Adaptive 3D Mesh Steganography Based on Feature-Preserving Distortion

TL;DR

This work introduces an adaptive 3D mesh steganography framework guided by a feature-preserving distortion (FPD) to minimize embedding impact while achieving high payload and robustness. It formulates a payload-limited sender (PLS) optimization and employs a D2I-based embedding domain with bitplane partitioning, complemented by a universal U\&A-BMP approach for efficient Q-layered STC embedding and retrieval. The distortion is built from selected NVT+ subfeatures to preserve mesh and steganalytic features, and improvements via vertex influence domains accelerate cost computations. Experimental results on PSB and PMN show state-of-the-art anti-steganalysis performance, with statistical validation and visualization confirming reduced perceptual impact and competitive capacity. The work provides open-source tooling and points to future directions for more general, robust embedding domains and distortion models.

Abstract

Current 3D mesh steganography algorithms relying on geometric modification are prone to detection by steganalyzers. In traditional steganography, adaptive steganography has proven to be an efficient means of enhancing steganography security. Taking inspiration from this, we propose a highly adaptive embedding algorithm, guided by the principle of minimizing a carefully crafted distortion through efficient steganography codes. Specifically, we tailor a payload-limited embedding optimization problem for 3D settings and devise a feature-preserving distortion (FPD) to measure the impact of message embedding. The distortion takes on an additive form and is defined as a weighted difference of the effective steganalytic subfeatures utilized by the current 3D steganalyzers. With practicality in mind, we refine the distortion to enhance robustness and computational efficiency. By minimizing the FPD, our algorithm can preserve mesh features to a considerable extent, including steganalytic and geometric features, while achieving a high embedding capacity. During the practical embedding phase, we employ the Q-layered syndrome trellis code (STC). However, calculating the bit modification probability (BMP) for each layer of the Q-layered STC, given the variation of Q, can be cumbersome. To address this issue, we design a universal and automatic approach for the BMP calculation. The experimental results demonstrate that our algorithm achieves state-of-the-art performance in countering 3D steganalysis. Code is available at https://github.com/zjhJOJO/3D-steganography-based-on-FPD.git.

Figures (10)

• Figure 1: Message embedding pipeline of the proposed adaptive 3D mesh steganography algorithm based on FPD.
• Figure 2: Illustration of three neighborhood patterns and their respective vertex influence regions. (a) $N_1(\boldsymbol{v}_i)$ is a set of 1-ring neighboring faces of $\boldsymbol{v}_i$. (c) $N_2(\boldsymbol{f}_i)$ a set of faces sharing edges with $\boldsymbol{f}_i$. (e) $N_3(\boldsymbol{f}_i)$ is a set of faces sharing vertices with $\boldsymbol{f}_i$. (b), (d), and (f) are the visualizations of the vertex influence domains corresponding to (a), (c), and (e), respectively. The modified vertices in (b), (d), and (f) are marked in red, and their corresponding vertex influence domains are painted pink.
• Figure 3: (a) Basic flow chart of the $Q$-layered STC. (b) A visual example of U$\&$A BMP with $\boldsymbol{I}=\{-1/10^{k_d},0,1/10^{k_d},2/10^{k_d}\}$ and $\boldsymbol{B}_{x}=\{\boldsymbol{B}_x^{(1)},\boldsymbol{B}_x^{(2)}\}$, where $\boldsymbol{B}^{(1)}_x=\{1,0,1\}$ and $\boldsymbol{B}_x^{(2)}=\{1,0,1\}$. Please note that $p^{\delta}_{ij}$ is short for $p(\delta_{ij}=\delta)$, and $\boldsymbol{A}$, except for its first row, records the BMP corresponding to $b'^{(l)}_{ij}=0$ only.
• Figure 4: Average OOB error $\bar{E}_{OOB}$ as a function of the relative payload for six types of distortion functions on (a) the PSB dataset (b) and PMN dataset.
• Figure 5: Average OOB error $\bar{E}_{OOB}$ obtained across different steganalyzers as a function of the relative payload for IFPD-CS, Chao, Li, VND/LSBR, and HPQ-R on the PSB dataset and PMN dataset.