网格谱系数下不可见性指导的鲁棒水印算法

doi:10.3969/j.issn.0255-8297.2025.03.002

摘要/Abstract

摘要： 在版权保护领域，网格水印技术是保护3D模型在传输过程中免受恶意攻击的关键技术，然而现有的网格水印算法并未充分联系空域和频域，对水印嵌入强度的设置规则不够清晰。针对此问题，本文提出了一种受不可见性指导的鲁棒水印算法（robust watermarkingalgorithm guided by invisibility,RWGI）。以三维网格的拉普拉斯变换为对象，在水印嵌入过程中对空域不可见性评价指标与频谱域嵌入强度的关系进行建模，使水印的嵌入受到不可见性指标的调控，保证了水印嵌入强度的按需量化；针对该指导的实施过程，设计了一种基于绝对值的谱系数寻优策略和一种简单高效的网格分块算法。实验表明，本文提出的算法具有良好的不可见性和对常见攻击的鲁棒性，且能保证水印嵌入强度对模型尺度的自适应。

关键词: 3D 版权保护, 不可见性, 网格谱水印, 网格拉普拉斯变换

Abstract: In the field of copyright protection, mesh watermarking is a key technology for protecting 3D models from malicious attacks during transmission. However, existing watermarking algorithms for 3D meshes often fail to effectively connect the spatial and frequency domains and the setting rule of watermark embedding strength is not clear enough. To solve this problem, we propose a robust mesh watermarking algorithm guided by invisibility (RWGI). Taking the Laplacian transform of a mesh as an example, we establish, for the first time during the watermark embedding process, a model that characterizes the relationship between the spatial-domain invisibility evaluation index and the spectraldomain embedding strength. In this way, the watermark embedding can be adaptively guided by the invisibility index, ensuring the quantification of the watermark embedding strength on demand. Additionally, we design a spectral coefficient optimization strategy based on absolute value, along with a simple yet efficient watermarking segmentation algorithm. Experimental results show that the proposed algorithm achieves strong invisibility, robustness against common attacks, and adaptive control of watermark embedding intensity with respect to model scale.

Key words: 3D copyright protection, invisibility, mesh spectral watermark, mesh Laplace transform

中图分类号:

TP309.2

吴肖, 黄樱, 宋春花, 关虎, 牛保宁. 网格谱系数下不可见性指导的鲁棒水印算法[J]. 应用科学学报, 2025, 43(3): 370-386.

WU Xiao, HUANG Ying, SONG Chunhua, GUAN Hu, NIU Baoning. Robust Watermarking Algorithm Guided by Invisibility Under Mesh Spectral Coefficients[J]. Journal of Applied Sciences, 2025, 43(3): 370-386.

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