Robust mesh watermarking against geometric distortions based on vertex valence distribution

3D mesh watermarking is an effective way to protect the copyright of 3D mesh models by imperceptibly embedding an ownership message into their geometric or topological information. The embedded watermark is supposed to be accurately extracted from the watermarked meshes after suffering various malicious or accidental geometric distortions during transmission, such as adding noise and smoothing. However, existing works rely on the geometric information of mesh models for watermark synchronization and extraction, resulting in poor robustness to geometric distortions. To address this issue, we propose a novel robust mesh watermarking scheme that is completely independent of geometric information. A watermark synchronization scheme is designed based on the Fiedler vector of the Kirchhoff matrix, upon which a watermark encoding strategy is introduced. Moreover, leveraging the vertex valence distribution of closed triangular meshes, we develop two topological embedding techniques to embed the watermark imperceptibly. Extensive experiments show that the proposed method achieves stronger robustness against geometric distortions, including similarity transformations, adding noise, smoothing, quantization, and even combination distortions, while maintaining the watermarked mesh quality compared with state-of-the-art methods.