Untitled

Frequency Domain

1. Fourier Transform and Frequency Domain: Implement a MATLAB script to compute the 2D 

Fourier Transform of a grayscale image, shift the zero-frequency component to the center, and 
display the magnitude spectrum.
img = imread('image.jpg');
gray_img = rgb2gray(img);
fft_img = fftshift(fft2(double(gray_img)));
magnitude_spectrum = log(1 + abs(fft_img));
imshow(magnitude_spectrum, []);

2. Smoothing Frequency Domain Filters: Write a MATLAB script to apply an ideal low-pass filter 

in the frequency domain to a grayscale image. Display the original and filtered images.

img = imread('image.jpg');
gray_img = rgb2gray(img);
fft_img = fftshift(fft2(double(gray_img)));
[M, N] = size(gray_img);
[X, Y] = meshgrid(1:N, 1:M);
D0 = 50; % Cut-off frequency
H = sqrt((X - N/2).^2 + (Y - M/2).^2) <= D0;
filtered_img = ifft2(ifftshift(H .* fft_img));
imshow(real(filtered_img), []);
3. High-Pass Filtering: Implement a script to apply an ideal high-pass filter to an image in the 
frequency domain.
img = imread('image.jpg');
gray_img = rgb2gray(img);
fft_img = fftshift(fft2(double(gray_img)));
[M, N] = size(gray_img);
[X, Y] = meshgrid(1:N, 1:M);
D0 = 50;
H = sqrt((X - N/2).^2 + (Y - M/2).^2) > D0;
filtered_img = ifft2(ifftshift(H .* fft_img));
imshow(real(filtered_img), []);


1. Image Degradation and Restoration Process

Question: Write a MATLAB script to simulate an image degradation process using a motion blur 

function and then restore the image using inverse filtering.
% Simulate Image Degradation
img = imread('image.jpg');
psf = fspecial('motion', 21, 11); % Motion blur PSF
degraded_img = imfilter(img, psf, 'conv', 'circular');
% Restore Image using Inverse Filtering
F_degraded = fft2(degraded_img);
F_psf = fft2(psf, size(img, 1), size(img, 2));
restored_img = ifft2(F_degraded ./ F_psf);
% Display Results
imshowpair(degraded_img, restored_img, 'montage');
2. Noise Models and Spatial Filtering
Question: Implement a MATLAB script to add Gaussian noise to an image and then apply a 5x5 median 
filter to reduce the noise.
% Add Gaussian Noise
img = imread('image.jpg');
noisy_img = imnoise(img, 'gaussian', 0, 0.01);
% Apply 5x5 Median Filter
filtered_img = medfilt2(noisy_img, [5 5]);
% Display Results
imshowpair(noisy_img, filtered_img, 'montage');