# Blurring an image using FFT (Fast Fourier Transform)

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Kanak Dhotre on 26 Sep 2021
Answered: yanqi liu on 27 Sep 2021
I have an image of a ramp (Fig 1.1). Since every row of in this image is the same, I just picked the first row and ran FFT over it, then since convolution is equivalent to multiplication in the frequency domain, I multiplied it with the FFT of a gaussian vector. But when I run IFFT over the product, I don't get a blur image, instead I just get a completely white image (Fig 1.2) . What am I doing wrong?
Figure 1.1
Figure 1.2
My Code:
%Import the image
I = imread("/MATLAB Drive/ramp.png");
%Convert to grayscale
I = rgb2gray(I);
imshow(I)
%Pick a row
row = I(1,:);
plot(row)
%Define the gaussian vector
time_vector = 1:500
gaussian_vector = gaussmf(time_vector,[1 0]);
%Compute IFFT(FFT()*FFT())
row_fill = ifft(fft(row).*fft(gaussian_vector))
plot(row_fill)
%Stack the resultant rows
I_fill = repmat(row_fill,500,1);
%Plot the resultant image
imshow(I_fill)
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### Answers (2)

Image Analyst on 27 Sep 2021
Try []:
imshow(I_fill, [])
but you'll likely notice no difference at all because of how smooth the function already is.
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yanqi liu on 27 Sep 2021
sir, may be use the follows code to ref
clc
close all
clear all
%Import the image
I = imread("https://www.mathworks.com/matlabcentral/answers/uploaded_files/750304/image.png");
%Convert to grayscale
I = rgb2gray(I);
imshow(I)
%Pick a row
row = I(1,:);
figure;plot(row)
%Define the gaussian vector
time_vector = 1:500;
gaussian_vector = gaussmf(time_vector,[1 0]);
%Compute IFFT(FFT()*FFT())
row_fill = ifft(fft(row).*fft(gaussian_vector));
plot(row_fill)
%Stack the resultant rows
I_fill = repmat(row_fill,500,1);
%Plot the resultant image
figure; imshow(mat2gray(I_fill))
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