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

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What is reversible data hiding?

The original cover can be losslessly restored after the embedded information is extracted.

Introduction

messagestego

cover

data embedding

data extraction &

cover restoration cover

message

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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.

Introduction

Where is reversible data hiding applied?

Media annotation;integrity authentication ...

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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

Introduction

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IntroductionType-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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Recursive Code construction [Kalker]

Key idea: the marked cover can be used to reconstruct the cover

1( )H x1 1( | )H x y

Introduction

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Observation INot only the marked cover can be used to reconstruct the cover, but also the reconstructed cover can help to extract message.

Two observations

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Two observations

Observation II

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Observation IIThe 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.

Two observations

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RZL coding (reverse zero-run length) [Wong]

How to embed data into all-zero cover

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.

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.

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Example: k = 2

How to embed data into all-zero cover

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How to embed data into all-zero cover

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Proposed method

Improved coding for all-zero cover

Improved recursive construction

x1: 0 1

y1: 0 1 1

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Example 2 (follows Example 1)

Proposed method

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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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2. Improving the scheme for JPEG images [Fridrich]

Improving Type-I Schemes

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3. Improving PS scheme for binary images [Ho]

Patterns of 4-length 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.

Test images

Improving Type-I Schemes

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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]

L. X. Luo, et al., ``Reversible Image Watermarking Using Interpolation Technique," IEEE Trans. Inf. Forensics and Security, 2010.

The proposed codes is used at the second embedding stage.Extension by embedding with two bins.

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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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Future work:Integer-domain reversible data hiding

Conclusion:

• An improved coding method for all-zero cover• An improved recursive construction • A reversible data hiding method for binary cover

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Thank you for your attention!