1. 3D mesh watermarking Wu Dan 2008.12.17

2. Introduction Spatial domain (00 EG) Transformed domain (02 EG) K=D-A; (D ii is a degree of vertex v i, A is an adjacency matrix.) Spectral analysis: eigenvector W i. Project vi onto the normalized eigenvector e i: (si,ti,ui)

3. Towards Blind Detection of Robust Watermarks in Polygonal Models Oliver Benedens and Christoph Busch, EG 2000

4. Watermarking algorithms VFA (vertex flood algorithm) high capacity but fragile AIE (affine invariant embedding) NBE (normal bin encoding) robust

5. VFA com be the center of mass of the start triangle with edge points Each set covers an interval of length W. This interval is subdivided as follows:

6. AIE Nielson norm:

7. AIE

8. Embedding process: embedding primitive :

9. NBE subdivided the Gaussian sphere into NB non overlapping bins. Each bin is uniquely defined by a bin center normal and a boundary angle f. Based on a secret key, we generate two disjunct sets of bin indices,

10. NBE consider the angle difference Xi j of a normal to the according center normal as a statistical sample.

11. result NBE+AIE+VFA

12. result

14. A public fragile watermarking scheme for 3D model authentication Chang-Min Chou, Din-Chang Tseng CAD 38 (2006)

15. Main idea x1 is used to indicate if v is a mark vertex (i.e., v is a watermark embedded vertex), x2 is used for embedding watermark wi, and x3 is used for embedding h(wi ), where h is a predefined hash function

17. embedding

18. embedding The causality problem and the convergence problem: an adjusting vertex.

19. extraction

20. Distortion control

21. results

22. An Oblivious Watermarking for 3-D Polygonal Meshes Using Distribution of Vertex Norms Jae-Won Cho, R é my Prost, and Ho-Youl Jung IEEE TRANSACTIONS ON SIGNAL PROCESSING, 1 2007

23. Main idea

24. METHOD I Watermark embedding 1. Cartesian coordinates are converted into spherical coordinates. 2. vertex norms are divided into distinct bins with equal range.

25. METHOD I Watermark embedding 1. Cartesian coordinates are converted into spherical coordinates. 2. vertex norms are divided into distinct bins with equal range. 3. After embedding, depending on the vertex norms belonging to the n bin are mapped into the normalized range of [0,1] by

26. METHOD I How to shift the mean to the desired level through modifying the value of vertex norms while staying within the proper range.

27. METHOD I Watermark embedding 4. the mean of each bin is changed. (The real vertex norm distribution in each bin is neither continuous nor uniform.)

28. METHOD I 5. Transformed vertex norms of each bin are mapped onto the original range. 6. the watermark embedding process is completed by combining all of the bins and converting the spherical coordinates to Cartesian coordinates.

29. METHOD I Watermark extraction

30. METHOD II Watermark embedding

31. results Mrms:

32. results

35. A new watermarking method for 3D model based on integral invariant Yu-Ping Wang and Shi-Min Hu April 2008

36. INTEGRAL INVARIANTS

37. How to compute integral invariants the area of a spherical triangle is:

38. How to compute integral invariants the volume invariant is:

39. Algorithm flow

41. Watermarking for 3D model Changing the area invariant

42. Watermarking for 3D model Changing the volume invariant

43. Watermarking a model Insertion 1. First, we choose a monochrome image as the watermark image. we transform it with an Arnold transformation. 2. we place balls centered on the model vertices, making sure that none of them intersect each other. 3. we change each invariant value (treated as floating point numbers) by modifying its bit notation,

44. Watermarking a model Insertion 4. We change the area invariants to embed the scrambled number and change the volume invariants to embed the watermark image. 5. By changing the invariants of each neighbor ball, the insertion process is accomplished.

45. Watermarking a model extraction 1. prepare an output image the same size as the watermarked image. 2. we compute the invariants and check the inserted bits. 3. If the assumed sequence number is in the range of the expected sequence number, we test whether the assumed part of the watermark image is the same as the real watermark image part. 4. since the watermark image is first scrambled, the output image after descrambling may lose some random pixels yet still show the information representing the copyright

46. Watermarking a model

47. results

50. Reversible Watermarking of 3D Mesh Models by Prediction-error Expansion Hao-tian Wu, Jean-Luc Dugelay