(k, n)-Image Reversible Data Hiding

(k, n)-Image Reversible Data Hiding
指導教授：張真誠博士洪國寶博士學　　生：黃英軒

Magic Matrix- Embedding
Cover pixel: 5 Secret data: 7 Stego pixel (the first image): 3 Stego pixel (the second image): 7

Magic Matrix- Extraction and Recovery
Stego pixel (the first image): 3 Stego pixel (the second image): 7 Secret data: 7

Experimental Results- Lena
C. Qin, C. C. Chang, and L. T. Liao, “An adaptive prediction-error expansion oriented reversible information hiding scheme,” Pattern Recognition Letters, vol. 33, no. 16, pp , 2012. C. F. Lee and H. L. Chen, “Adjustable prediction-based reversible data hiding,” Digital Signal Processing, vol. 22, no. 6, pp , 2012. H. W. Tseng and C. P. Hsieh, “Prediction-based reversible data hiding,” Information Sciences, vol. 179, no. 14, pp , 2009. C. F. Lee, H. L. Chen, and H. K. Tso, “Embedding capacity raising in reversible data hiding based on prediction of difference expansion,” Journal of Systems and Software, vol. 83, no. 10, pp , 2010. W. L. Tai, C. M. Yeh, and C. C. Chang, “Reversible data hiding based on histogram modification of pixel differences,” IEEE Transactions on Circuits and Systems for Video Technology, vol. 19, no. 6, pp , 2009. C. F. Lee and Y. L. Huang, “Reversible data hiding scheme based on dual stegano-images using orientation combinations,” Telecommunication Systems, vol. 52, pp , 2013.

Experimental Results- Baboon

Experimental Results F-16 Boat Barbara Tiffany

Analysis Advantage Disadvantage High embedding rate (1.55 bpp)
Good quality of the stego image (39.89 dB) Disadvantage If one of two stego images is lost, then the proposed method cannot extract secret data and recover the cover image.

Determine the embedding order 1 1 1 Cheating image Secret image Cheating image 1 1 1 Third embedded image First embedded image Second embedded image

Embedding rules If three secret bits are all 1, then modify the pixels in the first image and the last image. Otherwise, the cover pixel is increased directly by the secret bit. 1 1 1 First embedded image Second embedded image Third embedded image 5 7 8 5 4 5 5 6 Cover image First stego image Second stego image Third stego image 2 4 5 6

Embedding rules If three secret bits are all 1, then modify the pixels in the first image and the last image. Otherwise, the cover pixel is increased directly by the secret bit. 1 1 1 First embedded image Second embedded image Third embedded image 4 7 5 8 7 6 7 First stego image Second stego image Third stego image s = 1 7 8

Overflow and Underflow Problem
1 1 1 First embedded image Second embedded image Third embedded image 4 7 9 5 8 9 6 7 8 First stego image Second stego image Third stego image 2 -1 1 Underflow problem

Overflow and Underflow Problem
Solution Modify the pixels in the first and third images to discriminate between the embeddable pixel and non-embeddable pixel. 1 1 1 Cheating image Cheating image Secret image 4 7 9 5 8 9 6 7 8 3 First stego image Second stego image Third stego image 3

4 7 9 3 5 8 9 6 7 8 First stego image Second stego image Third stego image 1 1 1 First embedded image Second embedded image Third embedded image 5 Cover image 2 4 6

4 7 9 3 5 8 9 6 7 8 First stego image Second stego image Third stego image 1 1 1 1 First embedded image Second embedded image Third embedded image 7 5 Cover image s = 1 7 8

4 7 9 3 5 8 9 6 7 8 First stego image Second stego image Third stego image 1 1 1 First embedded image Second embedded image Third embedded image 5 7 8 Cover image 3

Experimental Results Image Hiding rate (bpp) PSNR (dB) SIQ-1 SIQ-2
Lena 1 51.14 Baboon 51.15 Barbara 51.13 Pepper Girl 51.12 Boat Goldhill Sailboat Tiffany Zelda Medical image 1 0.80 44.88 52.96 Medical image 2 0.84 45.78 52.71 Medical image 3 0.83 45.47 52.86 Medical image 4 0.79 44.79 53.46

Lena 1 51.14 52.39 Baboon 51.15 52.38 51.13 Barbara 52.40 51.12 Pepper Girl Boat 52.37 Goldhill Sailboat Tiffany Zelda Medical image 1 0.84 45.61 52.93 52.24 Medical image 2 0.92 47.67 51.84 Medical image 3 0.91 47.31 52.42 51.95 Medical image 4 0.89 46.91 52.14

Lena 1 51.13 51.74 51.71 Baboon 51.70 51.72 51.14 Barbara 51.73 Pepper Girl Boat 51.15 Goldhill Sailboat 51.12 Tiffany Zelda Medical image 1 0.86 46.07 52.24 52.22 51.93 Medical image 2 0.96 49.09 51.48 Medical image 3 0.95 48.65 51.75 51.54 Medical image 4 0.94 48.54 51.62

Lena 1 51.13 51.43 51.41 51.42 Baboon 51.12 51.15 Barbara Pepper 51.14 Girl 51.40 Boat Goldhill Sailboat Tiffany Zelda Medical image 1 0.87 46.27 51.93 51.94 51.78 Medical image 2 0.98 49.99 51.31 Medical image 3 0.97 49.49 51.45 51.46 51.34 Medical image 4 49.62 51.37

Experimental Results Lena Baboon
[18] C. F. Lee and H. L. Chen, “Adjustable prediction-based reversible data hiding,” Digital Signal Processing, vol. 22, no. 6, pp , 2012. [20] C. F. Lee, H. L. Chen, and H. K. Tso, “Embedding capacity raising in reversible data hiding based on prediction of difference expansion,” Journal of Systems and Software, vol. 83, no. 10, pp , 2010. [21] C. F. Lee and Y. L. Huang, “Reversible data hiding scheme based on dual stegano-images using orientation combinations,” Telecommunication Systems, vol. 52, pp , 2013. [29] Z. Ni, Y. Q. Shi, N. Ansari, and W. Su, “Reversible data hiding,” IEEE Transactions on Circuits and Systems for Video Technology, vol. 16, no. 3, pp , 2006. [40] H. W. Tseng and C. P. Hsieh, “Prediction-based reversible data hiding,” Information Sciences, vol. 179, no. 14, pp , 2009. [44] W. L. Tai, C. M. Yeh, and C. C. Chang, “Reversible data hiding based on histogram modification of pixel differences,” IEEE Transactions on Circuits and Systems for Video Technology, vol. 19, no. 6, pp , 2009.

Experimental Results Barbara Pepper

Robustness

Analysis Advantage High embedding rate (0.985 bpp)
Good quality of the stego image (50.48 dB) Great robustness

Reversible Hiding Scheme Based on Interpolation, Difference Expansion, and Histogram Shifting

Avoiding Overflow and Underflow Problems
160 161 157 158 156 150 149 148 255 160 155 150 253 Cover image Modified image Modification level: 2 Coordinates: (4, 4) 2 253 255 257

Embeddable pixel Reference pixel 160 161 157 158 156 150 149 148 253
155 150 Modification image Interpolation values Embeddable pixel 1 2 3 -1 -2 103 Reference pixel Interpolation errors

Histogram Generation Embeddable 1 2 3 -1 -2 103 Interpolation errors

Hiding spaces

Data Embedding 1 1 4 5 -1 -3 105 Secret bits: 1, 0, 0, 0, 1, 1, 1
1 1 4 5 -1 -3 105 Secret bits: 1, 0, 0, 0, 1, 1, 1 Embed “1” Interpolation errors Embed “0” Embed “0” Embed “1”

Data Embedding Stego image 1 2 4 5 -2 -3 -1 105 160 155 150
Interpolation errors Interpolation values 161 162 159 160 157 148 147 149 151 255 160 150 Stego image

Extraction and Recovery
160 155 150 160 161 162 159 157 150 148 147 149 151 255 Interpolation values Stego image Stego pixel 1 2 4 5 -2 -3 -1 105 Reference pixel Interpolation errors

2 4 5 -2 -3 -1 1 105 1 s = 1 s = 1 Interpolation errors s = 0 s = 0 s = 1 s = 0 s = 1

Image Recovery Hiding spaces

Image Recovery Interpolation error Modified image 1 2 3 -1 -2 103 160
1 2 3 -1 -2 103 160 155 150 Interpolation error Interpolation values 160 150 160 161 157 158 156 149 148 150 253 Modified image

Image Recovery Cover image Modified image Coordinates: (4, 4)
Modification level: 2 160 161 157 158 156 150 149 148 255 160 155 150 253 Cover image Modified image

Experimental Results

[14] W. Hong and T. S. Chen, “Reversible data embedding for high quality images using interpolation and reference pixel distribution mechanism,” Journal of Visual Communication and Image Representation, vol. 22, no. 2, pp , 2011. [20] C. F. Lee, H. L. Chen, and H. K. Tso, “Embedding capacity raising in reversible data hiding based on prediction of difference expansion,” Journal of Systems and Software, vol. 83, no. 10, pp , 2010. [29] Z. Ni, Y. Q. Shi, N. Ansari, and W. Su, “Reversible data hiding,” IEEE Transactions on Circuits and Systems for Video Technology, vol. 16, no. 3, pp , 2006. [40] H. W. Tseng and C. P. Hsieh, “Prediction-based reversible data hiding,” Information Sciences, vol. 179, no. 14, pp , 2009. [44] W. L. Tai, C. M. Yeh, and C. C. Chang, “Reversible data hiding based on histogram modification of pixel differences,” IEEE Transactions on Circuits and Systems for Video Technology, vol. 19, no. 6, pp , 2009.

Analysis Shifted errors Shifted interpolation errors

A Difference Expansion Based Reversible Information Hiding Scheme with High Stego Image Visual Quality

Non-embeddable Region
(105)10 = ( )2 (6)10 = ( )2 Extra data: 1

Data Embedding T = 1 Cover image P = 150 160 161 157 154 158 156 150
149 153 152 255 T = 1 e > T (Non-embeddable) Cover image e = 4 P = 150

149 153 152 255 T = 1 e ≤ T (Embeddable) s = 1 f1= 0 Cover image e = 1 e + s P = 153

149 153 152 255 e > T (Non-embeddable) f2 = 1 Cover image e = 3 P = 154

Data Embedding T = 1 Cover image 160 161 157 154 158 156 150 149 153
152 255 e ≤ T (Embeddable) s = 0 Cover image

Flag Bit Embedding F = {f1, f2} = { } 0, 1 (0110100 )2 1 = (104)10
= (104)10 ( )2 1 = (7)10

Analysis- Flag Bit f Embeddable prediction error -2T -T T 2T + 1
T 2T + 1 Overlapping region Type Flag bit Modified prediction error Non-embeddable prediction error 1

Flag Bit Extraction (104)10 = (01101000)2 Flag bits: 0, 1,
(7)10 = ( )2

160 161 157 154 158 156 150 149 155 152 255 (Non-embeddable) Stego image

160 161 157 154 158 156 150 149 155 152 255 f1 = 0 s = 1 Stego image P = 153 Note: Flag bits are {0, 1}

160 161 157 154 158 156 150 149 153 152 255 f2 = 1 Stego image

160 161 157 154 158 156 150 149 153 152 255 e ≤ T s = 0 Stego image 54

Image Recovery Extra data = { } 1, (0110100 )2 1 = (105)10 (0000011 )2
( )2 1 = (105)10 ( )2 1 = (6)10 55

Experimental Results F-16 Boats

C. Qin, C. C. Chang, and L. T. Liao, “An adaptive prediction-error expansion oriented reversible information hiding scheme,” Pattern Recognition Letters, vol. 33, no. 16, pp , 2012. H. W. Tseng and C. P. Hsieh, “Prediction-based reversible data hiding,” Information Sciences, vol. 179, no. 14, pp , 2009. C. F. Lee and H. L. Chen, “Adjustable prediction-based reversible data hiding,” Digital Signal Processing, vol. 22, no. 6, pp , 2012. C. F. Lee, H. L. Chen, and H. K. Tso, “Embedding capacity raising in reversible data hiding based on prediction of difference expansion,” Journal of Systems and Software, vol. 83, no. 10, pp , 2010. W. L. Tai, C. M. Yeh, and C. C. Chang, “Reversible data hiding based on histogram modification of pixel differences,” IEEE Transactions on Circuits and Systems for Video Technology, vol. 19, no. 6, pp , 2009.

Experimental Results Baboon Lena F-16 Boats

Prediction-Based Reversible Data Hiding Using the Difference of Neighboring Pixels

Non-embeddable Region
(104)10 = ( )2 (7)10 = ( )2 Cover image Extra data: 1

Determine Embeddable Pixels
d = |b – a| + |c – a| = 1 d < T  Embeddable pixel 101 255 254 100 P b c a Embeddable region

Data Embedding Embeddable region s = 1 101 255 254 100 P b c a P = 101
e + s P = 101

Data Embedding Embeddable region d = |255 – 255| + |101 – 255| = 154
P b c a d = |b – a| + |c – a| = 1 103 101 255 254 100 Embeddable region d = |255 – 255| + |101 – 255| = 154 d > T  Non-embeddable pixel

Data Embedding Embeddable region d = |254 – 254| + |255 – 254| = 1
P b c a 103 101 255 254 100 d = |b – a| + |c – a| = 1 Embeddable region d = |254 – 254| + |255 – 254| = 1 d < T (Embeddable pixel) s = 1 B = (3)10 = (11)2 s = 1 Overflow problem

Solution for Overflow and Underflow Problems
1 1 ( )2 = (105)10 ( )2 = (7)10 Stego image

Data Extraction B = (11)2 = (3)10 (105)10 = (0110101)2
(7)10 = ( )2 Stego image B = (11)2 = (3)10

103 101 255 254 100 Stego image B = 3 (Non-embedded pixel)

P b c a d = |b – a| + |c – a| = 1 103 101 255 254 100 Stego image d = |255 – 255| + |101 – 255| = 154 d > T  Non-embedded pixel

P b c a 103 101 255 254 100 Stego image d = |101 – 101| + |100 – 101| = 1 d < T Embedded pixel s = 1 P = 101

Image Recovery Extra data = { } 0, 1 (0110100 )2 1 = (105)10
( )2 1 = (105)10 ( )2 1 1 = (7)10 Stego image

Experimental results

Experimental results [56] Z. F. Zhao, H. Luo, Z. M. Lu, and J. S. Pan, “Reversible data hiding based on multilevel histogram modification and sequential recovery,” International Journal of Electronics and Communications (AEÜ), vol. 65, no. 10, pp , 2011. [43] D. M. Thodi and J. J. Rodriguez, “Expansion embedding techniques for reversible watermarking,” IEEE Transactions on Image Processing, vol. 16, no. 3, pp , 2007. [29] Z. Ni, Y. Q. Shi, N. Ansari, and W. Su, “Reversible data hiding,” IEEE Transactions on Circuits and Systems for Video Technology, vol. 16, no. 3, pp , 2006. [16] H. L. Jin, M. Fujiyoshi, and H. Kiya, “Lossless data hiding in the spatial domain for high quality images,” IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences vol. E90-A(4), pp. 771–7, 2007.

Experimental results

Analysis e e + s P

Secret Data Transformation Strategy

Secret Data Transformation
={0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 1, 0, 1, 0} {1, 0, 1} {1, 1, 0} {1, 1, 1} {1, 0, 0} Trio of secret bits Frequency Converted bits {0, 0, 0} 1 {0, 0, 1} {0, 1, 0} {0, 1, 1} {1, 0, 0} {1, 0, 1} {1, 1, 0} {1, 1, 1} 2 {0, 0, 0} {0, 0, 1} {0, 1, 0} {0, 1, 1}

Data Embedding ={0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 1, 0, 1, 0} 160 161 157 158 156 150 149 148 255 Cover image e =1 e + P = 157

160 161 157 158 156 150 149 148 255 Stego image P = 157

Secret Data Decoding S’ ={0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 1, 0, 1, 0} S ={1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 1, 1, 0, 0, 0, 0, 1, 0} Converted bits Trio of secret bits {0, 0, 1} {0, 0, 0} {1, 0, 1} {0, 1, 0} {1, 0, 0} {0, 1, 1} {1, 1, 0} {1, 1, 1}

Threshold K 2 3 4 ER (bpp) PSNR (dB) 1 0.512 44.4 44.437 44.471 0.707 42.231 42.269 0.708 42.304 0.817 40.967 41.005 41.04 0.878 40.124 40.165 40.199 5 0.913 39.535 39.573 39.606 6 0.937 39.102 39.138 39.171 7 0.952 38.774 38.807 38.837 8 0.964 38.513 38.548 38.579 9 0.972 38.318 38.353 38.381 10 0.978 38.163 38.197 38.226

Threshold K 2 3 4 ER (bpp) PSNR (dB) 1 0.172 42.745 42.757 42.766 0.275 39.617 39.627 39.637 0.364 37.496 37.506 37.515 0.441 35.92 35.931 35.94 5 0.505 34.692 0.506 34.702 34.711 6 0.559 33.691 33.7 33.71 7 0.604 32.853 32.862 32.871 8 0.642 32.137 32.147 32.154 9 0.677 31.52 31.528 31.536 10 0.706 30.978 30.986 30.995

Experimental Results- F-16

Experimental Results- Tiffany
Threshold K 2 3 4 ER (bpp) PSNR (dB) 1 0.415 43.851 43.88 43.904 0.594 41.321 41.35 0.595 41.376 0.714 39.746 39.774 39.801 0.792 38.667 38.694 38.721 5 0.842 37.859 37.886 0.843 37.913 6 0.875 37.228 37.257 0.876 37.282 7 0.898 36.714 36.741 36.766 8 0.916 36.286 36.312 36.337 9 0.929 35.925 35.951 35.974 10 0.94 35.619 35.642 35.665

Experimental Results- Boats

Experimental Results- Lake
Threshold K 2 3 4 ER (bpp) PSNR (dB) 1 0.223 42.957 42.971 42.981 0.344 39.917 39.931 39.941 0.443 37.861 37.877 37.889 0.528 36.367 36.38 36.393 5 0.599 35.209 0.6 35.221 35.234 6 0.662 34.292 34.305 34.318 7 0.717 33.553 33.565 33.578 8 0.763 32.949 32.963 32.975 9 0.802 32.448 32.46 32.474 10 0.835 32.027 32.042 32.055

Number of extra data

[18] C. F. Lee and H. L. Chen, “Adjustable prediction-based reversible data hiding,” Digital Signal Processing, vol. 22, no. 6, pp , 2012. [20] C. F. Lee, H. L. Chen, and H. K. Tso, “Embedding capacity raising in reversible data hiding based on prediction of difference expansion,” Journal of Systems and Software, vol. 83, no. 10, pp , 2010. [40] H. W. Tseng and C. P. Hsieh, “Prediction-based reversible data hiding,” Information Sciences, vol. 179, no. 14, pp , 2009.

Experimental Results Baboon F-16 Tiffany Boats

Conclusions Dual stego-images based reversible data hiding
High embedding capacity Good visual quality of stego images (k, n)-images reversible data hiding Cheating strategy Robustness Difference expansion based reversible data hiding One stego image Secret data transformation Reduction of distortion

(k, n)-Image Reversible Data Hiding

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