Journal of Jilin University(Engineering and Technology Edition) ›› 2024, Vol. 54 ›› Issue (4): 1065-1077.doi: 10.13229/j.cnki.jdxbgxb.20220647

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Stereo image zero watermarking algorithm based on Tucker decomposition and double scrambling encryption technology

Shao-cheng HAN1(),Peng ZHANG2,Huan LIU3,Bo WANG1   

  1. 1.Engineering Technology Training Center，Civil Aviation University of China，Tianjin 300300，China
    2.Tianjin Pinyuan Technology Co. ，Ltd，Tianjin 300300，China
    3.College of Electronic Information and Automation，Civil Aviation University of China，Tianjin 300300，China
  • Received:2022-05-25 Online:2024-04-01 Published:2024-05-17

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Abstract:

Aiming at the problems of stereo image copyright protection and the poor robustness of existing zero watermarking schemes against geometric attacks， a novel zero watermarking algorithm against geometric attacks is proposed for color stereo image based on Tucker decomposition and Fractional-order Jacobi-Eourier Moments （FJFM）. Firstly， the R， G and B channels of the left and right views of the original color stereo image are separated respectively. Then， the separated six channels are combined and treated as a third-order tensor for Tucker decomposition to obtain the first energy map containing the correlation between the left and right views. Secondly， the mixed low-order moment feature （MLMF） of the mean sub-image obtained by 4×4 non-overlapping blocking to the first energy map is calculated based on FJFM. Then the binary robust feature matrix is constructed according to the MLMF. Finally， the final authentication zero watermark is generated using the exclusive-or operation between the watermark encrypted by the double scrambling and encryption methods and the feature matrix scrambled using the proposed chaotic system. Experimental results show that the proposed algorithm shows strong robustness to the common non-geometric attacks such as adding noise， filtering and compression， and the NC values of watermark detection are more than 0.98. In addition， the proposed algorithm is overall superior to the comparison algorithms in resisting rotation， scaling， translation and the cropping geometric attacks.

Key words: zero watermarking, stereo image, geometric attack, Tucker decomposition, fractional-order Jacobi-Fourier moments

CLC Number: 

  • TP391

Fig.1

Schematic diagram of Tucker decomposition"

Fig.2

Stereo image Art and its six energy maps afterTucker decomposition"

Fig.3

Image reconstruction results under different parameters"

Fig.4

MSRE values under different parameters"

Table 1

MSE values under different attacks"

攻击方式及参数MSE攻击方式及参数MSE
无攻击0旋转5°0.006 3
高斯噪声0.050.035 2旋转25°0.010 6
椒盐噪声0.050.019 2旋转45°0.012 6
中值滤波9×90.037 6旋转90°0
维纳滤波9×90.024 4缩小0.5倍0.031 1
JPEG压缩100.019 9放大2倍0.002 6

Fig.5

Matrix transform scrambling results under different iteration times"

Fig.6

Results of scrambling using complete Latin squares"

Fig.7

2D chaotic map bifurcation diagrams"

Fig.8

Generation and detection process of zero watermark"

Table 2

Matrix filling rules"

Q1Q2Q3Q4
元素00110000100110010
元素11001111011001101

Fig.9

Stereo images Art， Computer， Flowers， Hoops"

Fig.10

Original watermark and its preprocessed result"

Table 3

Uniqueness detection （NC）"

ArtComputerFlowersHoops
Art1.000 00.565 90.634 20.669 8
Computer0.565 91.000 00.661 20.534 5
Flowers0.634 20.661 21.000 00.626 6
Hoops0.669 80.534 50.626 61.000 0

Fig.11

Security test"

Table 4

Test results of non-geometric attack"

攻击类型及

参数

NCArtComputerFlowersHoops
高斯噪声ANC0.997 40.992 21.000 01.000 0
0.1SNC0.989 60.981 70.994 80.989 6
椒盐噪声ANC0.997 40.997 41.000 01.000 0
0.1SNC0.997 40.992 21.000 01.000 0
中值滤波ANC1.000 00.994 81.000 01.000 0
9×9SNC1.000 00.992 21.000 00.994 8
维纳滤波ANC1.000 01.000 01.000 01.000 0
9×9SNC1.000 01.000 01.000 01.000 0
JPEG压缩ANC1.000 01.000 01.000 00.997 4
10SNC1.000 01.000 01.000 00.997 4
JPEG2000压缩ANC1.000 01.000 01.000 01.000 0
90SNC1.000 01.000 01.000 01.000 0

Table 5

Types and parameters of geometric attack"

序号攻击类型及参数序号攻击类型及参数
1旋转5°8向左平移20列
2旋转20°9向右平移20列
3旋转40°10中心剪切1/16
4缩小0.5倍11左上角剪切1/16
5放大2倍12右上角剪切1/16
6向上平移20行13左下角剪切1/16
7向下平移20行14右下角剪切1/16

Fig.12

Test results of geometric attack"

Table 6

Test results of combined attack"

序号非对称攻击对称攻击
攻击后的右视点ANC攻击后的左视点SNC
①

（0.994 8）

（0.987 0）

②

（0.989 6）

（0.981 7）

③

（1.000 0）

（1.000 0）

④

（1.000 0）

（1.000 0）

⑤

（0.997 4）

（0.992 2）

⑥

（0.994 8）

（0.992 2）

Table 7

Robustness comparison of different algorithms （ANC/SNC）"

序号攻击类型及参数文献［6］算法文献［9］算法文献［10］算法文献［13］算法文献［14］算法本文算法
平均值—/0.971 30.914 1/0.815 90.962 7/0.949 00.984 9/0.965 20.953 4/0.978 60.990 2/0.984 0
1高斯噪声0.1—/0.992 90.859 1/0.699 40.960 3/0.936 60.981 4/0.973 30.888 0/0.936 60.992 1/0.984 6
2椒盐噪声0.1—/0.995 80.881 7/0.751 00.976 7/0.963 70.992 0/0.989 30.922 6/0.967 30.996 3/0.993 5
3中值滤波9×9—/0.995 80.896 8/0.792 70.979 7/0.969 60.993 7/0.989 10.983 4/0.985 20.998 3/0.997 3
4维纳滤波9×9—/0.999 20.906 2/0.811 10.984 9/0.980 00.995 2/0.992 60.996 0/0.997 81.000 0/0.999 8
5JPEG压缩10—/0.996 30.909 1/0.818 40.990 5/0.985 70.993 2/0.989 90.987 6/0.985 40.999 6/0.999 0
6JPEG2000压缩90—/0.998 80.901 9/0.801 90.982 3/0.974 30.996 7/0.994 80.996 5/0.994 51.000 0/0.999 9
7旋转5°—/0.999 60.870 2/0.727 80.964 3/0.962 00.984 0/0.965 70.941 4/0.983 30.996 9/0.999 3
8旋转20°—/0.999 60.856 3/0.674 10.958 2/0.966 00.964 1/0.906 20.915 9/0.959 30.988 8/0.999 3
9旋转40°—/0.999 20.849 1/0.640 70.958 2/0.966 40.954 7/0.876 90.919 1/0.947 10.975 5/0.998 2
10缩小0.5倍—/1.000 00.932 1/0.863 90.998 6/0.997 20.994 9/0.995 40.999 4/0.999 41.000 0/1.000 0
11放大2.0倍—/1.000 00.985 3/0.970 50.999 7/0.999 50.995 2/0.995 20.999 8/0.999 91.000 0/1.000 0
12上移20行—/0.937 30.871 0/0.726 00.912 7/0.880 20.983 0/0.966 80.935 0/0.991 60.981 2/0.964 5
13下移20行—/0.932 70.870 3/0.723 60.913 2/0.883 80.983 3/0.962 20.931 7/0.982 70.981 7/0.964 2
14左移20列—/0.938 50.870 1/0.737 30.916 9/0.885 70.983 8/0.964 10.936 2/0.984 90.985 0/0.968 4
15右移20列—/0.913 10.871 5/0.737 30.915 2/0.884 50.985 9/0.971 50.938 6/0.986 00.980 6/0.965 0
16中心剪切1/16—/0.946 00.989 8/0.967 30.966 3/0.948 20.982 9/0.955 10.950 3/0.966 20.984 8/0.971 0
17左上角剪切1/16—/0.941 90.990 1/0.967 60.967 3/0.947 30.980 7/0.947 60.955 3/0.970 10.986 0/0.965 7
18右上角剪切1/16—/0.939 40.989 6/0.965 70.970 8/0.950 40.983 0/0.958 30.954 3/0.983 80.985 5/0.969 0
19左下角剪切1/16—/0.946 90.990 7/0.970 30.967 8/0.949 30.984 0/0.949 90.958 10.9 7680.985 4/0.970 6
20右下角剪切1/16—/0.953 40.990 7/0.970 80.969 9/0.949 80.985 7/0.960 40.959 6/0.973 80.987 0/0.970 2

Table 8

Timeliness test"

算 法零水印生成时间零水印检测时间总时间
文献［6］0.484 70.384 20.868 9
文献［9］0.201 00.131 90.332 9
文献［10］2.401 01.271 33.672 3
文献［13］1.313 30.638 51.951 7
文献［14］3.192 03.392 86.584 8
本文1.586 41.229 52.815 9
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