1. Zhejiang University Wavelet-based 3D mesh model watermarking Shi Jiao-Ying State Key Laboratory of CAD&CG, Zhejiang University, Hangzhou 310027

2. Zhejiang University Introduction Digital watermarking —an effective way of copyright protection Current watermarking technology focuses on media types like still images,and video and audio streams Research about 3D mesh model watermarking began in 1998

3. Zhejiang University The challenges of mesh watermarking (1)In watermark insertion process, arbitrary meshes lack a natural parameterization for frequency-based decomposition. (2) In watermark detection process, simplification and other attacks may modify the connectivity of the mesh. Introduction

4. Zhejiang University Introduction We construct a planar parameterization for arbitrary meshes. Geometric signals are transformed into 2D signals. Then we can apply any image watermarking algorithms for our geometry signals. Our Solutions

5. Zhejiang University Introduction We obtain a mesh with the topology of the original and the geometry of the attacked object. We use an optimization technique similar to E.Praun’s method to resample an attacked mesh using the original mesh connectivity. Our Solutions

6. Zhejiang University (1) The watermark can be embedded in all mesh attributes, including position coordinates, normal, color and texture coordinates etc. (2) All kinds of image frequency-domain watermarking algorithms can be applied to 3D models directly. Introduction The two advantages of our method:

7. Zhejiang University 3D Mesh Model Watermark System Original Signal F M Rectangle Signal F D Regular Sample Signal F U Watermark Regular Sample Signal F’ U Watermark Signal F’ M Plane ParameterizationSampling Image Watermark Algorithms Resampling & Inverse Mapping Figure 1: 3D mesh model watermark system framework. Processing stages are depicted as rectangles; rounded boxes represent input/output data of each stage.

8. Zhejiang University Figure 2: The progressive planar parameterization. The up line depicts the simplification process which transfers the original mesh M n into a tetrahedron M 0 ; then M 0 is mapped into a square D 0 ; then using the information generated during mesh simplification, such as Sp n, …,Sp i, Sp i-1, … to generate an square mesh with original resolution D n. Planar parameterization Original Signal F M Rectangle Signal F D Plane Parameterization

9. Zhejiang University Sampling Sampling: The 2D signal F D is adaptively sampled into a regular signal F U under the user specified precision threshold. Rectangle Signal F 0 Regular Sample Signal F U Sampling

10. Zhejiang University Watermark Insertion Figure 3: Watermark insertion process 2D original regular signal F U 2D watermarked regular signal F ‘ U Search significant subband coefficients DWT Inserting watermark Generating watermark IDWT (1) DWT of the 2D original regular signal (2) Significant coefficient search (3) Watermark insertion (4) IDWT of the coefficients with watermarks Regular Sample Signal F U Watermark Regular Sample Signal F’ U Image Watermark Algorithms

11. Zhejiang University Resampling & Inverse Mapping M 0 - Original Mesh M s - Mesh, which topology has been changed after attacks, needs to be resampled M r - Result Mesh after resampling and inverse mapping which topology has been recovered with that of M 0 by using optimization method. Watermark Regular Sample Signal F’ U Watermark Signal F’ M Resampling & Inverse Mapping

12. Zhejiang University Watermark Detection (1) DWT of original 2D regular signal and watermarked 2D regular signal (2) Watermark extraction (3) Calculation of the correlation DWT  Calculating correlation 2D detected regular signal 2D original regular signal Extracted watermark Watermark Watermark detection Figure 4: Watermark detection process + -

13. Zhejiang University Detection threshold analysis First set the correlation threshold experimentally. 10000 watermark vectors with length of 50 randomly generated. The original watermark is the 5000 th. The maximum correlation is around 0.47. We can set the correlation threshold to 0.5. Figure 5: Detection threshold analysis

14. Zhejiang University Results and Attack Analysis We implemented our algorithm in MSVC++ 6.0 on a P Ⅱ 350 machine. The test result in this section were obtained using a watermark length of m=50 coefficients, the scaling factors =0.2,=0.4. We ran each 5 times, using different random seeds, and report the median value. Table 1 shows the detection results for a host of attacks. Figure 6 ： Median of 5 tests for various attacks

15. Zhejiang University Figure 7 ： Watermarked models and some attacked models. Results and Attack Analysis

16. Zhejiang University Summary and Future work Our 3D mesh models watermark system framework has following characteristics: Watermark can be embedded in all mesh attributes, including position coordinates, normal, color and texture coordinates etc. All kinds of image frequency-domain watermarking algorithms can be applied to 3D models directly. Future work includes: Embedding the watermark in other mesh attributes, such as normal, color and texture coordinates etc; Appling more image frequency-domain watermark algorithms to 3D mesh models; Inserting the watermark in user specified position of 3D mesh models

17. Zhejiang University Thank You!