Prediction-Based Reversible Data Hiding

Prediction-Based Prediction-Based Reversible Data HidingReversible Data Hiding

Source: Information Sciences, vol. 179, no. 14, pp. 2460-2469, 2009.Authors: Hsien-Wen Tseng and Chi-Pin HsiehSpeaker: Chia-Chun Wu (吳佳駿 )Data: 2010/01/08

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OutlineOutlineIntroductionThe Proposed SchemeExperimental ResultsConclusions

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IntroductionIntroductionReversible data hiding

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Cover image

Secret data: 0101…

Public channel(Ex: Internet)

Stego-image

SenderSender InterceptorInterceptor

ReceiverReceiver

Secret data: 0101…

Cover image

The Proposed Scheme The Proposed Scheme (1/5)(1/5)

Embedding Algorithm◦ Side-match

prediction

2

)1,(),1(),(ˆ

yxpyxpyxp

),(),(ˆ yxpyxpd

4

24 36ˆ (2,2) 30

2

30 33 3

p

d

3336

2431(2,2) 33p

Predicted value

Pixel value

Prediction error

Stego pixel value

The Proposed Scheme The Proposed Scheme (2/5)(2/5)

Embedding Algorithm◦ Predefined threshold T

2/:3

2/:2

2/:1

TTdCase

TTdTCase

TdTCase

2/T T

Embedding secret bits

Pixel shifting

2/TT

Case 1 Case 2 Case 3

T2

TdCase

TdTCase

TdTCase

2':3

'2/:2

2':1

Extracting secret bits & recovery

Pixel shifting5

The Proposed Scheme The Proposed Scheme (3/5)(3/5)

Example of embedding procedure (Case 1)

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ˆ( , ) 33, ( , ) 30

30 33 3, 1

T

p x y p x y

d W

32/ T 5T / 2 7T T 102 T

[3,4] [5,6] [7,255]

d=3

ˆ ˆ( , ) 2 , if ( , ) ( , )'( , )

ˆ ˆ( , ) 2 , if ( , ) ( , )

p x y d W p x y p x yp x y

p x y d W p x y p x y

'( , ) 30 7 37

' 2 7

p x y

d d W

d'=7

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33362431

The Proposed Scheme The Proposed Scheme (4/5)(4/5)

Example of shifting procedure (Case 2)

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ˆ( , ) 38, ( , ) 32

32 38 6

T

p x y p x y

d

32/ T 5T / 2 7T T 102 T

[3,4] [5,6]

d=6

ˆ( , ) / 2 , if ( , ) ( , )'( , )

ˆ( , ) / 2 , if ( , ) ( , )

p x y T p x y p x yp x y

p x y T p x y p x y

'( , ) 38 2 36

' / 2 4

p x y

d d T

d'=4

7

[7,255]

38362831

The Proposed Scheme The Proposed Scheme (5/5)(5/5)

Example of shifting procedure (Case 3)

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ˆ( , ) 38, ( , ) 30

30 38 8

T

p x y p x y

d

32/ T 5T / 2 7T T 102 T

[3,4] [5,6]

d=8

ˆ( , ) / 2 , if ( , ) ( , )'( , )

ˆ( , ) / 2 , if ( , ) ( , )

p x y T p x y p x yp x y

p x y T p x y p x y

'( , ) 38 3 41

' / 2 11

p x y

d d T

d'=11

8

[7,255]

38362431

Overflow and UnderflowOverflow and Underflow

91 1001007

K=1 0+1=1 7-1=6

The Experimental Results The Experimental Results (1/5)(1/5)

Three test images

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1. Side Match

2. Horizontal Predictor

3. Vertical Predictor

4. Causal Weighted Average

5. Causal SVF

The Experimental Results The Experimental Results (2/5)(2/5)

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ˆ1. Horizontal Predictor: ( , ) ( 1, )

ˆ2. Vertical Predictor: ( , ) ( , 1)

3. Causal Weighted Average:

ˆ ( , ) [2 ( 1, ) 2 ( , 1) ( 1, 1) ( 1, 1)] 6

4. Causal SVF:

( , ) [ ( 1, ) ( ,

p x y p x y

p x y p x y

p x y p x y p x y p x y p x y

Avg x y p x y p x y

1

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1

1) ( 1, 1) ( 1, 1)] 4

( 1, ) ( 1, ) ( , 1) ( , 1)ˆ ( , )

( 1, ) ( , 1)

( , ) exp( ( ( , ) ( , ) ),

where is the controlling factor.

n

n

p x y p x y

p x y n w x y n p x y w x yp x y

w x y n w x y

w x i y j abs p x i y j Avg x y f

f

The Experimental Results The Experimental Results (3/5)(3/5)

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Table 6. Experimental results of predictors.

The Experimental Results The Experimental Results (4/5)(4/5)T=2

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[17] S. K. Yip, O. C. Au, H. M. Wong, C. W. Ho, “Generalized lossless data hidingby multiple predictors,” ISCAS 2006, pp. 21-24, May 2006.

Table 7. Comparisons between the proposed method and Yip et al.’s scheme.

The Experimental The Experimental Results Results (5/5)(5/5)Compare the proposed scheme with that of

Tian [14] and Celik [2] using grayscale image Lena◦ The propsoed scheme

T=2 Capacity 0.220 bpp PSNR 47.31dB

◦ Tian’s scheme Capacity 0.151 bpp PSNR 44.20dB

◦ Celik et al’s scheme Capacity 0.180 bpp PSNR 40.5dB

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ConclusionsConclusionsA high capacity and low distortion

reversible data hiding technique using prediction error expansion is proposed.

The correlation between the pixel and its neighboring pixels is considered to perform the difference expansion and the secret bit is embedded in difference.

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