1 简介

提出了一种基于正交拉丁方置乱+混沌的图像置乱加密算法.借助MATLAB2014软件平台编程实现,并研究了加密算法的抗破损能力.实验结果表明:该算法的加密效果良好,图像的抗破损能力强.

2 部分代码

% RegisterFourierMellin% This code is the result of my messing around with Matlab investigating % various image registration techniques.  I came across the excellent % (although perhaps a little messy and buggy) fm_gui_v2 from Adam Wilmer% here:% http://www.mathworks.com/matlabcentral/fileexchange/loadFile.do?objectId=3000&objectType=file% Because my needs are essentially the algorithm itself in a neat and tidy% format to enable an easier conversion to C++, I've extracted what I think% is the essence of the Fourier Mellin method into this file.  Obviously% I haven't included a GUI.  In order to test it, you need to set the first% two statements to load in 2 image files of the same size, in 8 bit grayscale.% I took lena and then used Gimp to rotate/shift/crop at various angles.% It isn't sub-pixel accurate, although I'm aware of methods to achieve% this by extracting the peaks around the peak of the phase correlation and% finding the maxima (least squares perhaps).  % The methods towards the end of the program are cribbed directly from% Adam's version.  I'm new to Matlab (been playing with it for less than% a fortnight), so I wasn't able to get my head around his log polar transform% or the final "blending" of the two images together.% I'd like to thank Adam for publishing his version.  Without it I'd never% have known I had to take the log polar transform of the magnitude of the% FFT, rather than the log polar transform of the original image!function combImage=RegnisterFourierMellin(I1,I2)    % The procedure is as follows (note this does not compute scale)    % (1)   Read in I1 - the image to register against    % (2)   Read in I2 - the image to register    % (3)   Take the FFT of I1, shifting it to center on zero frequency    % (4)   Take the FFT of I2, shifting it to center on zero frequency    % (5)   Convolve the magnitude of (3) with a high pass filter    % (6)   Convolve the magnitude of (4) with a high pass filter    % (7)   Transform (5) into log polar space    % (8)   Transform (6) into log polar space    % (9)   Take the FFT of (7)    % (10)  Take the FFT of (8)    % (11)  Compute phase correlation of (9) and (10)    % (12)  Find the location (x,y) in (11) of the peak of the phase correlation    % (13)  Compute angle (360 / Image Y Size) * y from (12)    % (14)  Rotate the image from (2) by - angle from (13)    % (15)  Rotate the image from (2) by - angle + 180 from (13)    % (16)  Take the FFT of (14)    % (17)  Take the FFT of (15)    % (18)  Compute phase correlation of (3) and (16)    % (19)  Compute phase correlation of (3) and (17)    % (20)  Find the location (x,y) in (18) of the peak of the phase correlation    % (21)  Find the location (x,y) in (19) of the peak of the phase correlation    % (22)  If phase peak in (20) > phase peak in (21), (y,x) from (20) is the translation    % (23a) Else (y,x) from (21) is the translation and also:    % (23b) If the angle from (13) < 180, add 180 to it, else subtract 180 from it.    % (24)  Tada!    % Requires (ouch):    % 6 x FFT    % 4 x FFT Shift    % 3 x IFFT    % 2 x Log Polar    % 3 x Phase Correlations    % 2 x High Pass Filter    % 2 x Image Rotation    % ---------------------------------------------------------------------    % Load first image (I1)   % I1 = imread('lena.bmp');    % Load second image (I2)   % I2 = imread('lena_cropped_shifted.bmp');    % Convert both to FFT, centering on zero frequency component    SizeX = size(I1, 1);    SizeY = size(I1, 2);    FA = fftshift(fft2(I1));    FB = fftshift(fft2(I2));    % Output (FA, FB)    % ---------------------------------------------------------------------    % Convolve the magnitude of the FFT with a high pass filter)    IA = hipass_filter(size(I1, 1),size(I1,2)).*abs(FA);      IB = hipass_filter(size(I2, 1),size(I2,2)).*abs(FB);      % Transform the high passed FFT phase to Log Polar space    L1 = transformImage(IA, SizeX, SizeY, SizeX, SizeY, 'nearest', size(IA) / 2, 'valid');    L2 = transformImage(IB, SizeX, SizeY, SizeX, SizeY, 'nearest', size(IB) / 2, 'valid');    % Convert log polar magnitude spectrum to FFT    THETA_F1 = fft2(L1);    THETA_F2 = fft2(L2);    % Compute cross power spectrum of F1 and F2    a1 = angle(THETA_F1);    a2 = angle(THETA_F2);    THETA_CROSS = exp(i * (a1 - a2));    THETA_PHASE = real(ifft2(THETA_CROSS));    %    combImage = plant;    for p=1:total_height        for q=1:total_width            if (combImage(p,q)==0)                combImage(p,q) = bleed(p,q);            end        end    end    % Show final image   % imshow(combImage, [0 255]); % ---------------------------------------------------------------------% Performs Log Polar Transformfunction [r,g,b] = transformImage(A, Ar, Ac, Nrho, Ntheta, Method, Center, Shape)% Inputs:   A       the input image%           Nrho    the desired number of rows of transformed image%           Ntheta  the desired number of columns of transformed image%           Method  interpolation method (nearest,bilinear,bicubic)%           Center  origin of input image%           Shape   output size (full,valid)%           Class   storage class of Aglobal rho;theta = linspace(0,2*pi,Ntheta+1); theta(end) = [];switch Shapecase 'full'    corners = [1 1;Ar 1;Ar Ac;1 Ac];    d = max(sqrt(sum((repmat(Center(:)',4,1)-corners).^2,2)));case 'valid'    d = min([Ac-Center(1) Center(1)-1 Ar-Center(2) Center(2)-1]);endminScale = 1;rho = logspace(log10(minScale),log10(d),Nrho)';  % default 'base 10' logspace - play with d to change the scale of the log axis% convert polar coordinates to cartesian coordinates and centerxx = rho*cos(theta) + Center(1);yy = rho*sin(theta) + Center(2);if nargout==3  if strcmp(Method,'nearest'), % Nearest neighbor interpolation    r=interp2(A(:,:,1),xx,yy,'nearest');    g=interp2(A(:,:,2),xx,yy,'nearest');    b=interp2(A(:,:,3),xx,yy,'nearest');  elseif strcmp(Method,'bilinear'), % Linear interpolation    r=interp2(A(:,:,1),xx,yy,'linear');    g=interp2(A(:,:,2),xx,yy,'linear');    b=interp2(A(:,:,3),xx,yy,'linear');  elseif strcmp(Method,'bicubic'), % Cubic interpolation    r=interp2(A(:,:,1),xx,yy,'cubic');    g=interp2(A(:,:,2),xx,yy,'cubic');    b=interp2(A(:,:,3),xx,yy,'cubic');  else    error(['Unknown interpolation method: ',method]);  end  % any pixels outside , pad with black  mask= (xx>Ac) | (xx<1) | (yy>Ar) | (yy<1);  r(mask)=0;  g(mask)=0;  b(mask)=0;else  if strcmp(Method,'nearest'), % Nearest neighbor interpolation    r=interp2(A,xx,yy,'nearest');  elseif strcmp(Method,'bilinear'), % Linear interpolation    r=interp2(A,xx,yy,'linear');  elseif strcmp(Method,'bicubic'), % Cubic interpolation    r=interp2(A,xx,yy,'cubic');  else    error(['Unknown interpolation method: ',method]);  end  % any pixels outside warp, pad with black  mask= (xx>Ac) | (xx<1) | (yy>Ar) | (yy<1);  r(mask)=0;end  % ---------------------------------------------------------------------% Returns high-pass filterfunction H = hipass_filter(ht,wd)% hi-pass filter function% ...designed for use with Fourier-Mellin stuffres_ht = 1 / (ht-1);res_wd = 1 / (wd-1);eta = cos(pi*(-0.5:res_ht:0.5));neta = cos(pi*(-0.5:res_wd:0.5));X = eta'*neta;H=(1.0-X).*(2.0-X);

3 仿真结果

4 参考文献

【图像加密】基于正交拉丁方置乱+混沌图像加密解密含Matlab源码

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