how can i blur an image by removing high frequencies of it's DFT

Hello everyone, I'm trying to blur an image by removing the high frequencies from the DFT of that image. after reading the image i used the fft command, now i have the frequencies but can't figure out how to remove the high ones

any suggestion??

Answer 1

[David Young]

There's a demo that does this here. Other such demos are available also if you look for them.

[hanan Sh]

thanks David your demo was helpful, i have one question though,

those lines ....

sigmaf = 10;

mask(1:N/2+1) = exp(-(f/(2*sigmaf)).^2);

mask(N:-1:N/2+2) = mask(2:N/2);

are they supposed to calculate the Gaussian mask???

[David Young]

Hi. Yes, that's what they do. The second line actually computes the Gaussian, and the third line reflects it to make the correct symmetry for a the DFT of a real signal.

Answer 2

[Walter Roberson]

zero them in the dft.

[hanan Sh]

i tried this. the result was black image

imdft= fft2(im);

for i=1:s(1)

for j=1:s(2)

for k=1:s(3)

if (imdft (i ,j ,k)> 0)

imdft (i ,j ,k)== 0;

end

end

end

end

imdft = uint8(ifft2(imdft));

figure, imshow(imdft);

[Dr. Seis]

You are using a logical equals "==" instead of an "=".

Answer 3

[Dr. Seis]

I modified an example I posted earlier. It generates a random 2D image and then applies a simple low-pass filter (i.e., sets high-frequencies beyond some cut-off to 0):

Nx = 32; % Number of samples collected along x dimension
Ny = 64; % Number of samples collected along y dimension
dx = .1; % x increment (i.e., Spacing between each column)
dy = .1; % y increment (i.e., Spacing between each row)

x = 0 : dx : (Nx-1)*dx;
y = 0 : dy : (Ny-1)*dy;

data_spacedomain = randn(Ny,Nx); % random 2D matrix

Nyq_kx = 1/(2*dx); % Nyquist of data in x dimension
Nyq_ky = 1/(2*dy); % Nyquist of data in y dimension
dkx = 1/(Nx*dx);   % x Wavenumber increment
dky = 1/(Ny*dy);   % y Wavenumber increment

kx = -Nyq_kx : dkx : Nyq_kx-dkx; % x wavenumber
ky = -Nyq_ky : dky : Nyq_ky-dky; % y wavenumber

data_wavenumberdomain = fftshift(fft2(data_spacedomain)); % transform data
data_wavenumberdomain_filtered = data_wavenumberdomain; % copy

% Set high-frequency components with hypot(kx,ky) > 2 to 0
for i1 = 1:Nx
  for j1 = 1:Ny
      if hypot(kx(i1),ky(j1)) > 2            
          data_wavenumberdomain_filtered(j1,i1) = 0;            
      end
  end
end

data_spacedomain_filtered = ifft2(ifftshift(data_wavenumberdomain_filtered));

figure;
subplot(3,1,1);
imagesc(kx,ky,abs(data_wavenumberdomain_filtered));
colorbar; v = caxis;
title(sprintf('Wavenumber Domain\n\nFiltered'));
xlabel('kx'); ylabel('ky');

subplot(3,1,2);
imagesc(kx,ky,abs(data_wavenumberdomain));
colorbar; caxis(v);
title('Unfiltered');
xlabel('kx'); ylabel('ky');

subplot(3,1,3);
imagesc(kx,ky,abs(data_wavenumberdomain_filtered-data_wavenumberdomain));
colorbar; caxis(v);
title('Difference');
xlabel('kx'); ylabel('ky');

figure;
subplot(3,1,1);
imagesc(x,y,data_spacedomain_filtered);
colorbar; v = caxis;
title(sprintf('Space Domain\n\nFiltered'));
xlabel('x'); ylabel('y');

subplot(3,1,2);
imagesc(x,y,data_spacedomain);
colorbar; caxis(v);
title('Unfiltered');
xlabel('x'); ylabel('y');

subplot(3,1,3);
imagesc(x,y,data_spacedomain_filtered-data_spacedomain);
colorbar; caxis(v);
title('Difference');
xlabel('x'); ylabel('y');

[chris crowley]

This code works, but is pretty slow. That for loop and be completely eliminated. Replace the for loop with:

[KX,KY] = meshgrid(ky,kx);
data_wavenumberdomain_filtered(hypot(KX,KY) > 2) = 0;

Instead of looping over each index and checking the if condition, this utilizes MATLABs vectorized functionality. This runs in fractions of a second for the images I have been trying it on as apposed to a few minutes it took the above code.