1. Reversible Data Hiding for Point-Sampled Geometry JOURNAL OF INFORMATION SCIENCE AND ENGINEERING Vol. 23, pp.1889-1900, 2007 PENG-CHENG WANG AND CHUNG-MING WANG Reporter: 陳德祐 2008/2/22

2. 2 Outline Introduction Reversible Data Hiding Point-Sampled Geometry Proposed scheme Conclusions Comments

3. 3 Reversible Information Hiding Scheme~Embedding (1/2) Embedding Payload Secret Key Cover Model Stego Model

4. 4 Reversible Information Hiding Scheme~Extraction (2/2) Secret Key Recovered Payload Extraction Stego Model Recovered Model Reversibility : can exactly recover the original model

5. 5 Classification of Information Hiding Spatial domain  Embed directly information in the spatial domain Geometry : coordinates of points Topology : connectivity among points Appearance attributes : color, normal, texture coordinate Transform domain  Exploit domain properties for information hiding DCT: Discrete Cosine Transform DFT: Discrete Fourier Transform DWT: Discrete Wavelet Transform

6. 6 Requirements of Data Hiding Security  Any data hiding approach must be secure Capacity  The amount of payload as large as possible Robustness  Robustness against various attacks has been less important, because the goal is hide a secret message  Light robustness, such as translation, rotation, and uniform scaling Imperceptibility  Embedding process must be without loss of perceptual quality of the cover model

7. 7 3D Models Representation Polygonal models Point-sampled geometries Parametric surfaces, e.g. non-uniform rational B-spline surfaces (NURBS) Constructive solid geometry (CSG) Voxels Motion data

8. 8 Polygonal Model Vertex, or point Edge

9. 9 Point-Sampled Geometry No edge information

10. 10 The proposed scheme Require one integer and 25 floating points of memory

11. 11 Embedding 1. 2. 3. 4.

12. 12 Sorting Points for Each Axis

13. 13 Interval Interval : State 3

14. 14 Each interval is considered an i-state object.  Prior to data embedding, the i is set to 2.  Embedding d (c bits) into each interval, the i is changed from two to 2 c+1. 2 intervals r=0r=1 2 c intervals 2 c+1 intervals

15. 15 Embedding d (c bits) into the interval, the new state The new X-coordinate value of P n+1 is r = 0  λ = X n +1 – X n n X 2  n X n P 2  n P Interval 1  n P 1  n X 0 1 n X 2  n X n P 2  n P Interval 1  n P 1  n X 01 r = 1  λ= X n +1 - ( X n +X n+2 )/2

16. 16 Embed a Bit into the Interval Secret key : generate a random sequence of intervals State: r =0 Embed a Bit 1 (c=1) Reversibility New state ---------->s = 01 (2) = 2 * 0 + 1 = 1 (10) Left shift r = 0  λ = X n +1 – X n

17. 17 Embed a Bit into the Interval State:r = 1 Embed a Bit 0 New state ----------> 10 (2) = 2 * 1 + 0 = 2 (10) Left shift r = 1  λ= X n +1 - ( X n +X n+2 )/2

18. 18 Embedding model Stego keySecret Payload modelCover modelcover and payload Recovered modelcover of centergravity and axes X-Y-Z model stego Attacked Extraction onRegistrati model Stego model stego of centergravity and axes X-Y-Z model stego of volumebounding theoflength axis-X

19. 19 Registration Correct the attacks of translation and rotation  Compute the 3 principal axes and gravity center of the attacked stego model  Translate the coordinates of the attacked stego model to its PCA-coordinate system  Translate the coordinates of the attacked stego model to the PCA-coordinate system of the stego model using the 3 principal axes and gravity center of the stego model Correct the attacks of uniform scaling  Compute the X -axis length of the bounding volume of the attacked stego model  Scale the attacked stego model so that the X -axis length of the scaled model is equal to the X -axis length of the stego model

20. 20 Registration X Z Y Stego model Attacked stego model Registration PCA attacked -----> PCA stego Coordinate translation Attacked model ----> Stego model Scaling Compute PCA axes and centroid of attacked stego model Given PCA axes and centroid of stego model Compute X-axis length of the bounding box of attacked stego model Given X-axis length of the bounding box of stego model

21. 21 Extraction 1. 2. 3.

22. 22 Extraction Find a sequence of intervals by the secret key, e.g. Extract a data bit from the interval by the X - coordinate value Restore the original X -coordinate value Repeat these steps for all the intervals

23. 23 Extraction State = 2 (10) = 10 (2) A bit 0 has been previously embedded Original state = 1 λ

24. 24 Data Capacity Model : m points Each axis : m/2 intervals Capacity = 3*m/2 bits= 1.5m bits Time complexity :

25. 25 56194 points 48485 points 35947 points 33591 points

26. 26 Experimental Results Cover Number of points Data capacity (bits) RMS ratio PCA execution time (seconds) Embedding execution time (seconds) Extraction execution time (seconds) Dinosaur56194839762.99 x 10 -6 0.0470.1560.032 Horse48485724563.78 x 10 -6 0.0470.0940.032 Bunny35947538625.26 x 10 -6 0.0320.0780.031 Venus33591503105.26 x 10 -6 0.0320.0780.016

27. 27 Conclusions The first ones to propose reversible data hiding algorithms for point-sampled geometry Improvement on the capacity Using little information to recover the original model Robustness against translation, rotation, and uniform scaling

28. 28 Comments Improve the capacity: 1.5m bits  3m bits  除 1st 不藏外，其他各點可依序 ( 亦可不依序 ) 藏 入 1 bit Distortion vs. capacity The capacity is high, but the scheme is not really reversible! (Euclidean distance  truncation error )

29. 可逆的向量地圖 資料隱藏演算法 第十七屆全國資訊安全會議 2007 ISC

30. 30 嵌入流程 ~ 訊息嵌入

31. 31 嵌入流程 ~ 訊息嵌入

32. 32 嵌入流程 ~ 訊息嵌入 Embed 1 Embed 0

33. 33 嵌入流程 ~ 訊息嵌入

34. 34