On the basis of a new orthogonal function system called V-systemover a triangular domain

this study proposes a frequency-based watermark algorithm for 3D models. Vertex information is acquired to construct “pseudo model” is constructed and is then parameterized so that the pseudo model can be expressed as a piecewise linear function over a triangular domain. The linear function is then orthogonally decomposed into a V-series

which has coefficients from which the V-spectrum is obtained. Finally

the watermark is embedded into the frequency domain by modifying the V-spectrum

such that a renewed V-spectrum is formed. The pseudo model is reconstructed by using the new V-spectrum and the basis function of the V-system

and the final watermarked model is built by replacing the vertex of the original 3D model by the vertex information of the watermarked pseudo model. The watermarked model created by the proposed algorithm has high fidelity

which is maintained even when multiple watermarks are embedded into a model.Moreover

the bit error rate of the extracted watermark is low

and the correlation coefficient between the original watermark and the extracted watermark is high. The proposed algorithm is theoretically proven to be robust against similarity transformations. Experiments conducted on the watermarked model show that the proposed method is robust against noise pollution

shearing

and smoothing.