Embedding Distortion Research Articles

A face cover perspective to \(\ell_{1}\) embeddings of planar graphs

It was conjectured by Gupta et al. [Combinatorica04] that every planar graph can be embedded into \(\ell_{1}\) with constant distortion. However, given an \(n\) -vertex weighted planar graph, the best upper bound on the distortion is only \(O(\sqrt{\log n})\) , by Rao [SoCG99]. In this paper we study the case where there is a set \(K\) of terminals, and the goal is to embed only the terminals into \(\ell_{1}\) with low distortion. In a seminal paper, Okamura and Seymour [J.Comb.Theory81] showed that if all the terminals lie on a single face, they can be embedded isometrically into \(\ell_{1}\) . The more general case, where the set of terminals can be covered by \(\gamma\) faces, was studied by Lee and Sidiropoulos [STOC09] and Chekuri et al. [J.Comb.Theory13]. The state of the art is an upper bound of \(O(\log\gamma)\) by Krauthgamer, Lee and Rika [SODA19]. Our contribution is a further improvement on the upper bound to \(O(\sqrt{\log\gamma})\) . Since every planar graph has at most \(O(n)\) faces, any further improvement on this result, will be a major breakthrough, directly improving upon Rao's long standing upper bound. Moreover, it is well known that the flow-cut gap equals to the distortion of the best embedding into \(\ell_{1}\) . Therefore, our result provides a polynomial time \(O(\sqrt{\log\gamma})\) -approximation to the sparsest cut problem on planar graphs, for the case where all the demand pairs can be covered by \(\gamma\) faces.

Incremental minimum distortion embedding for online structural damage classification.

The damage detection problem in structures diminishes the maintenance cost and extends the life of the structures. Online structural damage classification is a relevant topic in structural health monitoring since monitoring the structure using sensors can help decision-makers can rely on empirical evidence for making informed choices regarding the maintenance, repair, or replacement of structural components. Sensors generate high-dimensional data. To address this challenge, employing dimensionality reduction methods becomes essential. These methods help obtain a low-dimensional representation of the data. Traditional dimensionality reduction methods are trained on a fixed data set, and incorporating new data may require retraining the entire model. This study employed the Minimum Distortion Embedding (MDE) method incrementally, ensuring the maintenance of a consistent embedding as new data becomes available. This incremental embedding took advantage of an anchor constraint to pin the existing embedding in place, then embed the new points. An online structural classification methodology was developed using the incremental MDE and a stream based hoeffding tree classifier. Stream data processing differs from batch processing, as it involves the real-time consumption of each incoming data. The developed methodology was tested with data obtained by accelerometers in a laboratory scaled jacket-type wind turbine foundation. The structural damage classification problems had 5 different classes including the undamaged class and 4 different damage classes. The damage corresponded to a 5mm crack in four different structural elements of the wind turbine foundation. The results indicate the good behavior of the damage classification methodology supported by the high values of the classification metrics obtained.

Robust reversible watermarking of JPEG images

Robust reversible watermarking (RRW) is a potential technology for copyright protection and integrity authentication due to its ability in both robustness and reversibility. Currently, there is no detailed report on RRW of JPEG images. In this paper, we propose an RRW algorithm of JPEG images by selecting quantized discrete cosine transform coefficients to construct robust features for watermarking. In the proposed algorithm, a watermark sequence can be embedded into a JPEG image by shifting the histogram of its constructed robust features. For less embedding distortion, smaller file size, and higher structural similarity, an evaluation method has been designed to select those appropriate frequency bands for watermarking. On the receiver side, the watermark can be accurately extracted by reconstructing the robust features, and the original JPEG image can be restored losslessly by performing the inverse operation of the histogram shifting. Experimental results show that the watermark is robust to common image processing operations (e.g., JPEG recompression, JPEG2000 compression, WebP compression, and additive white Gaussian noise), and can effectively resist those attacks from the lossy channels in real life, such as the most popular apps Instagram and WeChat.

Global pixel-value-ordering framework with dynamic sequence partition for reversible data hiding

Recently, pixel-value-ordering (PVO) based reversible data hiding (RDH) methods have become hotspots in spatial domain RDH research. In PVO-based methods, the pixel value correlation within a local region is exploited for data embedding. To embed secret data, the cover images are partitioned into non-overlapped rectangle blocks to be sorted locally, and a lower embedding distortion is thus obtained. However, their embedding capacities are often limited by the fixed local blocks from which pixels are sorted. To maintain the advantages and overcome disadvantages of the PVO-based methods, a new global pixel-value-ordering (GPVO) framework is proposed in this paper. By applying our GPVO framework, a PVO-based method can utilize pixels from any position in the cover image rather than from local pixel blocks. Then, through the dynamic sequence partition realized by the GPVO framework for the first time, the embedding capacity of PVO-based methods can be greatly improved while reducing embedding distortion further reduced. Finally, we propose a two-stage pairwise embedding scheme to be applied to the sequences, aiming to achieve an advanced embedding performance. Experimental results illustrate that the proposed GPVO works better than other related state-of-the-art RDH methods.

Homomorphic encryption domain asymmetric fingerprinting scheme for 3D models of oblique photography

AbstractExisting copyright protection schemes for 3D models of oblique photography predominantly utilize digital watermarking technology, most of which suffer from shortcomings such as the potential false accusation of legitimate users and the inability to effectively trace unauthorized distributors. In response to these challenges, this article proposes a homomorphic encryption domain asymmetric fingerprinting scheme for 3D models of oblique photography. Initially, the fingerprints to be embedded are collaboratively generated by the transacting parties, with the publisher remaining unaware of the user's actual fingerprint. This approach ensures the effective implementation of the asymmetric nature of the fingerprinting scheme. Subsequently, potential geometric and non‐geometric attacks are considered prior to fingerprint embedding. Robustness is enhanced for the proposed solution through relative coordinate transformations and normalization procedures. Ultimately, the embedding and extraction of fingerprints are achieved through the application of an effective bit parity check method, in conjunction with the vertex‐paradigm projection length mapping mechanism and the Paillier homomorphic encryption system, minimizing embedding distortion while ensuring data security. Experimental results demonstrate that the proposed solution exhibits satisfying robustness against common manipulations, such as cropping, simplification, and geometric attacks. Additionally, the scheme effectively safeguards legitimate users from false accusations and accurately traces maliciously authorized users.

HAG-NET: Hiding Data and Adversarial Attacking with Generative Adversarial Network.

Recent studies on watermarking techniques based on image carriers have demonstrated new approaches that combine adversarial perturbations against steganalysis with embedding distortions. However, while these methods successfully counter convolutional neural network-based steganalysis, they do not adequately protect the data of the carrier itself. Recognizing the high sensitivity of Deep Neural Networks (DNNs) to small perturbations, we propose HAG-NET, a method based on image carriers, which is jointly trained by the encoder, decoder, and attacker. In this paper, the encoder generates Adversarial Steganographic Examples (ASEs) that are adversarial to the target classification network, thereby providing protection for the carrier data. Additionally, the decoder can recover secret data from ASEs. The experimental results demonstrate that ASEs produced by HAG-NET achieve an average success rate of over 99% on both the MNIST and CIFAR-10 datasets. ASEs generated with the attacker exhibit greater robustness in terms of attack ability, with an average increase of about 3.32%. Furthermore, our method, when compared with other generative stego examples under similar perturbation strength, contains significantly more information according to image information entropy measurements.

GAN-based adaptive cost learning for enhanced image steganography security

A well-defined cost function is a key issue for image steganography to minimize the embedding distortion. In recent years, deep learning has been introduced into image steganography to automatically learn embedding costs and improve steganographic security. For most existing generative adversarial network (GAN) based cost learning works, the generator usually adopts an encoder–decoder architecture. However, due to repeated encoding and decoding operations, this architecture is prone to information loss, making the generator difficult to well capture fine-grained image features. In this work, we propose a novel GAN-based image steganography work that improves the cost function by learning better embedding probability maps. Specifically, we design an attention mechanism to be integrated into the U-Net architecture, which enables the generator to concentrate on texture-rich regions of input images. Moreover, an extra input stream, namely the enhanced image, is introduced into the generator, improving the generator’s ability to learn structural features from input images. Different skip connections are used for different input streams to facilitate information flow between different layers. Extensive experimental results demonstrate that the proposed approach effectively learns the embedding probability maps and achieves superior security against various steganalysis attacks.

Leveraging coverless image steganography to hide secret information by generating anime characters using GAN

There has been a growing need for secure communication in recent years, particularly in the digital realm. Researchers have developed various text-hiding methods to address this need, but these methods often suffer from limitations such as low embedding capacity or high embedding distortion. However, current methods for information hiding require a large image database or have a low capacity for hiding information, which makes them impractical. To address these issues, we propose a coverless information-hiding method that generates anime characters through generative adversarial networks (GANs). This method converts secret information into an attribute label set for anime characters and uses the label set to generate anime characters directly. The quality of the generated anime characters was improved by the super-resolution GAN (SRGAN) model. The resulting images were used to communicate secret information on the digital channel. Numerous experiments were conducted to evaluate the performance of the proposed framework, including hiding capacity, image clarity, robustness and security. Results showed that the proposed framework outperforms existing text-hiding methods in terms of hiding capacity and robustness while maintaining image clarity and computation time. In conclusion, our proposed framework provides a secure and efficient solution for text encryption and decryption in feasible computation time using anime characters generated by a GAN. The framework has a high embedding capacity and low embedding distortion, making it a promising solution for secure communication in the digital world.

A reversible data hiding method based on bitmap prediction for AMBTC compressed hyperspectral images

In the transmission of hyperspectral images that have been compressed using absolute moment block truncation coding (AMBTC), confidentiality and security of crucial information is often a concern. Although many data hiding (DH) methods based on AMBTC work well in guaranteeing a large amount of secret information can be embedded, the requirements of actual user scenarios, such as reversibility and imperceptibility, are degraded sometimes. To address these challenges, we propose an embedding pattern that utilizes bitmap prediction to embed secret information within the bitmaps while preserving the standard format of AMBTC codes and enabling recovery of the cover image without loss. Our proposed method, therefore, belongs to the category of reversible data hiding (RDH) techniques. Since the embedding distortion (ED) reduction is an essential object, an adaptive embedding order based on the features of AMBTC codes is conducted. Furthermore, we propose a dynamical embedding scheme to reduce ED when we are striving to achieve a larger embedding capacity (EC).

Adaptive HEVC Video Steganography With High Performance Based on Attention-Net and PU Partition Modes

With the increasing popularity of digital video, video steganography has become a hot research topic in the field of covert communication and privacy protection. The existing prediction unit (PU) based video steganography often tends to result in large bit rate increase, which is also easily noticeable to the steganography analyst. To solve this problem, an adaptive steganography for HEVC video based on attention-net and PU partition modes is proposed. First, the distortion of modified PUs is analyzed from the perspective of rate distortion optimization at the group of pictures (GOP) level, and we find that modifying PU will lead to distortion accumulation and abnormal bitrate increase. Therefore, an adaptive distortion function based on the improved rate distortion cost is designed, and the embedding distortion is minimized by using Syndrome-Trellis Code (STC) steganography coding. Meanwhile, a super-resolution convolutional neural network with non-local sparse attention-net filter is proposed to replace the in-loop filter in HEVC to reconstruct the reference frame, thereby reducing the bitrate cost and improving the visual quality of stego-video. Experimental results show that the proposed algorithm can achieve superior perceptual quality and bitrate performance comparing with the sate-of-the-art works.

An efficient distortion cost function design for image steganography in spatial domain using quaternion representation

It is well known that an effective steganographic distortion cost function is essential for spatial image steganography in the framework of minimal distortion embedding. To define the embedding cost by exploiting the texture complexity characterized by the high-pass filtered image residuals has been a popular approach. In this paper, by incorporating the quaternion representation of cover images, the image complexity is evaluated in terms of quaternion magnitude and phase, and a quaternion magnitude-based distortion (QMD) and a quaternion phase-based distortion (QPD) can be defined accordingly. With Hadamard product of QMD and QPD, a novel distortion cost function, namely QMP (Quaternion Magnitude-Phase), is obtained, aiming to efficiently allocate embedding modifications in complex regions of cover images with rich texture contents to improve the statistical undetectability (i.e., security). In addition, the generalized QMP (GQMP) in exponential form is further developed to boost the security performance. Experimental results demonstrate that both the proposed QMP and its generalized variant GQMP can outperform the state-of-the-art schemes, e.g., S-UNIWARD, HiLL, and MiPOD, in terms of empirical security performance against steganalysis.

Semi-Fragile Reversible Watermarking for 3D Models Using Spherical Crown Volume Division

Aiming at the large distortion and low tampering localization accuracy of the existing semi-fragile reversible watermarking for 3D mesh models, a novel semi-fragile reversible watermarking for 3D models using spherical crown volume division is proposed. The crown volume of a sphere is divided to reduce the embedding distortion. The possible geometric and topological transformations are separately considered in the watermark generation, and the vertices of the one-ring neighbourhood are grouped to improve the tampering localization accuracy. Experimental results show that the proposed scheme can achieve better localization accuracy and lower embedding distortion than some state-of-the-art algorithms. It has good potential for the applications in integrity authentication for 3D mesh models.

JPEG Steganography With Content Similarity Evaluation.

Content similarity is a representative property of natural images, for example, similar regions, which is utilized by modern steganalysis. Existing JPEG steganographic methods mainly focus on the complexity of content but ignore content similarity. This article investigates content similarity to improve the undetectability of JPEG steganography. Specifically, the content similarity of DCT blocks and the 64 parallel channels is used to design the distortion function. Given a JPEG image, initial embedding costs are assigned for quantized DCT coefficients using an appropriate algorithm among the existing distortion functions. Then, the similarities of blocks and channels are used to update the initial embedding costs, respectively. After combination, the final distortion function can be obtained. Using syndrome trellis coding (STC), which achieves minimal embedding distortion with respect to a given distortion function, secret data are embedded into the cover image with a final distortion function. Experimental results show that our scheme achieves better undetectability than current state-of-the-art JPEG steganographic methods.

Deep fidelity in DNN watermarking: A study of backdoor watermarking for classification models

Backdoor watermarking is a promising paradigm to protect the copyright of deep neural network (DNN) models. In the existing works on this subject, researchers have intensively focused on watermarking robustness, while the concept of fidelity, which is concerned with the preservation of the model’s original functionality, has received less attention. In this paper, focusing on deep image classification models, we show that the existing shared notion of the sole measurement of learning accuracy is inadequate to characterize backdoor fidelity. Meanwhile, we show that the analogous concept of embedding distortion in multimedia watermarking, interpreted as the total weight loss (TWL) in DNN backdoor watermarking, is also problematic for fidelity measurement. To address this challenge, we propose the concept of deep fidelity, which states that the backdoor watermarked DNN model should preserve both the feature representation and decision boundary of the unwatermarked host model. To achieve deep fidelity, we propose two loss functions termed penultimate feature loss (PFL) and softmax probability-distribution loss (SPL) to preserve feature representation, while the decision boundary is preserved by the proposed fix last layer (FixLL) treatment, inspired by the recent discovery that deep learning with a fixed classifier causes no loss of learning accuracy. With the above designs, both embedding from scratch and fine-tuning strategies are implemented to evaluate the deep fidelity of backdoor embedding, whose advantages over the existing methods are verified via experiments using ResNet18 for MNIST and CIFAR-10 classifications, and wide residual network (i.e., WRN28_10) for CIFAR-100 task. PyTorch codes are available at https://github.com/ghua-ac/dnn_watermark.

An Adaptive IPM-Based HEVC Video Steganography via Minimizing Non-Additive Distortion

Recently, almost all the proposed adaptive video steganographic schemes are based on minimizing an additive embedding distortion. However, they ignore the hard fact that the additive embedding distortion is not quite suitable for video steganography because of the interplay of cover elements in video steganography. In this paper, an adaptive intra prediction mode based (IPM-based) video steganography is proposed by minimizing the non-additive distortion in HEVC. To reduce the complexity of minimizing the non-additive distortion, a multi-layered embedding structure combined with a proposed embed-ding distortion updating strategy is adopted to approximate the non-additive distortion in an additive form. Firstly, all IPMs are decomposed into multiple layers based on the distortion drift graph to offer multi-layered embedding. Each IPM in the same layer is considered to be independent, and syndrome-trellis code (STC) can be applied to embed the message segment into each layer with an additive distortion function sequentially. Then, a distortion function composed of self-distortion and drift-distortion is proposed to initialize the distortion of modifying each IPM. Finally, after embedding the first message segment into the IPMs in the first layer with the initialized distortions, an embedding distortion updating strategy is applied to update the distortions of the IPMs in the remaining layers dynamically. Ex-perimental results demonstrate that the proposed adaptive IPM-based video steganography can achieve much better perceptual quality and security performance than the state-of-the-art.

Reversible data hiding for JPEG images based on block difference model and Laplacian distribution estimation

Reversible data hiding (RDH) for JPEG images has attracted extensive attentions in recent years. As far, a number of related schemes have been proposed, which enhance the embedding performance by improving the strategies such as frequency selection and block sorting to choose appropriate embedding coefficients with the histogram shifting mechanism. Nevertheless, the existing methods do not fully consider the characteristics of DCT coefficients and lack accurate measurement on the embedding distortion. To address the above problems, we propose an improved general framework of RDH for JPEG images based on the Laplacian distribution model. The block difference model is first established for the alternating current (AC) coefficients fitting. Subsequently, the scale parameter is calculated to estimate the embedding efficiency of each AC coefficient, and the coefficients with high embedding efficiency are preferentially selected for embedding. Furthermore, the proposed framework can be combined with other JPEG RDH methods based on quantized DCT coefficient modification. Experimental results demonstrate that better performance in terms of both visual quality and file size preservation can be achieved with the proposed scheme compared with the state-of-the-art RDH schemes for JPEG images.

A Reversible Watermarking for 2D Engineering Graphics Based on Difference Expansion With Adaptive Interval Partitioning

To resolve the distortion resulting from the mismatch between the interval partition and the watermark distribution in the reversible watermarking based on difference expansion, an investigation is made to difference expansion with adaptive interval partitioning. It is found that the conventional floating number-based methods with uniform interval partitioning are not fully considering different watermark distributions, and the embedding distortion can be optimized. Thus, a reversible watermarking based on difference expansion with adaptive interval partitioning is put forward for 2D engineering graphics. Each interval is adaptively partitioned into 2^s sub-intervals, and the watermark is embedded via transforming the positions of the vertices to its corresponding sub-intervals. The watermark extraction is accomplished by acquiring the indices of the sub-intervals of the watermarked vertices, and the graphics recovery is achieved by moving the watermarked vertices to the reverse direction. Moreover, a new polar coordinate system is built to be invariant to overall geometric transformation and vertices rearrangement. Experimental results and analysis indicate that it maintains good authentication ability and semi-fragility. Furthermore, its imperceptibility is significantly improved compared with the existing watermarking schemes under the same experimental conditions.

A Highly Robust Reversible Watermarking Scheme Using Embedding Optimization and Rounded Error Compensation

The robust reversible watermarking (RRW) requires high robustness and capacity on the condition of reversibility and imperceptibility, which still remains a big challenge nowadays. In this paper, we propose a two-stage RRW scheme that improves robustness and capacity through embedding optimization and rounded error compensation. The first stage inserts a robust watermark into the selected Pseudo-Zernike moments (PZMs) by using an adaptive normalization method and an optimized embedding strategy. Specifically, the adaptive normalization method achieves both an invariance to pixel amplitude variation and a balance between robustness and imperceptibility, and the optimized embedding strategy reduces embedding distortions remarkably. The watermarked PZMs are inversely transformed to generate the robustly watermarked image, in which rounded errors caused in the inverse transformation is compensated elaborately and thus a larger capacity can be obtained at the same embedding distortion. The second stage embeds a reversible watermark consisting of errors between the robust watermark embedded image and the original one, aiming at achieving the reversibility in case of no attacks. Extensive experimental simulations show that the proposed scheme provides strong robustness against common signal processing, including AWGN, salt-and-pepper noise, JPEG, JPEG2000, median filtering, mean filtering, geometrical transformations involving rotation and scaling, and a compressive sensing attack exemplified by two-dimensional compressive sensing, which outperforms the state-of-the-art schemes. Our code is available at <uri xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">https://github.com/yichao-tang/PZMs-RRW</uri> .

SF-SGL: Solver-Free Spectral Graph Learning From Linear Measurements

This work introduces a highly-scalable spectral graph densification framework (SGL) for learning resistor networks with linear measurements, such as node voltages and currents. We show that the proposed graph learning approach is equivalent to solving the classical graphical Lasso problems with Laplacian-like precision matrices. We prove that given $O(\log N)$ pairs of voltage and current measurements, it is possible to recover sparse $N$-node resistor networks that can well preserve the effective resistance distances on the original graph. In addition, the learned graphs also preserve the structural (spectral) properties of the original graph, which can potentially be leveraged in many circuit design and optimization tasks. To achieve more scalable performance, we also introduce a solver-free method (SF-SGL) that exploits multilevel spectral approximation of the graphs and allows for a scalable and flexible decomposition of the entire graph spectrum (to be learned) into multiple different eigenvalue clusters (frequency bands). Such a solver-free approach allows us to more efficiently identify the most spectrally-critical edges for reducing various ranges of spectral embedding distortions. Through extensive experiments for a variety of real-world test cases, we show that the proposed approach is highly scalable for learning sparse resistor networks without sacrificing solution quality. We also introduce a data-driven EDA algorithm for vectorless power/thermal integrity verifications to allow estimating worst-case voltage/temperature (gradient) distributions across the entire chip by leveraging a few voltage/temperature measurements.

Demand-oblivious routing in complex networks under uncertainty

Real-world communication networks are complex networks, but designing load-balancing routing strategies in complex networks is not an easy task, especially when the traffic demand is under uncertainty. To hedge against such uncertainty, we propose a demand-oblivious routing strategy in complex networks (DOR-CN). Unlike traditional optimization-model-based methods, DOR-CN decouples the routing calculation with traffic demand by a randomized routing algorithm following the oblivious routing paradigm, and is able to achieve load-balancing without knowing the accurate traffic demand. In order to avoid the embedding distortion of complex networks, DOR-CN transfers the metric space of classical oblivious routing into the hyperbolic space. Theoretical derivation can prove that for arbitrary traffic demand matrix, the network congestion of DOR-CN routing strategy is under guaranteed. Experimental results demonstrate that DOR-CN can not only reduce network congestion, but also achieve better load-balancing performance and lower risk of route failures.