fft2frequency to spatial domainifft2Image Processing Toolbox
img = imread('sample.tif');imgFFT = fft2(double(img));img2 = ifft2(imgFFT);imshow(abs(fftshift(fftA)),[]);imshow(log(abs(fftshift(fftA))), []);clc; % Clear the command window.
close all; % Close all figures (except those of imtool.)
clear; % Erase all existing variables. Or clearvars if you want.
workspace; % Make sure the workspace panel is showing.
format short g;format compact;fontSize = 15;% Get noise-free original gray scale image.
grayImage = imread('eight.tif');% Get the dimensions of the image.
% numberOfColorChannels should be = 1 for a gray scale image, and 3 for an RGB color image.
[rows, columns, numberOfColorChannels] = size(grayImage);% Create noisy image from it.
noisyImage = imnoise(im2double(grayImage), 'Gaussian', 0, 0.01);% Define spatial filters as a 15x15 window.
gaussianSpatialFilter = fspecial('gaussian', 15, 1.0);% Do a filter by blurring with a Gaussian kernel in the spatial domain:
spatialDomainFilteredImage = imfilter(noisyImage, gaussianSpatialFilter, 'replicate');% Display results:
subplot(2, 4, 1); imshow(grayImage, []); title('Original Image', 'FontSize', fontSize); axis on;subplot(2, 4, 2); imshow(noisyImage, []); title('Noisy Image', 'FontSize', fontSize); axis on;subplot(2, 4, 3); imshow(gaussianSpatialFilter, []); title('Blur Kernel', 'FontSize', fontSize); axis on;subplot(2, 4, 4); imshow(spatialDomainFilteredImage, []); title('Image filtered with Gaussian in the spatial domain', 'FontSize', fontSize); axis on;% Define frequency domain filter the same size as the image.
gaussianFreqFilter = fspecial('gaussian', [rows, columns], 0.2*rows); % Keep the low frequencies.
% gaussianFreqFilter = ones(rows, columns); % Keep all frequencies.
% Fourier transform the noisy image.
freqDomainImage = fftshift(fft2(noisyImage));% Now do filtering in the frequency domain
filteredFreqDomain = freqDomainImage .* gaussianFreqFilter;% Now transform back to spatial domain:
spatialImage = real(ifft2(ifftshift(filteredFreqDomain)));% Display results:subplot(2, 4, 5); imshow(gaussianFreqFilter, []); title('Freq Domain Filter', 'FontSize', fontSize); axis on;subplot(2, 4, 6); imshow(log(abs(freqDomainImage)), []); title('Original Freq Domain Image', 'FontSize', fontSize); axis on;subplot(2, 4, 7); imshow(log(abs(filteredFreqDomain)), []); title('Filtered Freq Domain Image', 'FontSize', fontSize); axis on;subplot(2, 4, 8); imshow(spatialImage, []); title('Back in Spatial Domain', 'FontSize', fontSize); axis on;% Set up figure properties:
% Enlarge figure to full screen.
set(gcf, 'Units', 'Normalized', 'OuterPosition', [0, 0.04, 1, 0.96]);% Get rid of tool bar and pulldown menus that are along top of figure.
% set(gcf, 'Toolbar', 'none', 'Menu', 'none');
% Give a name to the title bar.
set(gcf, 'Name', 'Demo by ImageAnalyst', 'NumberTitle', 'Off')
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