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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
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Outline
Introduction Reversible Data Hiding Point-Sampled Geometry Proposed scheme Conclusions Comments
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Reversible Information Hiding Scheme~Embedding (1/2)
Embedding
Payload
Secret Key
CoverModel
StegoModel
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Reversible Information Hiding Scheme~Extraction (2/2)
Secret Key
RecoveredPayload
ExtractionStegoModel
RecoveredModel
Reversibility : can exactly recover the original model
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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
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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
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3D Models Representation
Polygonal models Point-sampled geometries Parametric surfaces, e.g. non-uniform ratio
nal B-spline surfaces (NURBS) Constructive solid geometry (CSG) Voxels Motion data
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Polygonal ModelVertex, or point
Edge
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Point-Sampled Geometry
No edge information
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The proposed scheme
Embedding model Stego
modelcover and
payload Recovered
modelcover of
centergravity
and axes X-Y-Z
keySecret
Payload
modelCover
model stego
AttackedExtractiononRegistrati
model
Stego
model stego of
centergravity
and axes X-Y-Z
model stego
of volumebounding
theoflength axis-X
Require one integer and 25 floating points of memory
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Embedding
Construct PCA-coordinate
system
Coordinate translation
Sorting for each axis
Embedding data
1.
2.
3.
4.
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Sorting Points for Each Axis
1X
1P
axis-X
1mP
mP
2P
2X 1mX mX
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Interval
axisXIntervalnX 2nX
nP 2nP
0 1 2 3 1i2i
Interval :
state-i
1np
State 3
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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 2c+1.
2 intervalsr=0 r=1
2c intervals 2c intervals
2c+1 intervals
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Embedding d (c bits) into the interval, the new state
The new X-coordinate value of Pn+1 is
r = 0 λ= Xn+1 – Xn
nX 2nX
nP 2nP
Interval
1nP
1nX
0 1nX 2nX
nP
2nP
Interval
1nP
1nX
0 1
r = 1 λ= Xn+1 - (Xn+Xn+2)/2
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Embed a Bit into the Interval
Secret key : generate a random sequence of intervals
State: r=0
Embed a Bit 1 (c=1)
nX 2nX0 1 2 3
nP
2nP
Interval
1nP
1nX
2
nX 2nX
nP
2nP
Interval
1nP
1nX
0 1
Before embedding After embedding
Reversibility
New state ---------->s = 01(2) = 2 * 0 + 1 = 1(10)Left shift
r = 0 λ= Xn+1 – Xn
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nX 2nX
nP 2nP
Interval
1nP
1nX
nX 2nX
nP 2nP
Interval
1nP
2
1nX
0 1 0 1 2 3
Before embedding After embedding
Embed a Bit into the Interval
State:r = 1Embed a Bit 0
New state ----------> 10(2)
= 2 * 1 + 0 = 2
(10)Left shift
r = 1 λ= Xn+1 - (Xn+Xn+2)/2
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Embedding model Stego
keySecret
Payload
modelCover
modelcover and
payload Recovered
modelcover of
centergravity
and axes X-Y-Z
model stego
AttackedExtractiononRegistrati
model
Stego
model stego of
centergravity
and axes X-Y-Z
model stego
of volumebounding
theoflength axis-X
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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 th
e attacked stego model Scale the attacked stego model so that the X-axis lengt
h of the scaled model is equal to the X-axis length of the stego model
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Registration
X
Z Y
Stego model
Attacked stego model
Registration
PCAattacked -----> PCAstego
Coordinatetranslation
Attacked model ----> Stego modelScaling
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
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Extraction
Coordinate translation
Sorting for each axis
Extraction data
Three PCA axes and centroid of 3D cover model
1.
2.
3.
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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
2nn XX
1nX
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nX 2nX
nP 2nP
Interval
1nP
2
1nX
0 1 2 3
Extraction
State = 2(10)
=
10(2)
A bit 0 has been previously embedded
Original state = 1
λ
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Data Capacity
Model : m points Each axis : m/2 intervals
Capacity = 3*m/2 bits= 1.5m bits
Time complexity : )log(O mm
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56194points
48485points
35947points
33591points
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Experimental Results
CoverNumber of
points
Data capacity
(bits)
RMSratio
PCA execution
time (seconds)
Embedding execution
time (seconds)
Extraction execution
time (seconds)
Dinosaur 56194 83976 2.99 x 10-6 0.047 0.156 0.032
Horse 48485 72456 3.78 x 10-6 0.047 0.094 0.032
Bunny 35947 53862 5.26 x 10-6 0.032 0.078 0.031
Venus 33591 50310 5.26 x 10-6 0.032 0.078 0.016
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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
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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 )
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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
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嵌入流程 ~訊息嵌入
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嵌入流程 ~訊息嵌入
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嵌入流程 ~訊息嵌入
Embed 1
Embed 0
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嵌入流程 ~訊息嵌入
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