### Capacity-Approaching.. - 14th Information Hiding Conference

```Capacity-Approaching Codes for Reversible
Data Hiding
Weiming Zhang, Biao Chen, and Nenghai Yu
Department of Electrical Engineering & Information Science
University of Science and Technology of China
Information Hiding Conference 2011
Introduction
What is reversible data hiding?
The original cover can be losslessly restored after the
embedded information is extracted.
message
cover
data
embedding
stego
data extraction
&
cover restoration
message
cover
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Introduction
What is reversible data hiding?
The original cover can be losslessly restored after the
embedded information is extracted.
Why is reversible data hiding needed?
In some applications, even any degradation of the
original cover is not allowed, such as medical imagery,
military imagery and law forensics.
Where is reversible data hiding applied?
Media annotation;
integrity authentication ...
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Introduction
How to do reversible data hiding?
Type-I: Binary feature sequence, generic compression
method (e.g., arithmetic coder);
Type-II: Integer operations: Difference Expansion (DE) or
Histogram Shifting (HS)— specific compression manner for
the histogram
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Introduction
Type-I: Basic model [Kalker]
d modifications
Embedding rate:
Distortion:
How to maximize embedding rate under any given distortion?
A rate-distortion problem
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Introduction
Theoretical upper bound [Kalker]
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Introduction
Recursive Code construction [Kalker]
Key idea:
the marked cover can be used to reconstruct the cover
H ( x1 )
H ( x1 | y1 )
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Two observations
Observation I
Not only the marked cover can be used to reconstruct the
cover, but also the reconstructed cover can help to extract
message.
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Two observations
Observation II
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Two observations
Observation II
The maximum capacity is achieved at D=p0－1/2;
 When D≤p0－1/2, the optimal embedding manner is that
only 0’s are allowed to be changed. (Corollary 1 of Theorem 2,
[Kalker])
Our strategy:
Only embed data into 0’s and skip 1’s;
At the decoder side, the embedding positions can be
recognized with the help of reconstructed cover.
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How to embed data into all-zero cover
RZL coding (reverse zero-run length) [Wong]
Message is divided into disjoint segments of k bits, each of which
is converted to a integer d∈[0,2k-1]; skip d zeros in the cover,
and flip the (d+1)th zero.
Our method: improve RZL by the idea of ZZW construction
A construction consists of two layers:
The outer layer: only embed one bit;
The inner layer: when embedding bit “1” in the outer layer,
embed another k bits with RZL; otherwise skip 2k zeros.
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How to embed data into all-zero cover
Example: k = 2
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How to embed data into all-zero cover
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Proposed method
Improved recursive construction
Improved coding for all-zero cover
x1 :
y1:
0
0
1
1
1
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Proposed method
Example 2 (follows Example 1)
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Comparison: Embedding efficiency vs. embedding rate
Embedding efficiency e is defined as number of bits embedded
by unit distortion, i.e. e=ρ/Δ=L/d.
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Comparison: Embedding efficiency vs. embedding rate
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Improving Type-I Schemes
(embedding in binary feature sequences)
1. Improving RS method for spatial images [Fridrich]
Texture
complexity of
pixel blocks is
used to construct
binary feature
sequence.
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Improving Type-I Schemes
1. Improving RS scheme for spatial images [Fridrich]
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Improving Type-I Schemes
2. Improving the scheme for JPEG images [Fridrich]
quantized DCT
coefficients
with value 0
and 1 are used
as binary feature
sequence.
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Improving Type-I Schemes
2. Improving the scheme for JPEG images [Fridrich]
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Improving Type-I Schemes
3. Improving PS scheme for binary images [Ho]
Test images
Patterns of 4length vector in
difference image are
used as binary
sequence.
Y.-A. Ho, et al., ``High capacity reversible data hiding in binary images using
pattern substitution,” Computer Standards and Interfaces, 2009.
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Improving Type-I Schemes
3. Improving PS scheme for binary images
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Improving Type-I Schemes
3. Improving PS scheme for binary images
Embed 260 bits
(a) Marked by PS
(b) Marked by improved PS
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Improving Type-II Scheme
Improving HS-based scheme for spatial images [Luo]
The proposed codes is used at the second embedding stage.
Extension by embedding with two bins.
L. X. Luo, et al., ``Reversible Image Watermarking Using Interpolation
Technique," IEEE Trans. Inf. Forensics and Security, 2010.
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Improving Type-II Schemes
3. Improving HS-based scheme for spatial images
(a) Lenna
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Improving Type-II Schemes
3. Improving HS-based scheme for spatial images
(b) Baboon
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Improving Type-II Schemes
3. Improving HS-based scheme for spatial images
(c) Boat
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Conclusion:
• An improved coding method for all-zero cover
• An improved recursive construction
• A reversible data hiding method for binary cover
Future work:
Integer-domain reversible data hiding
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