1. A public fragile watermarking scheme for 3D model authentication Chang-Min Chou, Din-Chang Tseng Computer-Aided Design Vol. 38 (Nov. 2006) 1154–1165 Reporter: T. Y. Chen 11 JUNE 2007

2. 2 Information Hiding – Simple Classification for 3D Models Lin 2005 Chou 2006

3. 3 Outline Introduction The Proposed Scheme –The watermark embedding scheme The multi-function embedding method The adjusting-vertex method –The watermark extraction scheme and tamper detection Distortion Control Experimental Results Conclusions

4. 4 Introduction~3D triangle meshes Introduction~3D triangle meshes (1/4) Example : Sphere1

5. 5 Introduction~3D triangle meshes Introduction~3D triangle meshes (2/4) Sphere1.WRL #VRML V2.0 utf8 # Produced by 3D Studio MAX VRML97 exporter, Version 8, Revision 0.92 # MAX File: sphere1.max, Date: Thu Dec 14 18:43:31 2006 DEF Sphere01 Transform { translation -0.3831 0 -1.533 children [ Shape { appearance Appearance { material Material { diffuseColor 0.6 0.8941 0.6 } geometry DEF Sphere01-FACES IndexedFaceSet { ccw TRUE solid TRUE coord DEF Sphere01-COORD Coordinate { point [ 0 27.08 0, 0 23.45 -13.54, -6.77 23.45 -11.73, -11.73 23.45 -6.77, -13.54 23.45 0, -11.73 23.45 6.77, -6.77 23.45 11.73, 0 23.45 13.54, 6.77 23.45 11.73, 11.73 23.45 6.77, 13.54 23.45 0, 11.73 23.45 -6.77, 6.77 23.45 -11.73, 0 13.54 -23.45, -11.73 13.54 -20.31, -20.31 13.54 -11.73, -23.45 13.54 0, -20.31 13.54 11.73, -11.73 13.54 20.31,

6. 6 Introduction~3D triangle meshes Introduction~3D triangle meshes (3/4) Sphere1.WRL 0 13.54 23.45, 11.73 13.54 20.31, 20.31 13.54 11.73, 23.45 13.54 0, 20.31 13.54 -11.73, 11.73 13.54 -20.31, 0 0 -27.08, -13.54 0 -23.45, -23.45 0 -13.54, -27.08 0 0, -23.45 0 13.54, -13.54 0 23.45, 0 0 27.08, 13.54 0 23.45, 23.45 0 13.54, 27.08 0 0, 23.45 0 -13.54, 13.54 0 -23.45, 0 -13.54 -23.45, -11.73 -13.54 -20.31, -20.31 -13.54 -11.73, -23.45 -13.54 0, -20.31 -13.54 11.73, -11.73 -13.54 20.31, 0 -13.54 23.45, 11.73 -13.54 20.31, 20.31 -13.54 11.73, 23.45 -13.54 0, 20.31 -13.54 -11.73, 11.73 -13.54 -20.31, 0 -23.45 -13.54, -6.77 -23.45 -11.73, -11.73 -23.45 -6.77, -13.54 -23.45 0, -11.73 -23.45 6.77, -6.77 -23.45 11.73, 0 -23.45 13.54, 6.77 -23.45 11.73, 11.73 -23.45 6.77, 13.54 -23.45 0, 11.73 -23.45 -6.77, 6.77 -23.45 -11.73, 0 -27.08 0] } coordIndex [ 0, 1, 2, -1, 0, 2, 3, -1, 0, 3, 4, -1, 0, 4, 5, -1, 0, 5, 6, -1, 0, 6, 7, -1, 0, 7, 8, -1, 0, 8, 9, -1, 0, 9, 10, -1, 0, 10, 11, -1, 0, 11, 12, -1, 0, 12, 1, -1, 1, 13, 14, -1, 1, 14, 2, -1, 2, 14, 15, -1, 2, 15, 3, -1, 3, 15, 16, -1, 3, 16, 4, -1, 4, 16, 17, -1, 4, 17, 5, -1, 5, 17, 18, -1, 5, 18, 6, -1, 6, 18, 19, -1, 6, 19, 7, -1, 7, 19, 20, -1, 7, 20, 8, -1, 8, 20, 21, -1, 8, 21, 9, -1, 9, 21, 22, -1,

7. 7 Introduction~3D triangle meshes Introduction~3D triangle meshes (4/4) Sphere1.WRL 9, 22, 10, -1, 10, 22, 23, -1, 10, 23, 11, -1, 11, 23, 24, -1, 11, 24, 12, -1, 12, 24, 13, -1, 12, 13, 1, -1, 13, 25, 26, -1, 13, 26, 14, -1, 14, 26, 27, -1, 14, 27, 15, -1, 15, 27, 28, -1, 15, 28, 16, -1, 16, 28, 29, -1, 16, 29, 17, -1, 17, 29, 30, -1, 17, 30, 18, -1, 18, 30, 31, -1, 18, 31, 19, -1, 19, 31, 32, -1, 19, 32, 20, -1, 20, 32, 33, -1, 20, 33, 21, -1, 21, 33, 34, -1, 21, 34, 22, -1, 22, 34, 35, -1, 22, 35, 23, -1, 23, 35, 36, -1, 23, 36, 24, -1, 24, 36, 25, -1, 24, 25, 13, -1, 25, 37, 38, -1, 25, 38, 26, -1, 26, 38, 39, -1, 26, 39, 27, -1, 27, 39, 40, -1, 27, 40, 28, -1, 28, 40, 41, -1, 28, 41, 29, -1, 29, 41, 42, -1, 29, 42, 30, -1, 30, 42, 43, -1, 30, 43, 31, -1, 31, 43, 44, -1, 31, 44, 32, -1, 32, 44, 45, -1, 32, 45, 33, -1, 33, 45, 46, -1, 33, 46, 34, -1, 34, 46, 47, -1, 34, 47, 35, -1, 35, 47, 48, -1, 35, 48, 36, -1, 36, 48, 37, -1, 36, 37, 25, -1, 37, 49, 50, -1, 37, 50, 38, -1, 38, 50, 51, -1, 38, 51, 39, -1, 39, 51, 52, -1, 39, 52, 40, -1, 40, 52, 53, -1, 40, 53, 41, -1, 41, 53, 54, -1, 41, 54, 42, -1, 42, 54, 55, -1, 42, 55, 43, -1, 43, 55, 56, -1, 43, 56, 44, -1, 44, 56, 57, -1, 44, 57, 45, -1, 45, 57, 58, -1, 45, 58, 46, -1, 46, 58, 59, -1, 46, 59, 47, -1, 47, 59, 60, -1, 47, 60, 48, -1, 48, 60, 49, -1, 48, 49, 37, -1, 61, 50, 49, -1, 61, 51, 50, -1, 61, 52, 51, -1, 61, 53, 52, -1, 61, 54, 53, -1, 61, 55, 54, -1, 61, 56, 55, -1, 61, 57, 56, -1, 61, 58, 57, -1, 61, 59, 58, -1, 61, 60, 59, -1, 61, 49, 60, -1] } ] }

8. 8 Introduction~ wmk. category The application purpose –Robust watermarking To achieve intellectual property protection of digital contents. To make the embedded watermarks remain detectable after being attacked. – Fragile watermarking To authenticate the integrity of digital contents. To detect the unauthorized modifications and locate the changed regions. The extraction strategies –Private (blind): Need the original model and watermark. –Public: In the absence of the original model and watermark. –Semi-public: Does not need the original model, but the original watermark is necessary. The embedding strategies –Geometry: To modifying the vertex coordinates. –Topology: To modifying the vertex connectivity.

9. 9 The causality problem –Arises when the neighboring relationship of a former processed vertex is influenced by the perturbing of its later processed neighboring vertices. The convergence problem –The original model has been heavily distorted before some vertices reach the predefined relationship. Introduction(2/2) Introduction (2/2)

10. 10 The Proposed Scheme The watermark embedding scheme The multi-function embedding method The adjusting-vertex method The watermark extraction scheme and tamper detection

11. Watermarked mesh M ’ Watermark embedding Watermark extraction

12. 12 The Proposed Scheme (embedding) A mesh M(V,C) –V is the vertex set, a vertex v(x 1,x 2,x 3 )  v’(x 1 ’,x 2 ’,x 3 ’) –C is the connectivity relationship A watermark W=(w 1,w 2, …,w n ) Keys: k w, k j q, k j d, h( ), j =2,3

13. 13 The Proposed Scheme (embedding) A vertex v(x 1,x 2,x 3 )  v ’ (x 1 ’,x 2 ’,x 3 ’ ) –x 1 is used to indicate if v is a mark vertex –x 2 is used for embedding watermark w i –x 3 is used for embedding h(w i ) If v is a mark vertex,  x 1 / k w  must be odd; otherwise x 1 ’ = x 1 + k w If v is a non-mark vertex,  x 1 / k w  must be even; otherwise x 1 ’ = x 1 + k w

14. 14 The Proposed Scheme (embedding) For a mark vertex v(x 1,x 2,x 3 ), Calculate the barycenters x 2 c and x 3 c x j c (the barycenter of x j ): the centroid of x j ’s neighbors x j is moved toward x j c to x j e, s.t. | x j c - x j e | is divisible by k j q kjqkjq kjqkjq kjqkjq

15. 15 The Proposed Scheme (embedding) Move x j e to x j ’ for embedding w i and h i (=h(w i )) kjqkjq kjqkjq kjqkjq

16. 16 The Proposed Scheme ) The Proposed Scheme (The causality problem ～ The “adjusting vertex” method ) The barycenters (x 2 and x 3 ) of a former processed vertex will be changed when any of its neighboring vertices was selected to be a mark vertex too and need to be perturbed. For each chosen mark vertex, we randomly assign an adjusting vertex from its neighboring vertices. The function of the adjusting vertex is to keep the barycenters of the mark vertex unchanged. To avoid the causality problem, the neighboring vertices of the previously selected mark vertices can’t be taken as adjusting vertices for later mark vertices.

17. 17 The Proposed Scheme ( co) The Proposed Scheme (the convergence problem) Most 3D fragile watermarking embedding schemes perturb the positions of a subset of vertices to keep them in some predefined relationship with their neighboring vertices. The convergence problem arises when the original model has been heavily distorted before some vertices reach the predefined relationship. The use of the “adjusting vertex” method guarantees that there is no endless perturbing while embedding watermarks; thus there is no convergence problem in the proposed method.

18. Watermarked mesh M ’ Watermark embedding Watermark extraction

19. 19 The Proposed Scheme (extraction) For each vertex, check its x 1 to see if it is a mark vertex For each mark vertex, –Extract w ’ from x 2 –Extract h ’ from x 3 –If h(w ’ ) ≠h ’, set the vertex and all its neighbors as suspicious vertices Report all the suspicious vertex

20. Detect and locate the modification

21. Distortion control kjqkjq kjqkjq kjqkjq

22. 22 Distortion control The smaller the values of k w and k q s are, the smaller the distortion is. d<10 -3 K w =10 -3 K q =10 -3.5 (vs. PSNR)

23. 23 The watermark digest method (invariant) WD: w m : the indices of the mark vertices w p : the required perturbing displacements

24. 24 Experimental Results

25. 25 Conclusions 1.The traverse order is not needed in the watermark extraction stage. 2.The adjusting vertex method can effectively limit the distortion ratio caused by watermark embedding. 3.Different functions are defined for the three coordinates of vertices. 4.The average distortion of the marked models is under user control. 5.The proposed scheme can detect and locate all unauthorized modifications. 6.The proposed scheme is public and a relative small key is needed for the watermark extraction. 7.The watermark digest method is proposed.

26. 26 1999, IEEE Computer Graphics and Applications, Watermarking 3D Objects for Verification, Boon-Lock Yeo and Minerva M. Yeung 2004, LNCS 2939, Authentication of 3-D Polygonal Meshes, Hsueh-Yi Lin, Hong-Yuan Mark Liao, Chun-Shien Lu and Ja- Chen Lin 2005, IEEE TRANSACTIONS ON MULTIMEDIA, Fragile Watermarking for Authenticating 3-D Polygonal Meshes, Hsueh- Yi Sean Lin, Hong-Yuan Mark Liao, Chun-Shien Lu, and Ja-Chen Lin 2005, International Multimedia Conference Proceedings of the 7th workshop on Multimedia and security, A fragile watermarking scheme for 3D meshes, Hao-Tian Wu, Yiu-Ming Cheung 2006, Computer-Aided Design, A public fragile watermarking scheme for 3D model authentication, Chang-Min Chou, Din- Chang Tseng 2007, IJCSNS, Technologies for 3D Model Watermarking: A Survey, Chang-Min Chou and Din-Chang Tseng

27. 27 Information Hiding – Simple Classification for 3D Models Lin 2005 Chou 2006 Transform domain?

28. 28 The scheme is not suitable for those models with flat surfaces. Those models cannot tolerate a small distortion. –Improve it or the phenomenon cannot be avoided. (compare with other schemes) –Perhaps, it raised by few adjusting vertices. Average them to all vertices not qualified as mark vertices. Combine some proposed schemes (proposed in this paper and that was reported last time) to develop an invertible fragile watermarking scheme. To develop a Semi-fragile watermarking scheme which is immune to affine transformation. … Read some outstanding 2d wmk schemes, usage, constrains Read more robust, transform domain, hiding schemes