[1]李雄军,廖日军,李金龙,等.图像Arnold变换中的准对称性问题与半周期现象[J].深圳大学学报理工版,2015,32(6):551-562.[doi:10.3724/SP.J.1249.2015.06551]
 Li Xiongjun,Liao Rijun,Li Jinlong,et al.Quasi-symmetry and the half-cycle phenomenon in scrambling degrees for images with pixel locations scrambled by Arnold transformation[J].Journal of Shenzhen University Science and Engineering,2015,32(6):551-562.[doi:10.3724/SP.J.1249.2015.06551]
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图像Arnold变换中的准对称性问题与半周期现象()
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《深圳大学学报理工版》[ISSN:1000-2618/CN:44-1401/N]

卷:
第32卷
期数:
2015年第6期
页码:
551-562
栏目:
电子与信息科学
出版日期:
2015-11-23

文章信息/Info

Title:
Quasi-symmetry and the half-cycle phenomenon in scrambling degrees for images with pixel locations scrambled by Arnold transformation
文章编号:
201506001
作者:
李雄军廖日军李金龙冼建标徐健杰黄培何小雨
深圳大学物理科学与技术学院,深圳  518060
Author(s):
Li Xiongjun Liao Rijun Li Jinlong Xian Jianbiao Xu Jianjie Huang Pei and He Xiaoyu
College of Physics Science and Technology, Shenzhen University, Shenzhen 518060, P.R.China
关键词:
计算机应用Arnold变换准对称性置乱变换置乱度半周期现象Fibonacci变换图像加密
Keywords:
computer application Arnold transformation quasi-symmetry scrambling transform scrambling degree half-cycle phenomenon Fibonacci transformation image encryption
分类号:
U 491.1
DOI:
10.3724/SP.J.1249.2015.06551
文献标志码:
A
摘要:
从广义Arnold变换的周期性及标准Arnold变换与Fibonacci的关系出发,推导k步Arnold变换的一次性等效变换矩阵,特别是半周期处的一次性变换矩阵,并分析其特点,证明图像经广义Arnold变换位置置乱后在置乱周期内呈现图像置乱度的准对称性,讨论当置乱周期为偶数时的半周期现象和置乱周期为奇数时的各种不同情况.研究结果表明,无论置乱周期为奇数还是偶数,图像乱度存在前半周期和后半周期的准对称性;对偶数周期情况,标准Arnold变换下,在置乱次数等于周期的一半时,一次性置乱变换矩阵为单位矩阵的整数倍;半周期处置乱图像更易呈现与原图相似的结构或内容信息;对于某些维数的图像,半周期处的一次性置乱变换为负的单位矩阵,此时图像为原图的水平加垂直镜像图像;广义Arnold变换下,偶数置乱周期变换的半周期处的一次性变换矩阵可能是标准Arnold变换的结果,或在此基础上叠加了一个位移量为图像维数一半的水平或垂直平移,因而仍然存在较明显的半周期现象.对于奇数周期,半周期现象虽然存在但一般不如偶数周期情况明显,更不易出现镜像或提前恢复原图的情况. 该研究可用于指导图像加密预处理中置乱次数选择和置乱乱度计算方法的评价与比较.
Abstract:
By referring to the periodicity of the general Arnold transformation and the relationship between standard Arnold transformation and Fibonacci transformation, we deduce the equivalent one-step transformation matrix for k times of Arnold transformation with pixel position scrambled, especially the one at the half-cycle of the scrambling period. We analyze their characteristics and provide a proof of the quasi-symmetry in scrambling degrees for images in one cycle. We discuss the half-cycle effect in scrambling degrees in scrambled images with even and odd scrambling periods respectively. Results show that there exists a quasi-symmetry in scrambling performance between the two half cycles regardless of the period being even or odd. In a standard Arnold transformation with a commonly even period, the one-step transform is equivalent to a simple scaling matrix transform which leads to the scrambled image at the half period with an obvious lower scrambling degree, where being the minus unitary matrix as a special case results in the scrambled image being the horizontal mirror image with an overlying vertical mirror image of the original image. For any general Arnold transformation with an even scrambling period, the one-step transformation at half cycle may be the same as the one-step transform for standard Arnold transform or with a translation of half of the image dimension superimposed, thus leading to a little less salient half-cycle phenomenon. For an Arnold transformation with an odd scrambling period, no such situation happens in general unless for images with very special contents and structure. The results can be applied in choice of scrambling time for the pre-processing in image encryption and the evaluation and comparison of image scrambling degree criteria.

参考文献/References:

[1] Arnold V J, Avea A. Ergodic problems of classica mechanics, mathematical Physics monograph series[M]. New York(USA):W A Benjamin Inc, 1968.
[2] Li Xiongjun. A generalized matrix-based scrambling transformation and its properties[C]// Proceedings of the 9th International Conference for Young Computer Scientists. Huangshan(China): IEEE, 2008: 1429-1434.
[3] Zou Jiancheng, Tie Xiaoyun. Arnold transformation of digital image with two dimensions and its periodicity[J]. Journal of North China University of Technology, 2000, 12(1): 10-14.(in Chinese)
邹建成,铁小匀.数字图像的二维Arnold变换及其周期性[J].北方工业大学学报,2000,12(1):10-14.
[4] Mao Leibo. Research on Arnold transformation algorithm and anti-Arnold transformation algorithm[J]. Journal of Chongqing Technology and Business University Natural Science Edition, 2012, 29(3): 16-21.(in Chinese)
毛雷波.Arnold变换及其逆变换[J].重庆工商大学大学学报自然科学版,2012,29(3):16-21.
[5] Wu Faen, Zou Jiancheng. Some necessary conditions for the periodicity of Arnold transformation of digital image with two dimensions[J]. Journal of North China University of Technology, 2001, 125(6): 66-69.(in Chinese)
吴发恩,邹建成.数字图像二维Arnold变换周期的一组必要条件[J].北方工业大学学报,2001,125(6):66-69.
[6] Wu Chengmao. An improved discrete arnold transform and its application in image scrambling and encryption[J]. Acta Physica Sinica, 2014, 63(9): 90504-1-090504-20.(in Chinese)
吴成茂. 离散Arnold变换改进及其在图像置乱加密中的应用[J].物理学报, 2014,63(9):90504-1-090504-20.
[7] Radharani S, Valarmathi M L. Content based image watermarking scheme using block SVD and Arnold transform [C]// International Conference on Electronics and Communication Systems (ICECS). Coimbatore(India): IEEE, 2014: 1-4.
[8] Mehta R, Vishwakarma V P, Rajpal N. Lagrangian support vector regression based image watermarking in wavelet domain [C]// The 2nd International Conference on Signal Processing and Integrated Networks (SPIN). Noida(India): IEEE, 2015: 854-859.
[9]  Li Xiongjun.A new measure of image scrambling degree based on grey level difference and information entropy[C]// Proceedings of International Conference on Computational Intelligence and Security. Washington D C:IEEE, 2008,1: 350 -354.
[10] Wang Xinxin,Bu Ting.An evaluation algorithm of image scrambling degree based on the image area[J]. Journal of Anhui University Natural Science Edition, 2011, 35(4): 48-52.(in Chinese)
王新新,布挺.基于图像表面积的置乱程度评价算法[J].安徽大学学报自然科学版,2011,35(4):48-52.
[11] Xu Jiangfeng,Yang You.Analysis of scrambling performance of encrypted image[J]. Computer Science,2006, 33(3): 110-113.(in Chinese)
徐江峰,杨有.加密图像之乱性能表面积的置乱性能分析[J].计算机科学,2006,33(3):110-113.
[12] Tan Yongjie, Hu Haizhi. A survey of assessment of image scrambling degree[J]. Computer and Digital Engineering, 2012, 40(4): 93-95.(in Chinese)
谭永杰,胡海芝.图像置乱效果评价算法综述[J].计算机与数字工程,2012,40(4): 93-95.
[13] Huang Liangyong, Xiao Degui. The best image scrambling degree of binary image based on Arnold transform[J]. Journal of Computer Applications, 2009, 29(2): 474-476.(in Chinese)
黄良永,肖德贵.二值图像Arnold变换的最佳置乱度[J].计算机应用,2009,29(2):474-476.
[14] Feng Xingang, Zhou Quan. A novel scrambling degree rule of digital image based on center of mass[J]. Journal of Electronics & Information Technology, 2008, 30(11): 2684-2687.(in Chinese)
冯新岗,周诠.基于质心的数字图像置乱度衡量准则[J].电子与信息学报,2008,30(11):2684-2687.
[15] Huang Xing, Zhang Minrui. Study on the image scrambling extent[J]. Geomatics and Information Science of Wuhan University, 2008, 33(5): 465-468.(in Chinese)
黄兴,张敏瑞.图像置乱程度的研究[J].武汉大学学报信息科学版,2008,33(5):465-468.
[16] Guo Linqin. On the image scrambling and scrambling degree[J]. Journal of Xi’an University of Arts and Science Natural Science Edition, 2013, 16(3): 49-52.(in Chinese)
郭琳琴.图像置乱及置乱度评价方法综述[J].西安文理学院学报自然科学版,2013,16(3):49-52.
[17] Yang Xiyang, Li Zhiwei. Image scrambling measurement based on chi-square statistic[J]. Journal of Xiamen University Natural Science, 2010, 49(6): 778-781.(in Chinese)
杨昔阳,李志伟.置乱均匀性的优度拟合统计分析[J].厦门大学学报自然科学版,2010,49(6):778-781.
[18] Liao Rijun, Li Xiongjun, Xu Jianjie, et al. Discussions on applications of Arnold transformation in binary image scrambling[J].Journal of Shenzhen University Science and Engineering, 2015, 32(4): 428-433.(in Chinese)
廖日军,李雄军,徐健杰,等.Arnold变换在二值图像置乱应用中若干问题讨论[J].深圳大学学报理工版,2015,32(4):428-433.

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备注/Memo

备注/Memo:
Received:2015-10-22;Accepted:2015-10-31
Foundation:University Student’s Innovation and Entrepreneurship Training Program Foundation of Shenzhen University(201510590079); 2015 Foundation for College Students’ Science and Technology Innovation Training Program (“Climbing” Program) of Guangdong Province (201510590079)
 Corresponding author:Associate professor Li Xiongjun.E-mail:lixj@szu.edu.cn
Citation:Li Xiongjun, Liao Rijun, Li Jinlong, et al. Quasi-symmetry and the half-cycle phenomenon in scrambling degrees for images with pixel locations scrambled by Arnold transformation[J]. Journal of Shenzhen University Science and Engineering, 2015, 32(6): 551-562.(in Chinese)
基金项目:广东省“攀登计划”资助项目(201560020006);深圳大学大学生创新创业训练计划资助项目(20151059 0079)
作者简介:李雄军(1966—),女(汉族),湖南省双峰县人,深圳大学副教授、博士.E-mail:lixj@szu.edu.cn
引文:李雄军,廖日军,李金龙,等.图像Arnold变换中的准对称性问题与半周期现象[J]. 深圳大学学报理工版,2015,32(6):551-562.
更新日期/Last Update: 2015-11-06