💥1 概述
Arnold变换因其具有周期性,在图像加密方面得到了广泛的应用.但在解密过程中,若要利用其周期性,则显得很费时,因此提出了一种新的Arnold反变换算法.该算法通过求解方程组来求得反变换.在此基础上,把二维Arnold变换用在正方形图像的情形推广到一般的矩形图像,即图像矩阵不是方阵的情况,扩大了其在图像加密中的应用.同时,从理论上又把二维Arnold反变换推广到了m维Arnold反变换.
📚2 运行结果
🎉3 参考文献
[1]卢振泰,黎罗罗.一种新的衡量图像置乱程度的方法[J].中山大学学报(自然科学版),2005(S1):126-129.
👨💻4 Matlab代码
主函数部分代码：
%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%arnold加解密过程仿真程序%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%% clear all;close all;clc; I=imread('lena256.png'); I=imresize(I,[256,256]); %要置乱的次数 num=50; figure(1); subplot(1,4,1);imshow(I,[]);title('原图'); subplot(1,4,2);imshow(I(:,:,1),[]);title('R'); subplot(1,4,3);imshow(I(:,:,2),[]);title('G'); subplot(1,4,4);imshow(I(:,:,3),[]);title('B'); I1(:,:,1)=uint8(arnold(I(:,:,1),num));%%%%%%%%%%%原调用函数 I1(:,:,2)=uint8(arnold(I(:,:,2),num)); I1(:,:,3)=uint8(arnold(I(:,:,3),num)); figure(2); subplot(1,4,1);imshow(I1,[]);title(['原图' num2str(num) '次置乱']); subplot(1,4,2);imshow(I1(:,:,1),[]);title(['R分量图' num2str(num) '次置乱']); subplot(1,4,3);imshow(I1(:,:,2),[]);title(['G分量图' num2str(num) '次置乱']); subplot(1,4,4);imshow(I1(:,:,3),[]);title(['B分量图' num2str(num) '次置乱']); C(:,:,1)=I1(:,:,1); C(:,:,2)=I1(:,:,2); C(:,:,3)=I1(:,:,3); imwrite(C,'加密图.bmp'); figure(5); % subplot(3,4,5);imhist(C);title('彩图扩散直方图'); subplot(2,3,1);imhist(C(:,:,1));title([num2str(num) '次置乱后R分量直方图']); subplot(2,3,2);imhist(C(:,:,2));title([num2str(num) '次置乱后G分量直方图']); subplot(2,3,3);imhist(C(:,:,3));title([num2str(num) '次置乱后B分量直方图']); % subplot(3,4,9);imhist(I1);title('原彩图扩散直方图'); subplot(2,3,4);imhist(I(:,:,1));title('原图R分量直方图'); subplot(2,3,5);imhist(I(:,:,2));title('原图G分量直方图'); subplot(2,3,6);imhist(I(:,:,3));title('原图B分量直方图'); figure(6); subplot(1,2,2); histogram(C(:,:,1),512,'Facecolor','r','FaceAlpha',1,'Edgecolor','none');title([num2str(num) '次置乱后RGB分量直方图']); hold on histogram(C(:,:,2),512,'Facecolor','g','FaceAlpha',1,'Edgecolor','none'); hold on histogram(C(:,:,3),512,'Facecolor','b','FaceAlpha',1,'Edgecolor','none'); box off; subplot(1,2,1); histogram(I(:,:,1),512,'Facecolor','r','FaceAlpha',1,'Edgecolor','none');title('原图RGB分量直方图'); hold on histogram(I(:,:,2),512,'Facecolor','g','FaceAlpha',1,'Edgecolor','none'); hold on histogram(I(:,:,3),512,'Facecolor','b','FaceAlpha',1,'Edgecolor','none'); box off; I2(:,:,1)=uint8(iarnold(C(:,:,1),num)); I2(:,:,2)=uint8(iarnold(C(:,:,2),num)); I2(:,:,3)=uint8(iarnold(C(:,:,3),num)); imwrite(I2,'解密图.bmp'); figure(4); subplot(1,4,1);imshow(I2,[]);title(['解密' num2str(num) '次图像']); subplot(1,4,2);imshow(I2(:,:,1),[]);title(['解密' num2str(num) '次R分量图像']); subplot(1,4,3);imshow(I2(:,:,2),[]);title(['解密' num2str(num) '次G分量图像']); subplot(1,4,4);imshow(I2(:,:,3),[]);title(['解密' num2str(num) '次B分量图像']);
