Using Radial Basis Function Networks for Watermark Determination in 3D Models

In this paper, we investigate the ability of a radial basis function network to determine the values of the watermark to be inserted in a 3D triangulated mesh model. The challenge in a watermarking algorithm is to achieve high watermark embedding capacity without causing perceptual distortion to the model. The proposed technique overcomes this challenge. The principal, mean and Gaussian curvature values computed at each vertex of the 3D model collectively represent the local geometry of the vertex and its neighborhood. These curvature values are used as input feature vectors to train the neural network. The amount of watermark to be inserted at a vertex is non-linearly proportional to these feature vectors. The neural network is trained with watermark values to learn this non-linear relationship. A wide range of 3D models are used to train the neural network such that the large variations in the geometry of the vertices is incorporated by the training phase. The algorithm adopts a non-blind extraction process to retrieve the watermark. Experimental results prove that the watermarking algorithm achieves imperceptibility, high capacity and robustness to noise and cropping attacks up to 20% level.