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Reversible data hiding for high quality images using

modification of prediction errors

Source: The Journal of Systems and Software, In Press, Corrected Proof, Available online 3 June 2009

Authors: Wien Hong, Tung-Shou Chen, and Chih-Wei ShiuPresenter: Chia-Chun WuDate: September 4, 2009

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OUTLINE

• INTRODUCTION

• RELATED WORKS

• PROPOSED SCHEME

• EXPERIMENTAL RESULTS

• CONCLUSIONS

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要解決的問題

• 此篇論文主要是利用相鄰像素值非常相近的特性，以周圍相鄰的像素值來對要進行隱藏的像素值先進行預測的動作，並計算預測值跟實際值的差值，接著結合 Ni等人提出來的直方圖無失真資料隱藏的方法，藉由調整預測誤差值來達到達到高容量、低失真的無失真資料隱藏的目的。

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INTRODUCTION (1/3)

Reversible data hiding(Lossless Data Hiding)

Modification of Prediction Errors (MPE)

Cover Image

Secret Data

LosslessEmbedding Stego-image

Stego-image LosslessExaction

LosslessCover Image

Secret Data

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INTRODUCTION (2/3)

• Reversible data hiding (Lossless Data Hiding)

• Application:– medical images, military photos, law

enforcement

• Challenges:– Capacity– Quality

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INTRODUCTION (3/3)

• Reversible data hiding schemes: – Difference expansion

• Reversible data embedding using a difference expansion, Jun Tian, IEEE Transactions on Circuits and Systems for Video Technology, vol. 13, no. 8, pp. 890 – 896, Aug. 2003

• Reversible watermark using the difference expansion of a generalized integer transform, Alattar, A.M. IEEE Transactions on Image Processing, vol. 13, no. 8, pp. 1147 - 1156, Aug. 2004

• Adaptive lossless steganographic scheme with centralized difference expansion, C.C. Lee, H.C. Wu, C.S. Tsai, and Y.P. Chu, Pattern Recognition, vol. 41, no. 6, pp. 2097-2106, 2008

– Histogram modification • Reversible data hiding, Z. Ni, Y.Q. Shi, N. Ansari, and W. Su, IEEE

Transactions on Circuits and Systems for Video Technology, vol.16, no.3, pp. 354 – 362, March 2006

• Hiding Data Reversibly in an Image via Increasing Differences between Two Neighboring Pixels, C.C. Lin and N.L. Hsueh, IEICE Transactions on Information and Systems, vol. E90–D, no.12, Dec. 2007

• A lossless data hiding scheme based on three-pixel block differences, C.C. Lin and N.L. Hsueh, Pattern Recognition vol. 41, no. 4, pp. 1415 – 1425, April 2008

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RELATED WORKS (1/3)

5 6 5 6 7

5 6 6 6 5

2 3 5 6 2

1 3 1 0 2

1 2 3 3 2

Histogram ofpixel values

Peak pointZero point

4 6 4 5 7

4 6 6 5 4

2 3 4 5 2

1 3 1 0 2

1 2 3 3 2

Original image

Stego image

Secret data embedding

101100unchanged

5 6 5 6 7

5 6 6 6 5

2 3 5 6 2

1 3 1 0 2

1 2 3 3 2

101100

Ni et al.’s method

Extracting

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min( , ) if max ,

max , if min ,

otherwise,i

a b c a b

p a b c a b

a b c

204 205

203 202

Thodi and Rodriguez’s method

Predicted value xi’ = 2 × pi / 2

Prediction error ei between xi and xi’ ei = xi – xi’Expanded prediction error Ei = 2 × ei + sj

a = 203, b = 205, c = 204, xi = 202

xi’ = 2 × 204 / 2 = 204

ei = xi – xi’= -2

If secret bit sj = 1, Ei = 2 × ei + sj = -3Stego-pixel

yi = xi’ + Ei. ( or yi = xi + ei + sj) yi = 204 + (-3) =201

pi = 204

RELATED WORKS (2/3)

c b

a xi

Embedding phase

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204 205

203 201

Thodi and Rodriguez’s method

Secret bit sj = LSB(yi),

yia

bc

yia

bc

sj = LSB(yi) = LSB(201) = 1Predicted value yi’ = 2 × pi’ / 2

Expanded prediction error Ei = yi – yi’

Prediction error ei = Ei / 2

xi = yi’ + ei (or xi = yi – ei – sj).

min( , ) if max ,

max , if min ,

otherwise,i

a b c a b

p a b c a b

a b c

yi’ = 2 × 204 / 2 = 204

pi’ = 204

Ei = 201 – 204 = -3

ei = -3/ 2 = -2

xi = 204 + (-2) = 202

RELATED WORKS (3/3)

Extracting phase

a = 203, b = 205, c = 204, yi = 201

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PROPOSE SCHEME (1/6)

More suitable

Histograms of prediction errors and histogram of pixels in the spatial domain for images Lena and Baboon.

11Embedding phase

PROPOSE SCHEME (2/6)

min( , ) if max ,

max , if min ,

otherwise,i

a b c a b

p a b c a b

a b c

Prediction error ei = xi – pi.

c ba x

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154 156 153 153

154

154

151

'1,1 1 157I p e

'1,2 1 149I p e

154 156 153 153

154 156 150 148

154 157 157 157

151 158 157 155

e1 = x1 – p1 = 0 : embeddable e = e + 1 = 1

c ≤ min (a, b) → p1 = 156

Secret = 1012

Original image IStego image I’

154 156

154

e2 = x2 – p2 = -4 : non-embeddable e2 = e2 – 1 = -5

p2 = 154

p5 = 150e5 = x5 – p5 = 7, all secret bits are embedded, set L=(2,2)

'2,2 5 157I p e

157 149

153156

157 148

158 157 157

158 157 155

PROPOSE SCHEME (3/6)

stoppinglocation L

13Extracting phase

PROPOSE SCHEME (4/6)

min( , ) if max ,

max , if min ,

otherwise,i

a b c a b

p a b c a b

a b c

Prediction error ei = xi – pi.

c ba x

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154 156 153 153

154

154

151

154 156 153 153

154 157 149 148

154 158 157 157

151 158 157 155

Original image IStego image I’

'' '1,1 1 156I p e

e1 = x1’ – p1’ = 1: secret bit = 1e = e - 1 = 0

c ≤ min (a, b) → p1’ = 156

156

'' '1,2 2 154 ( 4) 150I p e

e2 = x2’ – p2’ = -5: no secret bite = e + 1 = -4

p2’ = 154

154 156

154 150

156 153

157

153 153

149

'' '1,3 3 149 ( 1) 148I p e

e3 = x3’ – p3’ = -1: secret bit = 0

p3’ = 149

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PROPOSE SCHEME (5/6)

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154 156 153 153

154

154

151

154 156 153 153

154 157 149 148

154 158 157 157

151 158 157 155

Original image IStego image I’

'' '1,1 4 157I p e

e1 = x1’ – p4’ = 1: secret bit = 1e = e - 1 = 0

c ≤ min (a, b) → p4’ = 157

156 150 148154 157

154 157

157 149

158

'' '2,2 5 157I p e

e1 = x1’ – p5’ = 7L =(2,2): all embedded message has been extracted

p5’ = 150

157 157

158 157 155

PROPOSE SCHEME (6/6)

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EXPERIMENTAL RESULTS (1/6)

Experimental results of some commonly used images

pure payload of MPE - pure payload of Ni et al. methodIncreased payload

pure payload of Ni et al. method

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EXPERIMENTAL RESULTS (2/6)

Comparison of PSNR with same embedding capacity

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EXPERIMENTAL RESULTS (3/6)

Experimental results for 23 natural photographic test

images sized 768 × 512 (payload is measured in bits).

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EXPERIMENTAL RESULTS (4/6)

Experimental results for test images

20Capacity versus distortion performance of various methods for test images

EXPERIMENTAL RESULTS (5/6)

21Capacity versus distortion performance of various methods for test images

EXPERIMENTAL RESULTS (6/6)

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CONCLUSIONS

• The embedding capacity of proposed

scheme is much higher than that of Ni et al.’s

method.

• The visual quality of the proposed method is

better than that of Thodi’s method.

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此篇論文之優缺點

• 優點：– 因為一般影像而言，統計完預測誤值的結果後， Peak bin

的 index 都是 0 ，因此，跟 Ni. 等人的方法比起來，此方法不需額外記錄 Zero bin 及 Peak bin 的資訊。

– Ni. 等人的方法的方法，不論要藏入的資料量多大，整張影像中每個像素值都會被修改變動到，此方法利用 Stopping Location L來記錄 Secret Data 最後藏完時的座標位址，在這座標之後的像素值就完全不做任何修改或變動，來降低影像失真的程度。

• 缺點：– 跟 Ni. 等人的方法比起來，此方法要額外記錄及傳送

Stopping Location L的資訊給接收端。

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研究方向

• 本方法是藉由相鄰的 3 個像素值來進行預測的動作，若額外多考慮相鄰 1 個像素值的情況下或是利用其它預測的方法，也許可以提高預測的準確度，當預測的準確度愈高的情況下， Peak bin 就愈集中在 0 的地方，相對的最大可以隱藏的資料量就會提高 (Peak bin 的數量決定隱藏量的大小 ) 。