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Polygonal mesh watermarking using Laplacian coordinates

Yang, Ying; Ivrissimtzis, Ioannis


Ying Yang


We propose a watermarking algorithm for polygonal meshes based on the modification of the Laplacian coordinates. More specifically, we first compute the Laplacian coordinates (x; y; z) of the mesh vertices, then construct the histogram of the lengths of the (x; y; z) vectors, and finally, insert the watermark by altering the shape of that histogram. The watermark extraction is carried out blindly, with no reference to the host model. The proposed method is more robust than several existing high capacity watermarking algorithms. In particular, it is able to resist attacks such as translations, rotations, uniform scaling and vertex reordering, due to the invariance of the histogram of the Laplacian vector lengths under such transformations. Compared to the existing robust watermarking methods, our experiments show that the proposed method can better resist common mesh editing attacks, due to the good behaviour of the Laplacian coordinates under such operations.


Yang, Y., & Ivrissimtzis, I. (2010). Polygonal mesh watermarking using Laplacian coordinates. Computer Graphics Forum, 29(5), 1585-1593.

Journal Article Type Article
Publication Date Jul 1, 2010
Deposit Date Sep 28, 2010
Journal Computer Graphics Forum
Print ISSN 0167-7055
Electronic ISSN 1467-8659
Publisher Wiley
Peer Reviewed Peer Reviewed
Volume 29
Issue 5
Pages 1585-1593
Keywords Triangle mesh, watermarking, Laplacian coordinates.
Publisher URL