Hongxia Wang

CV
h-index8
24papers
365citations
Novelty49%
AI Score52

24 Papers

CVAug 11, 2022Code
Adaptive and Implicit Regularization for Matrix Completion

Zhemin Li, Tao Sun, Hongxia Wang et al.

The explicit low-rank regularization, e.g., nuclear norm regularization, has been widely used in imaging sciences. However, it has been found that implicit regularization outperforms explicit ones in various image processing tasks. Another issue is that the fixed explicit regularization limits the applicability to broad images since different images favor different features captured by different explicit regularizations. As such, this paper proposes a new adaptive and implicit low-rank regularization that captures the low-rank prior dynamically from the training data. The core of our new adaptive and implicit low-rank regularization is parameterizing the Laplacian matrix in the Dirichlet energy-based regularization, which we call the regularization AIR. Theoretically, we show that the adaptive regularization of \ReTwo{AIR} enhances the implicit regularization and vanishes at the end of training. We validate AIR's effectiveness on various benchmark tasks, indicating that the AIR is particularly favorable for the scenarios when the missing entries are non-uniform. The code can be found at https://github.com/lizhemin15/AIR-Net.

MMAug 28, 2023Code
UMMAFormer: A Universal Multimodal-adaptive Transformer Framework for Temporal Forgery Localization

Rui Zhang, Hongxia Wang, Mingshan Du et al.

The emergence of artificial intelligence-generated content (AIGC) has raised concerns about the authenticity of multimedia content in various fields. However, existing research for forgery content detection has focused mainly on binary classification tasks of complete videos, which has limited applicability in industrial settings. To address this gap, we propose UMMAFormer, a novel universal transformer framework for temporal forgery localization (TFL) that predicts forgery segments with multimodal adaptation. Our approach introduces a Temporal Feature Abnormal Attention (TFAA) module based on temporal feature reconstruction to enhance the detection of temporal differences. We also design a Parallel Cross-Attention Feature Pyramid Network (PCA-FPN) to optimize the Feature Pyramid Network (FPN) for subtle feature enhancement. To evaluate the proposed method, we contribute a novel Temporal Video Inpainting Localization (TVIL) dataset specifically tailored for video inpainting scenes. Our experiments show that our approach achieves state-of-the-art performance on benchmark datasets, including Lav-DF, TVIL, and Psynd, significantly outperforming previous methods. The code and data are available at https://github.com/ymhzyj/UMMAFormer/.

LGMar 27, 2023
Regularize implicit neural representation by itself

Zhemin Li, Hongxia Wang, Deyu Meng

This paper proposes a regularizer called Implicit Neural Representation Regularizer (INRR) to improve the generalization ability of the Implicit Neural Representation (INR). The INR is a fully connected network that can represent signals with details not restricted by grid resolution. However, its generalization ability could be improved, especially with non-uniformly sampled data. The proposed INRR is based on learned Dirichlet Energy (DE) that measures similarities between rows/columns of the matrix. The smoothness of the Laplacian matrix is further integrated by parameterizing DE with a tiny INR. INRR improves the generalization of INR in signal representation by perfectly integrating the signal's self-similarity with the smoothness of the Laplacian matrix. Through well-designed numerical experiments, the paper also reveals a series of properties derived from INRR, including momentum methods like convergence trajectory and multi-scale similarity. Moreover, the proposed method could improve the performance of other signal representation methods.

73.8CVMar 11Code
Guiding Diffusion Models with Semantically Degraded Conditions

Shilong Han, Yuming Zhang, Hongxia Wang

Classifier-Free Guidance (CFG) is a cornerstone of modern text-to-image models, yet its reliance on a semantically vacuous null prompt ($\varnothing$) generates a guidance signal prone to geometric entanglement. This is a key factor limiting its precision, leading to well-documented failures in complex compositional tasks. We propose Condition-Degradation Guidance (CDG), a novel paradigm that replaces the null prompt with a strategically degraded condition, $\boldsymbol{c}_{\text{deg}}$. This reframes guidance from a coarse "good vs. null" contrast to a more refined "good vs. almost good" discrimination, thereby compelling the model to capture fine-grained semantic distinctions. We find that tokens in transformer text encoders split into two functional roles: content tokens encoding object semantics, and context-aggregating tokens capturing global context. By selectively degrading only the former, CDG constructs $\boldsymbol{c}_{\text{deg}}$ without external models or training. Validated across diverse architectures including Stable Diffusion 3, FLUX, and Qwen-Image, CDG markedly improves compositional accuracy and text-image alignment. As a lightweight, plug-and-play module, it achieves this with negligible computational overhead. Our work challenges the reliance on static, information-sparse negative samples and establishes a new principle for diffusion guidance: the construction of adaptive, semantically-aware negative samples is critical to achieving precise semantic control. Code is available at https://github.com/Ming-321/Classifier-Degradation-Guidance.

IVJul 16, 2023
Untrained neural network embedded Fourier phase retrieval from few measurements

Liyuan Ma, Hongxia Wang, Ningyi Leng et al.

Fourier phase retrieval (FPR) is a challenging task widely used in various applications. It involves recovering an unknown signal from its Fourier phaseless measurements. FPR with few measurements is important for reducing time and hardware costs, but it suffers from serious ill-posedness. Recently, untrained neural networks have offered new approaches by introducing learned priors to alleviate the ill-posedness without requiring any external data. However, they may not be ideal for reconstructing fine details in images and can be computationally expensive. This paper proposes an untrained neural network (NN) embedded algorithm based on the alternating direction method of multipliers (ADMM) framework to solve FPR with few measurements. Specifically, we use a generative network to represent the image to be recovered, which confines the image to the space defined by the network structure. To improve the ability to represent high-frequency information, total variation (TV) regularization is imposed to facilitate the recovery of local structures in the image. Furthermore, to reduce the computational cost mainly caused by the parameter updates of the untrained NN, we develop an accelerated algorithm that adaptively trades off between explicit and implicit regularization. Experimental results indicate that the proposed algorithm outperforms existing untrained NN-based algorithms with fewer computational resources and even performs competitively against trained NN-based algorithms.

CVAug 24, 2024
TVG: A Training-free Transition Video Generation Method with Diffusion Models

Rui Zhang, Yaosen Chen, Yuegen Liu et al.

Transition videos play a crucial role in media production, enhancing the flow and coherence of visual narratives. Traditional methods like morphing often lack artistic appeal and require specialized skills, limiting their effectiveness. Recent advances in diffusion model-based video generation offer new possibilities for creating transitions but face challenges such as poor inter-frame relationship modeling and abrupt content changes. We propose a novel training-free Transition Video Generation (TVG) approach using video-level diffusion models that addresses these limitations without additional training. Our method leverages Gaussian Process Regression ($\mathcal{GPR}$) to model latent representations, ensuring smooth and dynamic transitions between frames. Additionally, we introduce interpolation-based conditional controls and a Frequency-aware Bidirectional Fusion (FBiF) architecture to enhance temporal control and transition reliability. Evaluations of benchmark datasets and custom image pairs demonstrate the effectiveness of our approach in generating high-quality smooth transition videos. The code are provided in https://sobeymil.github.io/tvg.com.

CVDec 31, 2025
OCP-LS: An Efficient Algorithm for Visual Localization

Jindi Zhong, Hongxia Wang, Huanshui Zhang

This paper proposes a novel second-order optimization algorithm. It aims to address large-scale optimization problems in deep learning because it incorporates the OCP method and appropriately approximating the diagonal elements of the Hessian matrix. Extensive experiments on multiple standard visual localization benchmarks demonstrate the significant superiority of the proposed method. Compared with conventional optimiza tion algorithms, our framework achieves competitive localization accuracy while exhibiting faster convergence, enhanced training stability, and improved robustness to noise interference.

80.5CRApr 2
Diffusion-Guided Adversarial Perturbation Injection for Generalizable Defense Against Facial Manipulations

Yue Li, Linying Xue, Kaiqing Lin et al.

Recent advances in GAN and diffusion models have significantly improved the realism and controllability of facial deepfake manipulation, raising serious concerns regarding privacy, security, and identity misuse. Proactive defenses attempt to counter this threat by injecting adversarial perturbations into images before manipulation takes place. However, existing approaches remain limited in effectiveness due to suboptimal perturbation injection strategies and are typically designed under white-box assumptions, targeting only simple GAN-based attribute editing. These constraints hinder their applicability in practical real-world scenarios. In this paper, we propose AEGIS, the first diffusion-guided paradigm in which the AdvErsarial facial images are Generated for Identity Shielding. We observe that the limited defense capability of existing approaches stems from the peak-clipping constraint, where perturbations are forcibly truncated due to a fixed $L_\infty$-bounded. To overcome this limitation, instead of directly modifying pixels, AEGIS injects adversarial perturbations into the latent space along the DDIM denoising trajectory, thereby decoupling the perturbation magnitude from pixel-level constraints and allowing perturbations to adaptively amplify where most effective. The extensible design of AEGIS allows the defense to be expanded from purely white-box use to also support black-box scenarios through a gradient-estimation strategy. Extensive experiments across GAN and diffusion-based deepfake generators show that AEGIS consistently delivers strong defense effectiveness while maintaining high perceptual quality. In white-box settings, it achieves robust manipulation disruption, whereas in black-box settings, it demonstrates strong cross-model transferability.

CVNov 28, 2025Code
DEAL-300K: Diffusion-based Editing Area Localization with a 300K-Scale Dataset and Frequency-Prompted Baseline

Rui Zhang, Hongxia Wang, Hangqing Liu et al.

Diffusion-based image editing has made semantic level image manipulation easy for general users, but it also enables realistic local forgeries that are hard to localize. Existing benchmarks mainly focus on the binary detection of generated images or the localization of manually edited regions and do not reflect the properties of diffusion-based edits, which often blend smoothly into the original content. We present Diffusion-Based Image Editing Area Localization Dataset (DEAL-300K), a large scale dataset for diffusion-based image manipulation localization (DIML) with more than 300,000 annotated images. We build DEAL-300K by using a multi-modal large language model to generate editing instructions, a mask-free diffusion editor to produce manipulated images, and an active-learning change detection pipeline to obtain pixel-level annotations. On top of this dataset, we propose a localization framework that uses a frozen Visual Foundation Model (VFM) together with Multi Frequency Prompt Tuning (MFPT) to capture both semantic and frequency-domain cues of edited regions. Trained on DEAL-300K, our method reaches a pixel-level F1 score of 82.56% on our test split and 80.97% on the external CoCoGlide benchmark, providing strong baselines and a practical foundation for future DIML research.The dataset can be accessed via https://github.com/ymhzyj/DEAL-300K.

LGOct 12, 2021Code
AIR-Net: Adaptive and Implicit Regularization Neural Network for Matrix Completion

Zhemin Li, Tao Sun, Hongxia Wang et al.

The explicit low-rank regularization, e.g., nuclear norm regularization, has been widely used in imaging sciences. However, it has been found that implicit regularization outperforms explicit ones in various image processing tasks. Another issue is that the fixed explicit regularization limits the applicability to broad images since different images favor different features captured by different explicit regularizations. As such, this paper proposes a new adaptive and implicit low-rank regularization that captures the low-rank prior dynamically from the training data. The core of our new adaptive and implicit low-rank regularization is parameterizing the Laplacian matrix in the Dirichlet energy-based regularization, which we call the regularization \textit{AIR}. Theoretically, we show that the adaptive regularization of AIR enhances the implicit regularization and vanishes at the end of training. We validate AIR's effectiveness on various benchmark tasks, indicating that the AIR is particularly favorable for the scenarios when the missing entries are non-uniform. The code can be found at https://github.com/lizhemin15/AIR-Net

CVJul 18, 2024
HPPP: Halpern-type Preconditioned Proximal Point Algorithms and Applications to Image Restoration

Shuchang Zhang, Hui Zhang, Hongxia Wang

Recently, the degenerate preconditioned proximal point (PPP) method provides a unified and flexible framework for designing and analyzing operator-splitting algorithms such as Douglas-Rachford (DR). However, the degenerate PPP method exhibits weak convergence in the infinite-dimensional Hilbert space and lacks accelerated variants. To address these issues, we propose a Halpern-type PPP (HPPP) algorithm, which leverages the strong convergence and acceleration properties of Halpern's iteration method. Moreover, we propose a novel algorithm for image restoration by combining HPPP with denoiser priors such as Plug-and-Play (PnP) prior, which can be viewed as an accelerated PnP method. Finally, numerical experiments including several toy examples and image restoration validate the effectiveness of our proposed algorithms.

CVAug 22, 2024
A Unified Plug-and-Play Algorithm with Projected Landweber Operator for Split Convex Feasibility Problems

Shuchang Zhang, Hongxia Wang

In recent years Plug-and-Play (PnP) methods have achieved state-of-the-art performance in inverse imaging problems by replacing proximal operators with denoisers. Based on the proximal gradient method, some theoretical results of PnP have appeared, where appropriate step size is crucial for convergence analysis. However, in practical applications, applying PnP methods with theoretically guaranteed step sizes is difficult, and these algorithms are limited to Gaussian noise. In this paper,from a perspective of split convex feasibility problems (SCFP), an adaptive PnP algorithm with Projected Landweber Operator (PnP-PLO) is proposed to address these issues. Numerical experiments on image deblurring, super-resolution, and compressed sensing MRI experiments illustrate that PnP-PLO with theoretical guarantees outperforms state-of-the-art methods such as RED and RED-PRO.

CRApr 21, 2025
Protecting Your Voice: Temporal-aware Robust Watermarking

Yue Li, Weizhi Liu, Dongdong Lin et al.

The rapid advancement of generative models has led to the synthesis of real-fake ambiguous voices. To erase the ambiguity, embedding watermarks into the frequency-domain features of synthesized voices has become a common routine. However, the robustness achieved by choosing the frequency domain often comes at the expense of fine-grained voice features, leading to a loss of fidelity. Maximizing the comprehensive learning of time-domain features to enhance fidelity while maintaining robustness, we pioneer a \textbf{\underline{t}}emporal-aware \textbf{\underline{r}}ob\textbf{\underline{u}}st wat\textbf{\underline{e}}rmarking (\emph{True}) method for protecting the speech and singing voice. For this purpose, the integrated content-driven encoder is designed for watermarked waveform reconstruction, which is structurally lightweight. Additionally, the temporal-aware gated convolutional network is meticulously designed to bit-wise recover the watermark. Comprehensive experiments and comparisons with existing state-of-the-art methods have demonstrated the superior fidelity and vigorous robustness of the proposed \textit{True} achieving an average PESQ score of 4.63.

OCNov 10, 2024
A novel algorithm for optimizing bundle adjustment in image sequence alignment

Hailin Xu, Hongxia Wang, Huanshui Zhang

The Bundle Adjustment (BA) model is commonly optimized using a nonlinear least squares method, with the Levenberg-Marquardt (L-M) algorithm being a typical choice. However, despite the L-M algorithm's effectiveness, its sensitivity to initial conditions often results in slower convergence when applied to poorly conditioned datasets, motivating the exploration of alternative optimization strategies. This paper introduces a novel algorithm for optimizing the BA model in the context of image sequence alignment for cryo-electron tomography, utilizing optimal control theory to directly optimize general nonlinear functions. The proposed Optimal Control Algorithm (OCA) exhibits superior convergence rates and effectively mitigates the oscillatory behavior frequently observed in L-M algorithm. Extensive experiments on both synthetic and real-world datasets were conducted to evaluate the algorithm's performance. The results demonstrate that the OCA achieves faster convergence compared to the L-M algorithm. Moreover, the incorporation of a bisection-based update procedure significantly enhances the OCA's performance, particularly in poorly initialized datasets. These findings indicate that the OCA can substantially improve the efficiency of 3D reconstructions in cryo-electron tomography.

CRMar 16, 2021
A survey of deep neural network watermarking techniques

Yue Li, Hongxia Wang, Mauro Barni

Protecting the Intellectual Property Rights (IPR) associated to Deep Neural Networks (DNNs) is a pressing need pushed by the high costs required to train such networks and the importance that DNNs are gaining in our society. Following its use for Multimedia (MM) IPR protection, digital watermarking has recently been considered as a mean to protect the IPR of DNNs. While DNN watermarking inherits some basic concepts and methods from MM watermarking, there are significant differences between the two application areas, calling for the adaptation of media watermarking techniques to the DNN scenario and the development of completely new methods. In this paper, we overview the most recent advances in DNN watermarking, by paying attention to cast it into the bulk of watermarking theory developed during the last two decades, while at the same time highlighting the new challenges and opportunities characterizing DNN watermarking. Rather than trying to present a comprehensive description of all the methods proposed so far, we introduce a new taxonomy of DNN watermarking and present a few exemplary methods belonging to each class. We hope that this paper will inspire new research in this exciting area and will help researchers to focus on the most innovative and challenging problems in the field.

LGSep 28, 2020
A Robust graph attention network with dynamic adjusted Graph

Xianchen Zhou, Yaoyun Zeng, Hongxia Wang

Graph Attention Networks(GATs) are useful deep learning models to deal with the graph data. However, recent works show that the classical GAT is vulnerable to adversarial attacks. It degrades dramatically with slight perturbations. Therefore, how to enhance the robustness of GAT is a critical problem. Robust GAT(RoGAT) is proposed in this paper to improve the robustness of GAT based on the revision of the attention mechanism. Different from the original GAT, which uses the attention mechanism for different edges but is still sensitive to the perturbation, RoGAT adds an extra dynamic attention score progressively and improves the robustness. Firstly, RoGAT revises the edges weight based on the smoothness assumption which is quite common for ordinary graphs. Secondly, RoGAT further revises the features to suppress features' noise. Then, an extra attention score is generated by the dynamic edge's weight and can be used to reduce the impact of adversarial attacks. Different experiments against targeted and untargeted attacks on citation data on citation data demonstrate that RoGAT outperforms most of the recent defensive methods.

LGJul 29, 2020
A regularized deep matrix factorized model of matrix completion for image restoration

Zhemin Li, Zhi-Qin John Xu, Tao Luo et al.

It has been an important approach of using matrix completion to perform image restoration. Most previous works on matrix completion focus on the low-rank property by imposing explicit constraints on the recovered matrix, such as the constraint of the nuclear norm or limiting the dimension of the matrix factorization component. Recently, theoretical works suggest that deep linear neural network has an implicit bias towards low rank on matrix completion. However, low rank is not adequate to reflect the intrinsic characteristics of a natural image. Thus, algorithms with only the constraint of low rank are insufficient to perform image restoration well. In this work, we propose a Regularized Deep Matrix Factorized (RDMF) model for image restoration, which utilizes the implicit bias of the low rank of deep neural networks and the explicit bias of total variation. We demonstrate the effectiveness of our RDMF model with extensive experiments, in which our method surpasses the state of art models in common examples, especially for the restoration from very few observations. Our work sheds light on a more general framework for solving other inverse problems by combining the implicit bias of deep learning with explicit regularization.

MMApr 18, 2018
An Improved Reversible Data Hiding Scheme by Changing Modification Direction of Partial Coefficients in JPEG Images

Yi Chen, Hongxia Wang

This paper first reviews the reversible data hiding scheme, of Liu et al. in 2018, for JPEG images. After that, a novel reversible data hiding scheme, in which modification directions of partial nonzero quantized alternating current (AC) coefficients are utilized to decrease distortion and file size increase caused by data hiding, is proposed. Experimental results have shown that the proposed scheme has indeed advantages in visual quality and smaller increase in file size of marked JPEG images while compared to the state-of-the-art scheme with the same embedding payload so far.

MMApr 18, 2018
Reversible Video Data Hiding Using Zero QDCT Coefficient-Pairs

Yi Chen, Hongxia Wang, Hanzhou Wu et al.

H.264/Advanced Video Coding (AVC) is one of the most commonly used video compression standard currently. In this paper, we propose a Reversible Data Hiding (RDH) method based on H.264/AVC videos. In the proposed method, the macroblocks with intra-frame $4\times 4$ prediction modes in intra frames are first selected as embeddable blocks. Then, the last zero Quantized Discrete Cosine Transform (QDCT) coefficients in all $4\times 4$ blocks of the embeddable macroblocks are paired. In the following, a modification mapping rule based on making full use of modification directions are given. Finally, each zero coefficient-pair is changed by combining the given mapping rule with the to-be-embedded information bits. Since most of last QDCT coefficients in all $4\times 4$ blocks are zero and they are located in high frequency area. Therefore, the proposed method can obtain high embedding capacity and low distortion.

MMApr 3, 2018
Intra-Frame Error Concealment Scheme using 3D Reversible Data Hiding in Mobile Cloud Environment

Yanli Chen, Hongxia Wang, Hanzhou Wu et al.

Data in mobile cloud environment are mainly transmitted via wireless noisy channels, which may result in transmission errors with a high probability due to its unreliable connectivity. For video transmission, unreliable connectivity may cause significant degradation of the content. Improving or keeping video quality over lossy channel is therefore a very important research topic. Error concealment with data hiding (ECDH) is an effective way to conceal the errors introduced by channels. It can reduce error propagation between neighbor blocks/frames comparing with the methods exploiting temporal/spatial correlations. The existing video ECDH methods often embed the motion vectors (MVs) into the specific locations. Nevertheless, specific embedding locations cannot resist against random errors. To compensate the unreliable connectivity in mobile cloud environment, in this paper, we present a video ECDH scheme using 3D reversible data hiding (RDH), in which each MV is repeated multiple times, and the repeated MVs are embedded into different macroblocks (MBs) randomly. Though the multiple embedding requires more embedding space, satisfactory trade-off between the introduced distortion and the reconstructed video quality can be achieved by tuning the repeating times of the MVs. For random embedding, the lost probability of the MVs decreases rapidly, resulting in better error concealment performance. Experimental results show that the PSNR values gain about 5dB at least comparing with the existing ECDH methods. Meanwhile, the proposed method improves the video quality significantly.

DSFeb 20, 2018
The Cut and Dominating Set Problem in A Steganographer Network

Hanzhou Wu, Wei Wang, Jing Dong et al.

A steganographer network corresponds to a graphic structure that the involved vertices (or called nodes) denote social entities such as the data encoders and data decoders, and the associated edges represent any real communicable channels or other social links that could be utilized for steganography. Unlike traditional steganographic algorithms, a steganographer network models steganographic communication by an abstract way such that the concerned underlying characteristics of steganography are quantized as analyzable parameters in the network. In this paper, we will analyze two problems in a steganographer network. The first problem is a passive attack to a steganographer network where a network monitor has collected a list of suspicious vertices corresponding to the data encoders or decoders. The network monitor expects to break (disconnect) the steganographic communication down between the suspicious vertices while keeping the cost as low as possible. The second one relates to determining a set of vertices corresponding to the data encoders (senders) such that all vertices can share a message by neighbors. We point that, the two problems are equivalent to the minimum cut problem and the minimum-weight dominating set problem.

MMJan 15, 2018
Reversible Embedding to Covers Full of Boundaries

Hanzhou Wu, Wei Wang, Jing Dong et al.

In reversible data embedding, to avoid overflow and underflow problem, before data embedding, boundary pixels are recorded as side information, which may be losslessly compressed. The existing algorithms often assume that a natural image has little boundary pixels so that the size of side information is small. Accordingly, a relatively high pure payload could be achieved. However, there actually may exist a lot of boundary pixels in a natural image, implying that, the size of side information could be very large. Therefore, when to directly use the existing algorithms, the pure embedding capacity may be not sufficient. In order to address this problem, in this paper, we present a new and efficient framework to reversible data embedding in images that have lots of boundary pixels. The core idea is to losslessly preprocess boundary pixels so that it can significantly reduce the side information. Experimental results have shown the superiority and applicability of our work.

MMJan 15, 2018
Ensemble Reversible Data Hiding

Hanzhou Wu, Wei Wang, Jing Dong et al.

The conventional reversible data hiding (RDH) algorithms often consider the host as a whole to embed a secret payload. In order to achieve satisfactory rate-distortion performance, the secret bits are embedded into the noise-like component of the host such as prediction errors. From the rate-distortion optimization view, it may be not optimal since the data embedding units use the identical parameters. This motivates us to present a segmented data embedding strategy for efficient RDH in this paper, in which the raw host could be partitioned into multiple subhosts such that each one can freely optimize and use the data embedding parameters. Moreover, it enables us to apply different RDH algorithms within different subhosts, which is defined as ensemble. Notice that, the ensemble defined here is different from that in machine learning. Accordingly, the conventional operation corresponds to a special case of the proposed work. Since it is a general strategy, we combine some state-of-the-art algorithms to construct a new system using the proposed embedding strategy to evaluate the rate-distortion performance. Experimental results have shown that, the ensemble RDH system could outperform the original versions in most cases, which has shown the superiority and applicability.

MMDec 11, 2017
A Graph-theoretic Model to Steganography on Social Networks

Hanzhou Wu, Wei Wang, Jing Dong et al.

Steganography aims to conceal the very fact that the communication takes place, by embedding a message into a digit object such as image without introducing noticeable artifacts. A number of steganographic systems have been developed in past years, most of which, however, are confined to the laboratory conditions where the real-world use of steganography are rarely concerned. In this paper, we introduce an alternative perspective to steganography. A graph-theoretic model to steganography on social networks is presented to analyze real-world steganographic scenarios. In the graph, steganographic participants are corresponding to the vertices with meaningless unique identifiers. Each edge allows the two vertices to communicate with each other by any steganographic algorithm. Meanwhile, the edges are associated with weights to quantize the corresponding communication risk (or say cost). The optimization task is to minimize the overall risk, which is modeled as additive over the social network. We analyze different scenarios on a social network, and provide the suited solutions to the corresponding optimization tasks. We prove that a multiplicative probabilistic graph is equivalent to an additive weighted graph. From the viewpoint of an attacker, he may hope to detect suspicious communication channels, the data encoder(s) and the data decoder(s). We present limited detection analysis to steganographic communication on a network.