使用頻域進行圖像處理 - 複製圖像

Question

我有一張由2張相同圖像組成的圖像，其中一張被翻譯。

input

現在，我要修復它。我使用變換傅立葉變換的性質如下：

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

我測量了兩幅圖像之間的距離：x距離是24像素，y距離是4像素。在代碼中：x_d和y_d。

然後，我剛剛從公式+ 1（1來自未翻譯的圖像）指數表達式的頻域圖像中的所有像素。

我想不出什麼問題...

這是我的代碼：

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 

這裏是結果：
result

任何幫助將不勝感激。 謝謝。

Answer 1

• 交換x和y在分割陣列
• fftshift
• 除去的定義添加-1在指數的argumend爲計數器

• 添加結果繪製

  一個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])