Chinese Journal of Computers   Full Text
Title	A New Spatial Domain Method for Watermarking in 3D Models
Authors	LIAO Xue-Liang WANG Yu-Ping
Address	(Department of Computer Science and Technology, Tsinghua University, Beijing 100084)
Year	2008
Issue	No.10(1848—1856)
Abstract &   Background	Abstract An invariable of affine transformation in 3D models, the Rate of Barycenter and Crosspoint(RBC) is proposed, and by using the invariable, a spatial domain method for watermarking in 3D models, called MICT method, is proposed. In the embedding process, this method first calculate the barycenter of the model, then after getting the line through the vertex and barycenter, it adopts the fast ray tracing method and gets the crosspoint of the line and the model. By modifying the RBC of the vertices, the Mark, Index, Content characters are embedded. In order to improve the robustness of the method, the watermark string is embedded multi-times. In the extracting process, we adopt the voting method to improve the accuracy of the extracted watermark, that is voting from 256 characters. For every character of the watermark string, they set the most voted character in the 256 characters as the right character. This method is a blind method, simple and useful. Theoretically, the embedded watermark is unchanged under some normal operations to the model such as affine transformation, vertex reorder and so on, and it can also resist some noise attack. The experiments have proved that it is robust under these operations. They also analyze embedding capacity by experiments. Keywords 3D models; digital watermark; affine transformation; spatial domain method; MICT method Background As the multimedia technology and internet develops very fast, more and more digital products are used over the internet, then the copyright of these products appears. As an important, 3D models begin prevailing recently. Digital watermarking has been studied over many years for the copyright protection of digital products, and ten or more years ago, most attention was paid on the audio, image, video. In 1997, the first article on 3D model watermarking was published by Ohcuchi. After then, a lot of algorithms were developed by more and more researchers. Generally speaking, there are two categories of algorithms for watermarking: spatial domain methods and frequency domain methods. Spatial domain methods embed watermark by modifying the coordinate of vertices, the color of texture points, the topology of the model, or other elements representing the model. The frequency domain methods first make transformation to the model and get the coefficients, then modify the coefficients to embed the watermark. In order to extract the watermark, the extracting algorithm should be designed as the embedding algorithm is designed, that is, a watermark system includes an embedding subsystem and an extracting subsystem corresponding to the embedding subsystem. Some extracting algorithms need the original model, they are called blind algorithm, and the other algorithms, which don’t need the original model, are called non-blind algorithm. There is no authoritative standard to evaluate which algorithm is better. For a given application, we can consider the following properties: (1)Robustness: The watermark should withstand different types of attacks; (2)Invisibility: The model should be modified just a little bit so that the embedded model be similar with the origin one; (3)Validation: The watermark should be extracted entirely; (4)Capacity: The mount of information that can embedded in the model. In this paper, the authors propose an invariable of affine transformation: The Rate of Barycenter and Crosspoint(RBC). Based on this invariable, they propose a new spatial domain method, and it is also a blind algorithm. In the embedding subsystem, the authors calculate the barycenter of the model, then the RBC of every point. By modifying the RBC of the vertices, they embed the information. In the extracting subsystem, they adopt the voting method to improve the accuracy of the extracted watermark. Theoretically, the embedded watermark is unchanged under some normal operations to the model such as affine transformation, vertex reorder and so on, and it can also resist some noise attack.