分数阶傅里叶变换MATLAB

clc; clear; image1 = imread('lena.jpg'); %image1 = imread('C:\Documents and Settings\603\桌面\work\lenawm.jpg'); %figure(1); %imagesc(real(image)); %colormap(gray); %axis('equal','tight','off'); %title('Original image'); image2 = imread('watermark1.jpg'); %L = [0,26200]; %M = [1000,144]; %var = [1000,100]; powers = [0.3,0.1]; %n = min([length(L),length(M),length(var)]); S = frft2d(image1,powers); D = frft2d(image2,powers); %显示原始图像 %figure(1); %imagesc(real(image1)); %colormap(gray); axis('equal','tight','off'); %title('原始图像'); %显示水印图案 %figure(2); %imagesc(real(image2)); %colormap(gray); axis('equal','tight','off'); %title('嵌入图像'); sizeS = size(S); %得到序列长度 [val, ix] = sort(abs(S(:)));%取绝对值，进行排序,一共是512*512个值，val是排序后的，ix是原来的位置 S = S(:);%将矩阵变换成列矩阵 %sizeD = size(D); C=size(image2);L=C(1);W=C(2); G=im2double(image2); B=G(:,:,1); y(L,W)=0; %加水印函数 for u = 1:1:L for v = 1:1:W Swm = S(ix(100001+u.*v)); y(u,v) = ix(100001+u.*v); shi = B(u,v).*(real(Swm)); xu = B(u,v).*(imag(Swm)); % Swst = shi/(real(Swm)) % Sws(u,v) = 255*Swst; Swm = complex(shi,xu); S(y(u,v)) = Swm; end; end; %y = y(:); %Sw = S; Sw = reshape(S,sizeS); wm_image = frft2d(Sw,-powers); %显示加水印后图像 figure(3); imagesc(real(wm_image)); colormap(gray); axis('equal','tight','off'); title('加水印后'); %显示图像的像素差的图像 %Q=double(wm_image)-double(image1); %figure(4); %imagesc(real(Q)); %colormap(gray);axis('equal','off'); %title('空间差值'); %提取函数 St = frft2d(image1,powers); %Sm = frft2d(wm_image,powers); sizeSt = size(St); [valt, ixt] = sort(abs(St(:))); St = St(:); %sizeSw = size(Sw); %[valw, ixw] = sort(abs(Sw(:))); Sws(L,W)=0; for u = 1:1:L for v = 1:1:W Swt = St(y(u,v)); % Sww = S(100001+u.*v); % Swt = St(ix(100001+(u.*v))); Sww = S(y(u,v)); % key1 = normrnd(0,sqrt(var(i)/2),M(i),1); % key2 = normrnd(0,sqrt(var(i)/2),M(i),1); % keys= [key1 key2]; shi=imag(Sww); sh=imag(Swt); Swst = shi/sh; Sws(u,v) = Swst; end; end; %sizeSws=size(Sws); Sws = reshape(Sws,L,W); %ws_image = frft2d(Sws,-powers); %St=reshape(St,sizeSt); %D1 = reshape(D,sizeD); %ws_image2 = frft2d(D,-powers); %figure(5); %imagesc(real(ws_image2)); %colormap(gray); axis('equal','tight','off'); %title('提取出的水印图像'); %Sws=doublegray(abs(Sws)); %C(L,W,1) = Sws(L,W); %C(L,W,2) = Sws(L,W); %C(L,W,3) = Sws(L,W); figure(6); imagesc(Sws); colormap(gray); axis('equal','tight','off'); title('显示提取出的水印图像');