Efficient robust zero-watermarking algorithm for 3D medical images based on ray-casting sampling and quaternion orthogonal moment

doi:10.11772/j.issn.1001-9081.2021050746

Journal of Computer Applications ›› 2023, Vol. 43 ›› Issue (4): 1191-1197.DOI: 10.11772/j.issn.1001-9081.2021050746

• Cyber security • Previous Articles

Efficient robust zero-watermarking algorithm for 3D medical images based on ray-casting sampling and quaternion orthogonal moment

Jian GAO¹, Zhi LI¹(), Bin FAN¹, Chuanxian JIANG²

^1.College of Computer Science and Technology，Guizhou University，Guiyang Guizhou 550025，China
^2.School of Information Science and Technology，Qiongtai Normal University，Haikou Hainan 571127，China

Received:2021-05-13 Revised:2023-02-21 Accepted:2023-02-24 Online:2021-09-24 Published:2023-04-10
Contact: Zhi LI
About author:GAO Jian， born in 1993， M. S. His research interests include graph visualization， information hiding， medical image analysis.
FAN Bin， born in 1996， M. S. His research interests include watermarking algorithm， medical image analysis.
JIANG Chuanxian， born in 1978， Ph. D.， professor. His research interests include information hiding， digital watermarking， image processing.
Supported by:
National Natural Science Foundation of China(62062023);Guizhou Science and Technology Plan Program(ZK［2021］-YB314);Natural Science Foundation of Hainan Province(619MS073)

基于光线投射采样和四元数正交矩的高效三维医学影像鲁棒零水印算法

高健¹, 李智¹(), 樊缤¹, 姜传贤²

^1.贵州大学计算机科学与技术学院，贵阳 550025
^2.琼台师范学院信息科学技术学院，海口 571127

通讯作者: 李智
作者简介:高健（1993—），男，山西大同人，硕士，主要研究方向：图形可视化、信息隐藏、医学影像分析；
樊缤（1996—），男，贵州遵义人，硕士，主要研究方向：水印算法、医学影像分析；
姜传贤（1978—），男，湖南长沙人，教授，博士，主要研究方向：信息隐藏、数字水印、图像处理。
基金资助:
国家自然科学基金资助项目(62062023);贵州省科技计划项目（ZK［2021］?YB314）;海南省自然科学基金资助项目(619MS073)

Abstract

Abstract:

Aiming at the copyright protection problem of 3D medical images and the simultaneous expansion problem of watermark storage capacity caused by the increase of the number of images to be protected， a robust zero-watermarking algorithm based on ray-casting sampling and polar complex exponential moment was proposed. Firstly， a sampling algorithm based on ray-casting was proposed to sample the features of 3D medical images composed of multiple sequences of 2D medical images and describe these features in 2D image space. Secondly， a robust zero-watermarking algorithm for 3D medical images was proposed. In the algorithm， three 2D feature images of coronal， sagittal planes and cross section of the 3D medical image were obtained by ray-casting sampling， and the three 2D feature images were transformed by polar complex exponential to obtain the quaternion orthogonal moment. Finally， the zero-watermarking information was constructed by using the quadratic orthogonal moment and Logistic chaotic encryption. Simulation results show that the proposed algorithm can maintain the bit correctness rate of zero-watermarking extraction above 0.920 0 under various common image processing attacks and geometric attacks； the watermark storage capacity of the proposed algorithm can be improved with the increase of the volume of 3D medical image data， and the storage capacity of the proposed algorithm has been improved by 93.75% at least compared to the other 2D medical image zero-watermarking algorithms for comparison.

Key words: 3D medical image, ray-casting sampling, quaternion orthogonal moment, Logistic chaotic encryption, robustness

摘要：

针对三维医学影像的版权保护问题，以及随着待保护图像数量增加而导致的水印存储容量同步增加的问题，提出了一种基于光线投射采样和极复指数矩的三维医学影像鲁棒性零水印算法。首先，提出了一种基于光线投射的采样算法，对多张二维医学图像序列构成的三维医学影像进行特征采样并在二维图像空间中进行描述；其次，提出了一种针对三维医学影像的鲁棒性零水印算法，所提算法通过光线投射采样获取三维医学影像的冠状面、矢状面和横切面的3个二维特征图像，将3个二维特征图像进行极复指数变换获得四元数正交矩；最后，使用四元数正交矩和Logistic混沌加密构建零水印信息。仿真实验结果表明，在各种常见的图像处理攻击和几何攻击下所提算法能够保持零水印提取的比特正确率在0.920 0以上，水印存储容量随着三维医学影像的数据增多而提升，与其他优秀的二维医学图像零水印算法相比，所提算法的存储容量至少提升了93.75%。

关键词: 三维医学影像, 光线投射采样, 四元数正交矩, Logistic混沌加密, 鲁棒性

CLC Number:

TP309.7

Jian GAO, Zhi LI, Bin FAN, Chuanxian JIANG. Efficient robust zero-watermarking algorithm for 3D medical images based on ray-casting sampling and quaternion orthogonal moment[J]. Journal of Computer Applications, 2023, 43(4): 1191-1197.

高健, 李智, 樊缤, 姜传贤. 基于光线投射采样和四元数正交矩的高效三维医学影像鲁棒零水印算法[J]. 《计算机应用》唯一官方网站, 2023, 43(4): 1191-1197.

Figures/Tables 15

Fig. 1 3D medical image

Fig. 2 Representation of voxel and its neighborhoods

Fig. 3 Ray-casting sampling algorithm

Fig. 4 Logistic mapping

Fig. 5 Generation process of zero-watermarking algorithm

Tab. 1 Experiment results of cropping attacks

攻击类别	参数值	BCR	PSNR/dB
左上裁剪	1/8	1.000 0	17.43
	1/4	1.000 0	11.89
	1/2	0.939 5	6.72

Tab. 2 Experiment results of scaling attacks

攻击类别	缩放比例/%	BCR	PSNR/dB
缩小	25	0.924 4	25.75
	50	1.000 0	30.50
	75	1.000 0	34.44
放大	125	1.000 0	38.35
	150	1.000 0	41.16
	200	1.000 0	40.10

Tab. 3 Experiment results of filtering attacks

攻击类别	参数值	BCR	PSNR/dB
中值滤波	3×3	1.000 0	21.87
	5×5	0.988 3	16.47
	7×7	0.984 4	15.28
高斯低通滤波	1.0	1.000 0	20.70
	1.5	1.000 0	15.77
	2.0	0.986 3	15.00

Tab. 4 Experiment results of rotating attacks

攻击类别	旋转角度/（°）	BCR	PSNR/dB
逆时针旋转	5	1.000 0	23.98
	15	1.000 0	22.23
	30	0.972 7	21.17
	45	0.963 9	20.69

Tab. 5 Experiment results of noise attacks

攻击类别	方差	BCR	PSNR/dB
高斯噪声	0.01	1.000 0	22.14
	0.02	1.000 0	20.17
	0.03	0.975 6	18.77
椒盐噪声	0.01	1.000 0	23.84
	0.02	0.987 3	21.91
	0.03	0.987 3	20.75

Tab. 6 Experiment results of JPEG compression

攻击类别	质量因子	BCR	PSNR/dB
JPEG压缩	10	0.937 5	29.42
	30	0.984 4	33.67
	70	0.988 3	35.48
	90	1.000 0	42.19

Tab. 7 Experiment results of multiple attacks

攻击1	攻击2	攻击3	BCR
JPEG压缩（30）	中值滤波（3×3）	旋转（30°）	0.953 2
左上裁剪（1/4）	中值滤波（3×3）	缩放（50%）	0.997 9
左上裁剪（1/8）	缩放（75%）	旋转（30°）	0.958 3
椒盐噪声（0.01）	高斯噪声（0.01）	—	1.000 0
旋转（30°）	高斯噪声（0.03）	—	0.988 3
旋转（15°）	高斯低通（1.0）	缩放（150%）	1.000 0

Tab. 8 Robustness comparison against single attack between proposed algorithm and other algorithms

算法	不同攻击（参数值）下的BCR
算法	高斯噪声（0.01）	椒盐噪声（0.03）	JPEG压缩（30）	中值滤波（3×3）	缩放（50%）	旋转（45°）	左上裁剪（1/8）	左上裁剪（1/2）
本文算法	1.000 0	0.987 3	0.984 4	1.000 0	1.000 0	0.963 9	1.000 0	0.939 5
文献［21］算法	0.975 6	0.969 7	0.997 1	0.985 2	0.994 1	0.906 3	1.000 0	0.631 8
文献［24］算法	0.971 5	0.930 2	0.991 6	0.982 2	0.956 2	0.684 5	0.774 4	—
文献［31］算法	0.990 1	0.941 2	0.996 1	0.983 6	0.992 0	—	—	—
文献［26］算法	0.999 7	0.999 7	0.937 1	0.996 1	—	—	—	—

Tab. 9 Robustness comparison against multiple attacks between proposed algorithm and other algorithms

攻击1	攻击2	BCR
攻击1	攻击2	本文算法	文献［21］算法	文献［24］算法
椒盐噪声（0.03）	缩放（125%）	0.987 3	0.960 9	—
JPEG（30）	高斯噪声（0.03）	0.970 5	0.963 9	—
旋转（2°）	JPEG（10）	0.937 5	—	0.909 6
中值滤波（5×5）	高斯噪声（0.03）	0.970 4	—	0.905 6

Tab. 10 Zero-watermarking storage capacity

数据集	三维图像尺寸	存储容量/bit
数据集	三维图像尺寸	本文算法	文献［16］算法	文献［23］算法
ABIDE	$256 × 256 × 170$	2 048	348 160	116 054
ADNI	$256 × 256 × 48$	2 048	98 304	32 768
ICBM	$256 × 256 × 172$	2 048	352 256	117 419

Tab. 10 Zero-watermarking storage capacity

数据集	三维图像尺寸	存储容量/bit
数据集	三维图像尺寸	本文算法	文献［16］算法	文献［23］算法
ABIDE	$256 × 256 × 170$	2 048	348 160	116 054
ADNI	$256 × 256 × 48$	2 048	98 304	32 768
ICBM	$256 × 256 × 172$	2 048	352 256	117 419

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Efficient robust zero-watermarking algorithm for 3D medical images based on ray-casting sampling and quaternion orthogonal moment

基于光线投射采样和四元数正交矩的高效三维医学影像鲁棒零水印算法

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