MATLAB: How to determine or generate the appropriate threshold value from the Fourier(Frequency) domain of an image

digital image processingImage Processing Toolboximage segmentation

I am working on a code to extract the edges of any image using Fourier Transform but i have two(2) disturbing issues. Please find my codes and pictures of the stages of the image attached below. It is open for corrections and comments.
(i) I need the edges to display as black and others(background, etc) as white as against the edges been displayed as white as i have in the resulting image.
(ii) I also need a situation whereby when i convert an image to its frequency domain, I want to be able to determine the best threshold value through the frequency domain(probably having my codes generate the appropriate threshold value) rather than assuming a threshold value(e.g.30) for the edge extraction as this did not really effectively eradicate or smoothen out the ripples in the resulting image.
% Read in a standard image Standardimage = 'AEESS2.jpg'; Originalimage = imread(Standardimage);
% Display the original image imshow(Originalimage);
%Convert Original image to grayscale and display. grayImage = rgb2gray(Originalimage); imshow(grayImage);
% Display the original grayscale image. subplot(2, 2, 1); imshow(grayImage, [0 255]); title('Original Grayscale Image in its Spatial Domain', 'FontSize', 10); % Enlarge the figure to full screen. % set(gcf, 'Position', get(0,'Screensize')); set(gcf, 'units','normalized','outerposition',[0 0 1 1]);
% Compute the FFT. FFTImage = fft2(grayImage); % Shift the zero frequency location from (0,0)to the center of the display % and take log in order to have a clearer display. centeredFFTImage = log(fftshift(real(FFTImage))); % Display the FFT image. subplot(2, 2, 2); imshow(centeredFFTImage, []); title('Visually Enhanced Frequency Domain of the Original Grayscale Image', 'FontSize', 9);
% Zero out the corners. window = 30; FFTImage(1:window, 1:window) = 0; FFTImage(end-window:end, 1:window) = 0; FFTImage(1:window, end-window:end) = 0; FFTImage(end-window:end, end-window:end) = 0;
% Shift the zero frequency location from (0,0)to the center of the display % and take log in order to have a clearer display. centeredFFTImage = log(fftshift(real(FFTImage))); subplot(2, 2, 3); imshow(centeredFFTImage, []); title('Visually Enhanced Frequency Domain of the Filtered image', 'FontSize', 10);
% Taking the Inverse FFT to convert the high pass filtered %image back to Spatial domain. output = ifft2(FFTImage); % Display the output. subplot(2, 2, 4); imshow(real(output), [0 255]); title('High Pass Filtered Image converted back to the Spatial Domain', 'FontSize', 10);

Best Answer

For (i), just threshold
binaryImage = filteredImage < 2; % or whatever.
Edges will be black and everything else will be white.
for (ii) you need to determine this by trial and error. There is no divine method that says exactly when an edge turns from a sharp edge to a more gradual wrinkle - that's a judgement call on your part. So you need to determine how big the blackening rectangle in your Fourier domain should be.
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