A 3-D mesh watermarking with uncomplicated frequency selectivity

Abstract

This paper describes a correlation-based watermarking technique with the fast Fourier transforms (FFTs) for three-dimensional (3-D) mesh models. For generating a watermark with desirable properties, similar to a pseudonoise (PN) signal, an impulse signal on a two-dimensional (2-D) space is spread through the FFT, multiplications of a complex sinusoid signal, and the inverse FFT. This system easily incorporate a frequency selectivity property, because zero-valued components in the multiplication block prevent the energy of the impulse signal at appropriate frequencies. As a result, the proposed approach requires no additional transform, such as the discrete cosine transform and wavelet transform. Since the amount of information that can be stored in the watermark depends on the size of a spread space, the elimination of the subband transform increases a payload of the watermark in a previous paper. The watermark, i.e., spread impulse signal, is embedded into 3-D data aligned by the principle component analysis (PCA). In the detection procedure, after realigning the watermarked mesh model through the PCA, we map the 3-D data on the 2-D space via block segmentation and averaging operation. The 2-D data are processed by the inverse system, i.e., the FFT, the division of the complex sinusoid signal, and the inverse FFT. From the resulting 2-D signal, we detect the position of the maximum value as a signature.