使用频域的图像处理 - 复制图像

Question

我有一张图片，由两张相同的图片组成，其中一张已翻译。

input

现在，我想修复它。我用的是transform fourier的翻译属性：

$f(x-x_0,y-y_0)\leftrightarrowF(u,v)e^{-2{\pi}i(ux_0/{N}+ vy_0/M)}$

我测量了两张图片之间的距离：x距离是24像素，y距离是4像素。在代码中：x_d 和 y_d.

然后我就将频域图像中的所有像素除以公式+1的指数表达式（1来自未翻译的图像）。

我想不通是什么问题...

这是我的代码：

function [  ] = f(  )
%UNTITLED Summary of this function goes here
%   Detailed explanation goes here

FileName='dog.tif';

%--- Read Image ---
im = readImage(FileName);
imshow(im);

%--- apply FFT on the given image ---
fftIm = fftshift(fft2(im));

%--- apply LOG and abs for plotting the transform --- 
fLog = log(1 + abs(fftIm));

%----modify the image in the frequency domain-------
fftImMod=fftIm;
x_d=24;           %x distance between the 2 images
y_d=4;            %y distance between the 2 images
N = 305;        %the dimensions of the image NxM = 305x305 
M = 305;        %the dimensions of the image NxM = 305x305 

for r=1:size(fftIm,1)

      for k=1:size(fftIm,2)

          divisionVal =  1+exp((-2*(pi)*1i)*(r*x_d/N + k*y_d/M));

          fftImMod(r,k)=fftIm(r,k)/divisionVal;

      end;
  end;

%--- apply LOG and abs for plotting the modified transform --- 
fLogAfterMod = log(1 + abs(fftImMod));

%--- return to the image space ---
result=ifft2(fftshift(fftImMod));

% --- display results ---
colormap(gray)
subplot(2,2,1),imagesc(im); title('Original Image')
subplot(2,2,2),imagesc(fLog); title('Fourier Image')
subplot(2,2,3),imagesc(fLogAfterMod); title('Modified Fourier')
subplot(2,2,4),imagesc(real(result)); title('Result Image')

end

结果如下：
result

如有任何帮助，我们将不胜感激。谢谢。

Answer 1

在除法数组的定义中交换了 x 和 y
删除了 fftshift
在计数器的指数参数中添加了 -1

为结果绘图添加了 BW 限制

%UNTITLED Summary of this function goes here
%   Detailed explanation goes here
FileName='/tmp/me4iX.jpg';
%--- Read Image ---
im = imread(FileName);
im=im(:,:,1)

%--- apply FFT on the given image ---
fftIm = (fft2(im));

%--- apply LOG and abs for plotting the transform --- 
fLog = log(1 + abs(fftIm));

%----modify the image in the frequency domain-------
fftImMod=fftIm;
x_d=24;           %x distance between the 2 images
y_d=4;            %y distance between the 2 images
N = 305;        %the dimensions of the image NxM = 305x305 
M = 305;        %the dimensions of the image NxM = 305x305 

for r=1:size(fftIm,1)
      for k=1:size(fftIm,2)
          divisionVal(r,k) =  1+exp((-2*(pi)*1i)*((r-1)*y_d/N + (k-1)*x_d/M));    
      end;
  end;


  fftImMod=fftIm./divisionVal;

%--- apply LOG and abs for plotting the modified transform --- 
fLogAfterMod = log(1 + abs(fftImMod));

%--- return to the image space ---
N=60;
result=ifft2((fftImMod([1:N end-N-2:end],[1:N end-N-2:end])));

% --- display results ---
colormap(gray)
subplot(2,2,1),imagesc(im); title('Original Image')
subplot(2,2,2),imagesc(fLog); title('Fourier Image')
subplot(2,2,3),imagesc(fLogAfterMod); title('Modified Fourier')
subplot(2,2,4),imagesc(abs(result)); title('Result Image')
%set(gca,'clim',[0 250])

使用频域的图像处理 - 复制图像

Image processing using the frequency domain - duplicate image

matlab

fft

transform

image-processing