This paper describes a blind watermarking scheme through cyclic signal processing. Due to various rapid networks, there is a growing demand of copyright protection for multimedia data. As efficient watermarking of images, there exist two major approaches: a quantization-based method and a correlation-based method. In this paper, we proposes a correlation-based watermarking technique of three-dimensional (3-D) polygonal models using the fast Fourier transforms (FFTs). For generating a watermark with desirable properties, similar to a pseudonoise signal, an impulse signal on a two-dimensional (2-D) space is spread through the FFT, the multiplication of a complex sinusoid signal, and the inverse FFT. This watermark, i.e., spread impulse signal, in a transform domain is converted to a spatial domain by an inverse wavelet transform, and 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. For 3-D bunny models, detection rates and information capacity are shown to evaluate the performance of the proposed method.

In this letter, we address geometry coding of 3-D mesh models. Using a joint prediction, the encoder predicts vertex positions in the layer traversal order. After we apply the joint prediction algorithm to eliminate redundancy among vertex positions using both position and angle values of neighboring triangles, we encode those prediction errors using a uniform quantizer and an entropy coder. The proposed scheme demonstrates improved coding efficiency for various VRML test data.