How to find specific frequency from image?

I have taken the Fourier transform of the following image (showing zoomed image to better explain my question):

and got the following result after taking the log:

basic idea is to remove the frequencies of the white and black circles with the low pass filter i.e., get the frequency values of brighter points of vertical and horizontal white lines in Fourier image.

Attached is the shifted magnitude after FFT:

I am using 'ginput' command to select value from fourier image but am getting no luck in that and exponent to remove log results in Inf. Any suggestions on how to remove these frequencies and how to get their values?

[Anton Semechko]

First issue. The DFT of the image should have the same dimensions as the original image. In your case, it does not. Post your code here so we can see how you computed the DFT.

[waqas]

Hi Anton,

Yeah I have uploaded zoomed image as it is not possible to see black and white dots without that. Size of image and DFT are the same in original code.

A = imread('QR_short.png');
figure(1);
imshow(A);
if ~islogical(A)
B = rgb2gray(A);
else
    B=A;
end
% C = edge(B,'canny');
% imshow(C)
C= B;
fft_im = fft2(B);
ffts=fftshift(fft_im);

freqPeaks= figure(2);
plot(abs(ffts));

S= log(abs(ffts));
figure(3);
fourier_fig = imshow(S,[]);
zoom(figure(3))
[kx,ky]= ginput(3);

P.S I am new to DIP.

Answer 1

[Image Analyst]

If you just want to set black circles (islands) in a sea of white to white, and white circles in a sea of black to black, I think the simplest, and most accurate, way is to do it in the spatial domain. Just find the spots using thresholding and bwareafilt(), then set those to the opposite color. Very simple.

[waqas]

I have a QR code in the image which i need to extract. Therefore I need to remove these black dots. Would your method work for that?

Answer 2

[Image Analyst]

OK, try this, if you just want to get rid of the circles:

clc;    % Clear the command window.
close all;  % Close all figures (except those of imtool.)
clearvars;  % Erase all existing variables. Or clearvars if you want.
workspace;  % Make sure the workspace panel is showing.
format long g;
format compact;
fontSize = 20;

folder = pwd;
baseFileName = 'capture.jpg';
% Get the full filename, with path prepended.
fullFileName = fullfile(folder, baseFileName);
% Check if file exists.
if ~exist(fullFileName, 'file')
  % The file doesn't exist -- didn't find it there in that folder.
  % Check the entire search path (other folders) for the file by stripping off the folder.
  fullFileNameOnSearchPath = baseFileName; % No path this time.
  if ~exist(fullFileNameOnSearchPath, 'file')
    % Still didn't find it.  Alert user.
    errorMessage = sprintf('Error: %s does not exist in the search path folders.', fullFileName);
    uiwait(warndlg(errorMessage));
    return;
  end
end
rgbImage = imread(fullFileName);
% Display the image.
subplot(2, 3, 1);
imshow(rgbImage, []);
title('Original Image', 'FontSize', fontSize, 'Interpreter', 'None');
hp = impixelinfo;
axis('on', 'image'); % Make sure image is not artificially stretched because of screen's aspect ratio.

% Get the dimensions of the image.
% numberOfColorChannels should be = 1 for a gray scale image, and 3 for an RGB color image.
grayImage = rgbImage; % Initialize.
[rows, columns, numberOfColorChannels] = size(grayImage);
if numberOfColorChannels > 1
  % It's not really gray scale like we expected - it's color.
  % Use weighted sum of ALL channels to create a gray scale image.
%   grayImage = rgb2gray(grayImage);
  % ALTERNATE METHOD: Convert it to gray scale by taking only the green channel,
  % which in a typical snapshot will be the least noisy channel.
  grayImage = grayImage(:, :, 1); % Take red channel.
end

% Display the image.
subplot(2, 3, 2);
imshow(grayImage, []);
title('Gray Scale Image', 'FontSize', fontSize, 'Interpreter', 'None');
hp = impixelinfo;
axis('on', 'image'); % Make sure image is not artificially stretched because of screen's aspect ratio.

%------------------------------------------------------------------------------
% Set up figure properties:
% Enlarge figure to full screen.
set(gcf, 'Units', 'Normalized', 'OuterPosition', [0, 0.04, 1, 0.96]);
drawnow;

% Display the histogram.
subplot(2, 3, 2);
imhist(grayImage);
grid on;
title('Histogram of Gray Scale Image', 'FontSize', fontSize, 'Interpreter', 'None');

% Find the black spots
binaryImage = grayImage > 128;
blackSpots = ~binaryImage;

% Find the size of the black spots.
props = regionprops(blackSpots, 'Area');
allAreas = [props.Area]
% They seem to be in the 100-500 pixel range.
% Extract blobs of only that size.
blackSpots = bwareafilt(blackSpots, [100, 500]);

% Display the black spots image.
subplot(2, 3, 3);
imshow(blackSpots, []);
caption = sprintf('Black Spots Image');
title(caption, 'FontSize', fontSize, 'Interpreter', 'None');
hp = impixelinfo;
axis('on', 'image'); % Make sure image is not artificially stretched because of screen's aspect ratio.
drawnow;

% Set these to white
binaryImage(blackSpots) = true;
% Display the binary image.
subplot(2, 3, 4);
imshow(binaryImage, []);
caption = sprintf('Binary Image');
title(caption, 'FontSize', fontSize, 'Interpreter', 'None');
hp = impixelinfo;
axis('on', 'image'); % Make sure image is not artificially stretched because of screen's aspect ratio.
drawnow;

% Now get rid of black spots
% They seem to be in the 100-500 pixel range.
% Extract blobs of only that size.
binaryImage = bwareafilt(binaryImage, [500, inf]);

% Display the final image.
subplot(2, 3, 5);
imshow(binaryImage);
axis('on', 'image'); % Make sure image is not artificially stretched because of screen's aspect ratio.
caption = sprintf('Final Image.');
title(caption, 'FontSize', fontSize);
drawnow;

[waqas]

Thank you for the detailed comment. I think the QR code would still be unreadable. With your approach the black contours will still render major error % in QR code. Current limit is 25% error correction in QR code. Attached is the large scale image with QR code for better explanation.

[Image Analyst]

Well you never said (until now) that it was a QR code.

It may be that the dithering is so severe/corrupted that you'll never get the true binary pattern.

What I'd do first is to look in the File Exchange to see if there is code to read QR codes and see if any works with your severely corrupted images. If not, and you don't want to use a commercial QR code reader and want to write it yourself in MATLAB, then you'll have to do what I said and first find the centers of the corner squares. Then set up a template to read the image at the grid locations.

[waqas]

I realized later that information about QR code should have been included in main question as well. Apologies for that.

I saw few QR readers in file exchange. I will try your suggestions as well.

Don’t you think information loss could be avoided with FFT as I mentioned in the main thread? I am not an expert but to me white horizontal and vertical lines are because of black and white dots and may be gray cirlces are representing those black curved in the background of main image for white circles. But for this I would need the frequency value which was the main question in the first place.

Let me know if you can guide me on this. Till then I will try to work around your suggested method.

BR

[Image Analyst]

See attached demo on FFT filtering to remove periodic noise (ripple). As you can see, it's not perfect.

[waqas]

Thank you for the files. I am working on them. I do have one question. Since circles are the most frequent objects therefore there frequency would be closer central and will be low frequency value as well. Therefore I am choosing smaller values for the location of spikes with a little modification in the code. However, I am unable to understand to how to understand this part.

% Exclude the central DC spike.  Everything from row 115 to 143.
brightSpikes(1000:1500, :) = 0;
imshow(brightSpikes);
title('Bright spikes other than central spike', 'FontSize', fontSize);

[waqas]

Hi Image Analyst,

I found the solution of the problem with notch filter but that only works for the case when image is perfectly in-plane (or we take original pattern). If we take the image with a camera at some angle, to mimic distortion, then notch filter does not work.

I tried to work around with your code of mask filter and am only filtering the highest frequencies other than DC component but the end result is just a noisy signal. Can you you guide on where exactly am I making the mistake?

Attached are the image and the updated code. (changed the format from tiff to jpg)