In this section, we provide the resultant of embedding capacity and image quality to demonstrate the performance of our proposed scheme. In our experiment, ten gray images with size 512×512, which are depicted in Fig. 4.1 and Fig. 4.2, are used, and the secret message is obtained by random generation. To estimate the image quality, we applied the function of peak-signal-to-noise-ratio (PSNR), which is defined as Eq. (21). To estimate the embedding capacity, the function of ER (Embedded Ratio; bpp) is adopted, where ER = Total Embedded bits / Size of Cover image. In the experiment, the embedding cost C is set to 30 at the first level. Then, the C value is added by 0.5 at each of the following levels.
255 ),
( log 10
2
10 MSE
PSNR (21) where MSE is the mean square error between the cover image and the stego-image.
(a) (b) (c)
(d) (e)
Fig. 4.1 The cover images with size 512×512; (a) Airplane; (b) Baboon; (c) Boat; (d) Lena; (e) Peppers.
(a) (b) (c)
(d) (e)
Fig. 4.2 The cover images with size 512×512; (a) Barb; (b) Girl; (c) Gold; (d) Toys; (e) Zelda.
Table 4.1. Each image’s capacity, PSNR, and the prediction M at every level.
(high-capacity tactic A, embedding cost C = 30)
Image Airplane Baboon Boat Lena Peppers
Level 1 Capacity 103956 31719 58759 99936 85550
PSNR 51.17 55.10 51.01 49.06 48.91
M M1 M4 M2 M1 M1
Level 4 Capacity 272609 130702 192922 255913 223195
PSNR 43.12 43.69 41.60 40.92 39.82
M M3 M2 M2 M2 M4
Level 7 Capacity 394342 207013 277664 363636 306574
PSNR 39.15 39.47 38.23 36.18 37.38
M M1 M2 M2 M2 M1
Level 10 Capacity 479299 270876 353120 432191 388137
PSNR 35.84 37.38 35.63 34.48 35.44
M M1 M2 M2 M4 M4
Level 20 Capacity 687704 470440 510963 629919 570497
PSNR 31.65 32.46 30.02 29.49 30.31
M M4 M4 M2 M2 M2
Table 4.2. Each image’s capacity, PSNR, and the prediction M at every level.
(high-capacity tactic A, embedding cost C = 30)
Image Barb Girl Sailboat Toys Zelda
Level 1 Capacity 50725 86178 40767 64181 87860
PSNR 52.96 48.92 55.08 50.38 48.93
M M2 M2 M2 M2 M2
Level 4 Capacity 172365 231638 170258 178750 225523
PSNR 42.05 39.14 43.58 40.61 39.28
M M2 M1 M2 M2 M1
Level 7 Capacity 252192 314262 255873 256342 287933
PSNR 38.54 36.26 39.61 36.74 36.71
M M2 M2 M2 M2 M1
Level 10 Capacity 329451 378355 337084 315602 347859
PSNR 36.32 33.83 37.23 34.323 34.10
M M2 M2 M2 M2 M2
Level 20 Capacity 528247 499396 565915 458959 453375
PSNR 30.87 28.97 32.07 28.78 29.30
M M2 M2 M2 M2 M2
Table 4.3. Each image’s capacity, PSNR, and the prediction M at every level.
(high-quality tactic B, embedding cost C = 30)
Image Airplane Baboon Boat Lena Peppers
Level 1 Capacity 103956 16873 60215 90345 79711
PSNR 51.17 61.70 47.56 49.39 49.65
M M1 M3 M1 M4 M4
Level 4 Capacity 282135 61429 207521 239069 209481
PSNR 43.30 53.90 39.95 41.37 40.23
M M4 M3 M3 M3 M2
Level 7 Capacity 398864 112359 338425 331799 299571
PSNR 40.12 48.48 37.23 39.88 38.73
M M4 M1 M3 M3 M3
Level 10 Capacity 507270 144627 466401 416004 362713
PSNR 37.64 47.72 34.51 38.00 37.27
M M2 M3 M1 M3 M3
Level 20 Capacity 731523 264966 654985 623648 533181
PSNR 33.05 44.20 32.23 34.58 32.81
M M1 M3 M4 M3 M3
Table 4.4. Each image’s capacity, PSNR, and the prediction M at every level.
(high-quality tactic B, embedding cost C = 30)
Image Barb Girl Sailboat Toys Zelda
Level 10 Capacity 318176 371309 291936 218396 235411
PSNR 45.14 38.35 42.11 37.03 35.23
M M3 M3 M4 M3 M3
Level 20 Capacity 509590 509539 381307 367762 423027
PSNR 39.69 35.79 35.14 35.03 32.99
M M3 M3 M4 M3 M3
Tables 4.1, 4.2, 4.3 and 4.4 show that our approach will choose the best prediction method M at every level. Therefore we can embed more secret data more efficiently at every. Moreover, because the predictions have different characteristics, it can avoid using the same prediction at every level and some regions of pixels change may too large.
Table 4.5. The compared result among our approach (embedding cost C = 30), Lin’s, Hsiao’s and Yang’s schemes.
Images Lin et al.’s Airplane 362847 286488 367392 397712 742082 750408
Baboon 230079 138398 162544 184468 576014 575917
Boat 314196 266724 307937 294944 510963 513744
Lena 346568 303700 309166 420986 596903 604839
Peppers 342175 303736 356450 374837 570497 557048 Average 319173 259809 300698 334589 599291 600391
Ratio 53.16% 43.27% 50.08% 55.72% 99.81% 100%
PSNR 30.19 30.00 30.26 30.25 30.27 32.75
From the compared result in Table 4.5, we can find out that our approach clearly have more capacity when the PSNR values are similar. We promote at least 44%
capacity than that of other methods. The reason is that our approach uses the more suitable prediction method at every level. We also have some overhead. For each level we need 80 bits to record four peak points and zero points, 32 bits for TH, and 2 bits for the prediction M. If we hide 20 levels, we need 2280 bits to record the overhead.
Table 4.6 shows the comparison among Hu et al.’s method [23], Luo et al.’s method [24], Li et al.’s method [16], Hong’s method [25], Li et al.’s method [19], and our proposed scheme. From this table, our scheme has better image quality than that of other methods when the size of the embedded bits is 20000. The reason is that our approach forbids some prediction errors entering the process of pixel shifting and we use four different prediction methods. The threshold TH strategy in our proposed scheme has efficiently eliminated the distortion caused by pixel shifting. It therefore has good performance of PSNR than that of the previous works. Fig. 4.3 shows the PSNR values between our approach using tactic A and Yang-Tsai method [12] based on various embedded capacities. From Fig. 4.3, the average PSNR value of Yang-Tsai method is 52.52 dB, and our approach is about 61.18 dB, which is significantly improved by 8.66 dB.
Fig. 4.3 The PSNR comparison of Lena image between our approach and Yang and Tsai’s scheme based on various hiding payload.
Table 4.6. The compared result between our approach and other schemes, for an embedding capacity of 20000 bits.
Image Hu et al.
[23]
Luo et al.
[24]
Li et al.
[16]
Hong [25]
Li et al.
[19]
Our Approach (capacity)
Our Approach (R)
Lena 52.86 53.83 54.82 54.92 55.93 61.32 62.02
Airplane 54.63 55.43 56.84 58.58 59.26 62.33 62.33
Peppers 50.64 52.19 52.55 52.16 53.31 57.32 61.42
Sailboat 50.69 52.17 53.25 52.03 53.19 57.78 57.63
Average 52.21 53.41 54.37 54.42 55.42 59.69 60.85
In addition, we also compared the result with the previous work of Lee et al.’s scheme, as shown in Table 4.7. From this table, it is obvious that the averaged stego-image qualities of Lean and Baboon in our scheme are larger than that of Lee et al.’s scheme. As shown in Fig. 4.4, our scheme with tactic A has better image quality than previous works [10, 12, 15, 20] with the same embedding capacities.
Table 4.7. Comparison between Lee et al.’s scheme and our proposed scheme with the same embedding ratio.
Lee et al.’s scheme
[13] Our approach (capacity) Our approach (R)
ER(bpp) PSNR ER(bpp) PSNR ER(bpp) PSNR
Lena 0.14 48.47 0.14 58.59 0.14 58.89
0.98 32.17 0.98 46.92 0.98 46.30
Baboon 0.05 48.25 0.05 62.92 0.05 63.11
0.62 30.02 0.62 46.48 0.62 47.39
(a) (b)
Fig. 4.4 Comparison results among our proposed scheme and other reversible schemes for images: (a) Lena; (b) Baboon.
As shown in Fig.4.5 and Fig. 4.6, the original images and the stego-images are shown for comparison when the capacities are approaching to 300000 bits using tactic A. It is visually difficult to distinguish between the original image and the stego-image for both Lena and Baboon by human eyes.
(a) (b)
Fig.4.5 (a) Original image Lena. (b) Stego-image Lena with capacity =300288 bits and PSNR =39.054 dB.
(a) (b)
Fig.4.6 (a) Original image Baboon. (b) Stego-image Baboon with capacity =317015 bits and PSNR =36.304 dB.
Table 4.8 shows the occurrence times of overflow for each image after 20-level data hiding. Compared to the capacity of each image, these overflow data can be easily hidden into the stego-image.
Table 4.8. Each image’s overflow after 20-level data hiding.
Images Airplane Baboon Boat Lena Peppers
Overflow 0 21 8 0 1644
Images Barb Girl Sailboat Toys Zelda
Overflow 251 539 0 2214 0