Arnold变换在二值图像置乱应用中若干问题讨论  

Discussions on applications of Arnold transformation in binary image scrambling

作　　者：廖日军 李雄军[1] 徐健杰 李金龙[1] 冼建标 何小雨[1] 

机构地区：[1]深圳大学物理科学与技术学院,深圳518060

出　　处：《深圳大学学报（理工版）》2015年第4期428-433,共6页Journal of Shenzhen University(Science and Engineering)

基　　金：深圳大学大学生创新创业训练计划项目(201510590079)~~

摘　　要：针对二值图像的特点,讨论了二维Arnold变换在二值图像置乱中的置乱周期问题,提出一种快速Arnold变换策略,即少点置乱法,分析比较Arnold逆变换方法,针对一步恢复原图中直接求矩阵乘方会产生当矩阵元素过大超出运算精度限制时的结果错误问题,提出一种迭代取模伴随矩阵逆变换法.研究结果表明,经Arnold置乱的二值图像,其置乱周期有可能是Arnold变换周期的1/2;只对二值图像中占像素比例较小的像素进行置乱的变换策略,可提高置乱速度;对变换矩阵迭代取模后再求伴随矩阵,可得到正确的一步恢复矩阵.二值图像Arnold变换中,综合应用少点置乱法和一步恢复图像方法,可显著提高变换与反变换的速度.Considering the characteristics of binary images scrambled by Arnold transformation, we discuss the scrambling period for binary images and propose an efficient Arnold transformation strategy, namely scrambling on fe- wer pixels （SFP）. By analyzing and comparing different anti-Arnold transformation methods, we present a one-step image recovery method, the adjoint matrix recovery after iteratively moduloing （AMRAIM）, which aims to avoid the error caused by accuracy limitations when directly computing the transform matrix power. Experimental results show that the scrambling period for scrambled binary images may be one half of that of the Arnold transformation depending on the image contents. The calculation speed is improved by scrambling pixels with less proportion in constituting the binary image. By iteratively moduloing the transformation matrix, we obtain the one-step Arnold transformation and its adjoint matrix for anti-Arnold transformation, which recovers the original image in a single step. Combining SFP and ARMAIM in binary image scrambling by Arnold transformation, the computational efficiency is improved.

关 键 词：计算机应用 置乱变换 ARNOLD变换 二值图像 Arnold逆变换 图像加密 

分 类 号：U491.1[交通运输工程—交通运输规划与管理]