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Linear correlations between spatial and normal noise in triangle meshes
Ying Yang, Norbert Peyerimhoff and Ioannis Ivrissimtzis

accepted to IEEE Transactions on Visualization and Computer Graphics

Abstract: We study the relationship between the noise in the vertex coordinates of a triangle mesh and normal noise. First, we compute in closed form the expectation for the angle \(\theta\) between the new and the old normal when uniform noise is added to a single vertex of a triangle. Next, we propose and experimentally validate an approximation and lower and upper bounds for \(\theta\) when uniform noise is added to all three vertices of the triangle. In all cases, for small amounts of spatial noise that do not severely distort the mesh, there is a linear correlation between \(\theta\) and simple functions of the heights of the triangles and thus, \(\theta\) can be computed efficiently. The addition of uniform spatial noise to a mesh can be seen as a dithered quantisation of its vertices. We use the obtained linear correlations between spatial and normal noise to compute the level of dithered quantisation of the mesh vertices when a tolerance for the average normal distortion is given.

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	Polygonal mesh watermarking using Laplacian coordinates Ying Yang and Ioannis Ivrissimtzis Computer Graphics Forum (Proceedings of Eurographics/ACM SIGGRAPH Symposium on Geometry Processing 2010), vol. 29, no. 5, pp. 1585 - 1593, 2010 Abstract: 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. [PDF] [BibTeX]

	A contrast-sensitive reversible visible image watermarking technique Ying Yang, Xingming Sun, Hengfu Yang, Chang-Tsun Li, and Rong Xiao IEEE Transactions on Circuits and Systems for Video Technology, vol. 19, no. 5, pp. 656 - 667, May 2009 Abstract: A reversible (also called lossless, distortion-free, or invertible) visible watermarking scheme is proposed to satisfy the applications, in which the visible watermark is expected to combat copyright piracy but can be removed to losslessly recover the original image. We transparently reveal the watermark image by overlapping it on a user-specified region of the host image through adaptively adjusting the pixel values beneath the watermark, depending on the human visual system-based scaling factors. In order to achieve reversibility, a reconstruction/ recovery packet, which is utilized to restore the watermarked area, is reversibly inserted into non-visibly-watermarked region. The packet is established according to the difference image between the original image and its approximate version instead of its visibly watermarked version so as to alleviate its overhead. For the generation of the approximation, we develop a simple prediction technique that makes use of the unaltered neighboring pixels as auxiliary information. The recovery packet is uniquely encoded before hiding so that the original watermark pattern can be reconstructed based on the encoded packet. In this way, the image recovery process is carried out without needing the availability of the watermark. In addition, our method adopts data compression for further reduction in the recovery packet size and improvement in embedding capacity. The experimental results demonstrate the superiority of the proposed scheme compared to the existing methods. [PDF] [BibTeX]

	Removable visible image watermarking algorithm in the discrete cosine transform domain Ying Yang, Xingming Sun, Hengfu Yang, and Chang-Tsun Li SPIE Journal of Electronic Imaging, vol. 17, no. 3, pp. 033008-1–033008-11 Jul.-Sep. 2008 Abstract: A removable visible watermarking scheme, which operates in the discrete cosine transform (DCT) domain, is proposed for combating copyright piracy. First, the original watermark image is divided into 16×16 blocks and the preprocessed watermark to be embedded is generated by performing element-by-element matrix multiplication on the DCT coefficient matrix of each block and a key-based matrix. The intention of generating the preprocessed watermark is to guarantee the infeasibility of the illegal removal of the embedded watermark by the unauthorized users. Then, adaptive scaling and embedding factors are computed for each block of the host image and the preprocessed watermark according to the features of the corresponding blocks to better match the human visual system characteristics. Finally, the significant DCT coefficients of the preprocessed watermark are adaptively added to those of the host image to yield the watermarked image. The watermarking system is robust against compression to some extent. The performance of the proposed method is verified, and the test results show that the introduced scheme succeeds in preventing the embedded watermark from illegal removal. Moreover, experimental results demonstrate that legally recovered images can achieve superior visual effects, and peak signal-to-noise ratio values of these images are>50 dB. [PDF] [BibTeX]