference images as features to carry out classification, and these simple histogram features work well in terms of both detection accuracy and computational complexity. Actually, experimental results demonstrate that, with only 112 features, the proposed method outperforms some state-of-the-art works.

Many highly sensitive detectors for least significant bit (LSB) matching steganography have been proposed so far, but few of them can locate the embedding payload. Assuming a number of stego images with payload placed in the same locations are provided, Ker presented a residual-based method to identify the payload-carrying locations for LSB matching. In this paper, we put forward two novel residuals and theoretically prove their reliability for LSB matching detection. Experimental results show that the proposed weighted l1and l2residuals significantly outperform the previous work in terms of both detection performance and computational complexity. Even very small payload can be perfectly detected and precisely located as long as adequate stego images are available.

Prediction-error expansion (PEE) develops Tian's difference expansion technique by performing reversible data embedding in the prediction-error histogram. As the prediction accuracy greatly affects the embedding performance, the PEE-based algorithms depend heavily on image's spatial redundancy. However, one drawback of these algorithms is that the modification of pixels may distort the high correlation in their local regions, and thus affect the prediction accuracy. To deal with this problem, we propose an adjustment process named "compensation" to compensate for the already modified pixels, before using them for prediction. Combining PEE and compensation together, a new reversible image watermarking algorithm is then presented. Comparisons with state-of-the-art works indicate that the compensation technique may benefit reversible watermarking in term of capacity-distortion behavior.

Prediction-error expansion (PEE) is an important technique of reversible watermarking which can embed large payloads into digital images with low distortion. In this paper, the PEE technique is further investigated and an efficient reversible watermarking scheme is proposed, by incorporating in PEE two new strategies, namely, adaptive embedding and pixel selection. Unlike conventional PEE which embeds data uniformly, we propose to adaptively embed 1 or 2 bits into expandable pixel according to the local complexity. This avoids expanding pixels with large prediction-errors, and thus, it reduces embedding impact by decreasing the maximum modification to pixel values. Meanwhile, adaptive PEE allows very large payload in a single embedding pass, and it improves the capacity limit of conventional PEE. We also propose to select pixels of smooth area for data embedding and leave rough pixels unchanged. In this way, compared with conventional PEE, a more sharply distributed prediction-error histogram is obtained and a better visual quality of watermarked image is observed. With these improvements, our method outperforms conventional PEE. Its superiority over other state-of-the-art methods is also demonstrated experimentally.

In this paper, a recently proposed reversible image watermarking algorithm based on reversible contrast mapping (RCM) is further developed. The integer transform, RCM, which is originally defined on a pair of integers, is extended to integer array of arbitrary length. Based on this generalization, the embedding capacity can be significantly increased. Meanwhile, the embedding distortion is well controlled by a suitable selection of embeddable pixel blocks. In fact, the hidden data is priorly embedded into the blocks that introduce less distortion. Furthermore, the proposed scheme does not need additional data compression, and it has low computational complexity. The experiments verify that the novel scheme outperforms the original RCM-based method and some state-of-the-art reversible watermarking algorithms, especially the ones based on integer transform.

In this paper, a content-adaptive steganographic scheme is proposed. The novel scheme can be viewed as an improvement of the conventional LSB matching. In this scheme, we take advantage of embedding redundancy in LSB matching to select modification direction (i.e., increasing or decreasing the pixel value by 1), and the dependency of neighboring pixels is taken into consideration. More specifically, if the secret message bit does not match the LSB of the corresponding cover pixel value, the choice of modification direction is not random but a specific selection, in order to hold the correlation of neighboring pixels as far as possible. The resulting stego image looks more like a natural one, and smooth to some extent. Comparing with LSB matching and other state-of-the-art steganography, higher level security of the proposed scheme is experimentally verified. In addition, the proposed approach can be also applied in LSB-based steganography to enhance the security.

This paper proposes a novel steganalyzer for detecting one of the most popular steganography, LSB matching (also known as “±1 embedding”). The histogram of difference image (the differences of adjacent pixels), which is usually a generalized Gaussian distribution centered at 0, is exploited for deriving statistical features. We have proved theoretically that the peak-value of the histogram would decrease after LSB matching embedding, while the renormalized histogram (the ratio of the histogram to the peak-value) would increase. Then we take the peak-value and the renormalized histogram as features for classification. Extensive experimental results show that the proposed steganalytic method outperforms some previous ones.

Many reversible watermarking algorithms have been proposed in the literature, and all of these solutions put emphasis on high embedding capacity with low distortion. In this paper, a novel reversible image watermarking method based on integer transform is presented. Through taking pixel block of arbitrary size as embedding unit, the method can provide a very high embedding capacity. For instance, it can embed as large as 1.85 bits per pixel in “Lena”. Besides, by pre-estimating the embedding distortion, one can suitably select embeddable blocks so that the visual quality of the watermarked image is well guaranteed. Furthermore, extensive experiments show that the novel method performs better than some state-of-the-art algorithms.

Reversible watermarking is a special watermarking technique which allows one to extract both the hidden data and the exact original signal from the watermarked content. In this paper, a recently introduced reversible image watermarking method based on prediction-error expansion is further investigated and improved. Instead of taking the pixels with small prediction-error as embedding pixels (i.e., the pixels that carry watermark bits), we propose to select these pixels in a dynamical way. In fact, we can pre-calculate the embedding distortion for each possible choice of embedding pixels, and determine the one with minimal distortion. We see that, with this choice of embedding pixels, the distortion is reduced comparing with the original method, and thus, the proposed approach has a better performance. In addition, experimental results show that the novel method outperforms some state-of-the-art algorithms.

In this letter, an efficient integer transform based reversible watermarking is proposed. We first show that Tian's difference expansion (DE) technique can be reformulated as an integer transform. Then, a generalized integer transform and a payload-dependent location map are constructed to extend the DE technique to the pixel blocks of arbitrary length. Meanwhile, the distortion can be controlled by preferentially selecting embeddable blocks that introduce less distortion. Finally, the superiority of the proposed method is experimental verified by comparing with other existing schemes.

In this paper, we present an improved method for detecting LSB matching steganography in gray-scale image. Our improvements focus on three aspects: (1) instead of using the amplitude of local extrema of the image's histogram in the previous work, we turn to considering the sum of the amplitude of each point in the histogram; (2) incorporating the calibration (downsample) technique with the current method; (3) the sum/difference image (which is defined as the sum or difference of two adjacent pixels in the original image) is taken into consideration to provide additional statistical features. Extensive experimental results show that the novel steganalyzer out-performs the previous ones.

Matrix embedding is proved an effective way to improve embedding efficiency of steganography, and usually, higher dimensional matrix will provide better embedding efficiency. However, the sender might suffer huge computational complexity when employing high dimensional matrix. In this paper, a variation of matrix embedding is proposed. Instead of finding a coset leader as the modification of the cover image (which is the most time consuming step in matrix embedding), we turn to finding a vector in the coset which has relatively small Hamming weight. Such a vector can be found at reduced computational cost. Consequently, higher dimensional matrix can be used for practically implementable matrix embedding. The parity check matrix of random linear code is used in the experiments. It has shown that the proposed scheme can enhance the practicability and efficiency of the conventional matrix embedding.

In order to enhance the steganographic security, higher embedding efficiency (average number of secret data bits embedded per one embedding change) is desired. Matrix embedding is a well-known steganographic scheme that can improve the embedding efficiency. However, the embedding cost (running time) is expensive when employing high dimensional matrix, while higher dimensional matrix usually provides better embedding efficiency. In this paper, we construct a specific matrix for matrix embedding, in which data embedding procedure can be implemented with linear computational complexity. The novel scheme is computationally efficient, and meanwhile it leads to a relatively good embedding efficiency.

Embedding efficiency, which is defined as the average number of secret data bits embedded per one embedding change, is an important attribute directly influencing the security of steganography. Higher embedding efficiency is usually expected to get more secure steganographic method. In this paper, by incorporating two previously introduced techniques: the ldquosum and difference covering setrdquo (SDCS) and the ldquowet paper coderdquo (WPC), a novel double-layered embedding method is presented. As compared with the original SDCS-based steganography, the novel method can embed more bits without introducing additional embedding distortion, therefore the embedding efficiency is improved. In summary, the proposed method provides some steganographic schemes with diverse embedding rates and good embedding efficiency.

Recently, a significant improvement of the well-known least significant bit (LSB) matching steganography has been proposed, reducing the changes to the cover image for the same amount of embedded secret data. When the embedding rate is 1, this method decreases the expected number of modification per pixel (ENMPP) from 0.5 to 0.375. In this letter, we propose the so-called generalized LSB matching (G-LSB-M) scheme, which generalizes this method and LSB matching. The lower bound of ENMPP for G-LSB-M is investigated, and a construction of G-LSB-M is presented by using the sum and difference covering set of finite cyclic group. Compared with the previous works, we show that the suitable G-LSB-M can further reduce the ENMPP and lead to more secure steganographic schemes. Experimental results illustrate clearly the better resistance to steganalysis of G-LSB-M.

In this paper, based on a careful investigation on the calibration (downsample) technique, we improve two detectors for detecting LSB matching: calibrated HCF COM and calibrated adjacency HCF COM. Instead of using the COM (center of mass) of the HCF (histogram characteristic function), we consider the ratio of the histogram's DFT coefficients of the image to the corresponding coefficients of the down-sampled image. Moreover, we propose to down-sample only for non-oscillating pixels. With a same level of computational complexity, the new detectors thus obtained are better than the old ones, especially for uncompressed images.

As an important attribute directly influencing the steganographic scheme, the embedding efficiency is defined as the average number of random data bits per one embedding change. In this paper, we propose a novel approach to improve the embedding efficiency of LSB matching based on the sum and difference covering set (SDCS) of finite cyclic group. We show that the suitable choice of SDCS will lead to a new steganographic scheme which is more efficient than LSB matching. Then we illustrate that the new scheme keeps the statistical imperceptibility of LSB matching. The detailed constructions of SDCS are given and some related problems are also discussed.