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

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

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

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 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 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 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 Polygonal Model Vertex, or point Edge

9 Point-Sampled Geometry No edge information

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

11 Embedding

12 Sorting Points for Each Axis

13 Interval Interval : State 3

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 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 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 * = 1 (10) Left shift r = 0  λ = X n +1 – X n

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

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 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 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 Extraction

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

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

points points points points

26 Experimental Results Cover Number of points Data capacity (bits) RMS ratio PCA execution time (seconds) Embedding execution time (seconds) Extraction execution time (seconds) Dinosaur x Horse x Bunny x Venus x

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 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 )

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 嵌入流程 ~ 訊息嵌入

31 嵌入流程 ~ 訊息嵌入

32 嵌入流程 ~ 訊息嵌入 Embed 1 Embed 0

33 嵌入流程 ~ 訊息嵌入

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