This document discusses taking the Fourier transform of an image containing lines, shifting the transform so that low frequencies are at the center, and removing some of the Fourier coefficients around the edges to reconstruct the image while filtering out some high frequency information. It loads an image, takes its Fourier transform, shifts it, and removes coefficients outside a central region before taking the inverse Fourier transform and displaying the reconstructed image.

8. • >> I1=imread('lines1.png');
• >> imshow(I1);
• >> A1=fft2(I1);
• >> A2=fftshift(A1);
• >> imshow(A2);

9. fft transform for the strip
lines image

10. Original image

11. • I1=imread('lines1.png');
• figure(1), imshow(I1);
• A1=fft2(I1);
• A2=fftshift(A1);
• figure(2),imshow(A2);
•
• [m,n]=size(A2);
•
• %%%%%%%%%%%%%%%%%%%%%%%%%%%%%Here we retrieve part of the image fourier
•
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%coefficients%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%
•
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%
•
• A3=A2(0.4*m:m,0.4*n:n);
•
• figure(3),imshow(uint8(ifft2(A3)));
•
• title('Restructuring the image after removing some fourier coefficients');

13. A3=A2(0.4*m:m,0.4
*n:n);
figure(3),imshow(ui
nt8(abs((ifft2(A3))))
);
title('Restructuring
the image after
removing some
fourier
coefficients');

14. • close all,clear all,clc
• I1=imread('lines2.png');
• figure(1), imshow(I1);
• A1=fft2(I1);
• A2=fftshift(A1);
• [m,n]=size(A2);
• nn=max(max(A2));
• for i=1:m
• for j=1:n
• if A2(i,j)==nn
• l=i
• p=j
• end
• end
• end
• xx=(A2==nn);
• figure(2),imshow(A2);
•
• [m,n]=size(A2);
•
• %%%%%%%%%%%%%%%%%%%%%%%%%%%%%Here we retrieve part of the image fourier
• %%%%%%%%%%%%%%%%%%%%%%%%%%%%%coefficients%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
• %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
•
• A3=A2(0.45*m:m,0.45*n:n);
•
• figure(3),imshow(uint8(abs((ifft2(A3)))));
•
• title('Restructuring the image after removing some fourier coefficients');

18. The peak is at the
center for vertical lines
and horizontal lines