How can I determine or generate the appropriate threshold value from the Fourier(Frequency) domain of an image ?

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);

Answer 1

[Image Analyst]

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.

[Dipps]

Thanks image Analyst for your answer, i really appreciate it. I now understand the trial and error for the edge detection. But i still have a slight issue. I seem to be confused on where exactly to apply the code you suggested(binaryImage = filteredImage < 2;). My code is as below, kindly help suggest the right line to apply it because i keep getting a wrong output display. Thanks in anticipation of your response.

% 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;

FFTImage2 = FFTImage < 2;

% 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(FFTImage2))); 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(FFTImage2); % 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);

Please find attached a copy of the sample image.

Thanks

[Dipps]

% 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;

On a second note, Please, I need a detailed description on what exactly each of the lines of the above codes means and their functions because I feel I have a wrong or blurry understanding of it. I seem to understand every other aspect of the main code but these set of codes seem quite convincing to me.

I will be very grateful if you can explain it to me.

Thanks for your assistance.

[Image Analyst]

What, specifically is confusing? Because I see exceptionally well commented code with descriptive variable names, much, much better than typical users' code, and even rivaling the quality and amount of comments I put into my demos. Pretty much every line of code has an explanation so I'm not sure what else to add.

[Image Analyst]

Oh wait, I just found out it IS my code . It was a custom demo I wrote for someone but didn't save in my grab bag of permanent demos. http://www.mathworks.com/matlabcentral/answers/13307#answer_26790

[Dipps]

Yea...exactly, it is your code. I got it from the same source.I read, comprehend and applied it. It helped me get a clearer and practical understanding on edge detection using Fourier Transform.

In the first question, I did not get where exactly to insert the codes to change the edges to black and others to white. I keep getting a False result as seen in the above result image. Kindly help state the exact point to insert the code.

Thanks

[Image Analyst]

An edge is a gradient, so it will have a positive spike before the edge and a negative spike after the edge, or vice versa. You can get either one, and depending on how you threshold it, the spike (either positive or negative) can be either black or white.

edges = edgeImage > 4;
edges = edgeImage < -4;

It doesn't matter much. Try each if you want.

[Dipps]

Good Day, Thanks so much for your answers and help, God bless your Heart. Please i need you to do me a favor. I have attached the original image i used in the code. Kindly copy and paste the codes in your Matlab window and held edit and include the additional codes that will turn or convert the edge lines from white to black and the other background to white. This will give you an idea of where i seem to be having problem because i keep getting an unsual image results. You can then post me the edited code here.

Thanks in expectant of your kind response. God Bless you.

Regards.

here is the code;

 % 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);

Thanks once again.