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Received：19 May 2021，
Revised：10 September 2021，
Accepted：17 September 2021，
Published：16 January 2022
移动端阅览
在计算机图形学中，3D形状可有多种表示形式，包括网格、体素、多视角图像、点云、参数曲面和隐式曲面等。3D网格是常见的表示形式之一，其构成3D物体的顶点、边缘和面的集合，通常用于表示数字3D物体的曲面和容积特性。在过去的20年中，基于3D网格载体的虚拟现实、实时仿真和交叉3维设计已经在工业，医疗和娱乐等场景得到广泛应用，以3D网格为载体的水印技术、隐写和隐写分析技术也受到研究者的关注。相比于图像与音视频等载体的隐写，3D网格具备嵌入方式灵活与载体形式多变等其自身的优势。本文回顾了3D网格隐写和隐写分析的发展，并对现有研究工作进行了系统的总结和分类。根据嵌入方式和嵌入位置将隐写算法分成4类：两态调制隐写、最低位隐写、置换隐写和变换域隐写；根据特征提取角度将隐写分析算法分为2类：通用型隐写分析和专用型隐写分析。随后，介绍了每个类别的技术，综合安全性、鲁棒性、容量以及运算效率分析了各类算法的优劣性，总结当前的发展水平，并提供了不同嵌入率下两种数据集上隐写分析算法之间的性能比较。最后讨论了3D隐写和隐写分析现有技术的局限性，并探讨了潜在的研究方向，旨在为后续学者进一步推动3D隐写和隐写分析技术提供指导。
Three-dimensional (3D) meshes have been mainly used to illustrate virtual surfaces and volumes. 3D meshes have implemented in industrial
medical
and entertainment applications over the past decade
which are of great practical significance for 3D mesh steganography and steganalysis. The application of 3D geometry as host object has been focused over the past few years based on image
audio files and videos processing method in early steganography and steganalysis. Cost effective 3D hardware stimulates the widespread use of 3D meshes in the evolving of the computer aided design(CAD) industry to real-world end-user applications such as virtual reality (VR)
web integration
Facebook support
video games
3D printing and animated movies. Hence
the development of computer graphics has facilitated the production
application and distribution of the emerging generation of 3D geometry digital media. Moreover
the flexible data structure of 3D geometry provides enough space to host security information
making it ideal for use a cover object for steganography. A 3D mesh consists of a set of triangular faces
which is to form an approximation of a real 3D object. A 3D mesh has 3 different synthesized factors: vertices
edges
and faces; a mesh can also be taken as the integration of geometry connectivity
where the geometry provides the 3D positions of all its vertices
and connectivity
which provides the information hidden between different adjacent vertices. A systematic overview of 3D mesh steganography and steganalysis has been issued related to computer graphics and security. The objective projects in the context of the types of steganographic and steganalytic methods have been reviewed in literature. Quantitative evaluation has been conducted from the perspective of security assessment simultaneously. The target of this task is to demonstrate the evaluation procedures in the 3D mesh steganography and steganalysis methods as a whole. It is essential to recognize a growing number of efforts on how to improve the anti-steganalysis efforts in the case of steganographer side and how to improve the steganalysis ability in the case of the steganalyzer side. Some standard evaluation metrics
an overall summary
and an understanding of relevant research results have been evaluated based on the previous analyses. Unlike image steganography which embeds data by modifying pixel values
3D mesh steganography modifies vertex coordinates or vertex order to embed data. In the latest literature analysis of 3D steganography and steganalysis of Girdhar and Kumar's work
steganography is divided into three categories (geometrical domain
topological domain and representation domain)
which reflects the robustness of the algorithms to attacks
and steganalysis is briefly introduced. The entire communities of 3D steganography and steganalysis have to be further promoted. For instance
the geometrical domain can still be divided into two-state domain and the least significant bit(LSB) domain. In addition
the concepts of "steganography" and "watermarking" can be used interchangeably. Watermarking seeks robustness
protects copyright ownership and reduces the counterfeiting of digital multimedia
while steganography seeks un-detectability used for covert communication. They focus has been primarily on analyzing the robustness of the existing methods
while the undetectability of steganography is a more important property because of its practical requirement: covert communication. A more comprehensive survey
a clear taxonomy and several criteria for evaluating robustness and un-detectability has been offered. Conversely
hidden data has been used into reversible data hiding and steganography. For the structure of 3D data
the 3D mesh and RGBD image have been mainly concentrated. 3D meshes as carriers and steganographic techniques have been considered. The steganographic techniques into several domains (two-state domain
LSB domain
permutation domain and transform domain) in a subdivision way have been divided with no small embedding capacities. This demonstration has evolved common digital attacks including affine transform attack
vertex reordering attack
noise addition attack
smoothing attack and simplification attack. In addition
3D mesh steganalysis has been divided into two aspects (general steganalysis and specific steganalysis). For overall steganalysis
there are YANG208 features
local feature set(LFS)52 features
LFS64 features
LFS76 features
LFS124 features
normal voting tensor(NVT)+ features and 3D wavelet feature set(WFS)228 features respectively. Current methods have revealed strong weaknesses and strengths from which we can learn for future work. In order to evaluate the performance of various steganographic and steganalytic methods clearly
it is important to identify standards for users friendly. Meanwhile
the steganographic performance based on three general requirements (i.e.
security
capacity and robustness) has been evaluated. Ensemble learning is an effective way to produce a variety of base classifiers
from which a new classifier with a better performance can be derived
and ensemble classifier is used to evaluate steganalysis performance
a common tool for steganalysis. The datasets proposed are suitable for the princeton segmentation benchmark and the Princeton ModelNet
where the former has 354 objects and the latter has 12 311 mesh objects with 40 categories. Some promising future research directions and challenges in improving the performance of 3D mesh steganography and steganalysis have been highlighted. 3D mesh steganography research has been summarized as following: 1) combining the permutation domain and LSB domain; 2) designing spatial steganographic models; 3) designing steganalysis-resistant permutation steganographic methods; 4) designing 3D mesh batch steganography methods and 5) designing 3D-printing-material-based robust steganography methods. Open issues of 3D mesh steganalysis has been summarized as bellows: 1) rich steganalytic features designation for universal blind steganalysis; 2) designing deep-learning-based steganalysis methods; 3) designing a finer distance metric to improve the steganalysis of permutation steganography and 4) cover source mismatch problem.
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