A New Watermarking Algorithm For3D Mesh Based On V System Over Triangular Domain

This paper mainly study a new orthogonal function system, based on V-system, over triangular domain, this paper proposes a frequency-based watermark algorithm for3D models. The V-system over triangular domain have an unique algorithm, first of all, aiming at the information of the vertex, a "pseudo model" is constructed, and parameterized so that the pseudo model can be expressed as a piecewise linear function over triangular domain. The linear function is then orthogonally decomposed into a V-series, and the V-spectrum is obtained from the coefficients of the V-series. Finally, the watermark is embedded into the frequency domain by modifying the V-spectrum, and a renewed V-spectrum is formed in this way. Using the new V-spectrum and the basis function of the V-system, the pseudo model is reconstructed, and the final watermarked model is built by replacing the vertex of the original3D model by the vertex information of the watermarked pseudo model. The watermarked model created by the proposed algorithm has high fidelity. Even if multiple watermarks are embedded into a model, the model still maintains high fidelity, and the bit error rate of the extracted watermark is low, the correlation coefficient between the original watermark and the extracted watermark is high. It is theoretically proved that the proposed algorithm is robust againstsimilarity transformations. In addition to this, experiments conducted on watermarked model show that our method is also robust against noise pollution, shearing and smoothing.