coordinates of high frequency

Is there any way to find points or coordinates of high frequencies in a 2d image?

[Abhishek Tiwari]

Are you referring to points that occur the most frequently or the points with maximum intensity?

[Jonas]

or the strongest frequency acquired from 2d fft spectrum?

Answer 1

[Rahul]

Hi @AAS,

I understand that you want to find the coordinates of high frequency from a 2d image.

If you wish to find the coordinates of strongest frequency acquired from 2d fft spectrum, you can follow the following method:

• Convert the image to the frequency domain using 'fft2' function.
• Shift frequency components to center at zero frequency using 'fftshift' function.
• Obtain the magnitude spectrum to identify and threshold the highest frequencies.

% Considering 'img' to be the variable for the 2d Image
img = rgb2gray(img);

% Converting 'img' to frequency domain using 'fft2' function
% Shifting the Zero Frequncy component using 'fftshift' function
F = fft2(double(img));
F_shifted = fftshift(F);

% Obtaining the magnitude spectrum of frequencies
magnitude = abs(F_shifted);
magnitude = log(1 + magnitude);
magnitude = mat2gray(magnitude);

threshold = 0.7; % Using a threshold to obtain high frequncies. Can be adjusted according to use-case.
high_freq_mask = magnitude > threshold;

% Finding Coordinates of High Frequencies
[row, col] = find(high_freq_mask);

hold on;
plot(col, row, 'r*');
title('High Frequency Points');

If you wish to find the coordinates of highest frequency based on occurrance, you can follow the following method:

• Identify features from the 2d Image using 'detectSURFFeatures' function.
• Using 'selectStrongest' function from the identified points to extract the points occurring most frequently.
• If required, 'kmeans' function can be leveraged to obtain clusters of high frequnecy points and showcase their centers.

% Considering 'img' to be the variable for the 2d Image
img = rgb2gray(img);

% Detect features
points = detectSURFFeatures(img);

% Extract and plot the strongest points
strongestPoints = points.selectStrongest(100); % 100 can be changed accoridng to use-case
imshow(img); hold on;
plot(strongestPoints);

% Perform clustering using 'kmeans' function and plot centers
coordinates = strongestPoints.Location;
[idx, C] = kmeans(coordinates, 5); % Example with 5 clusters, can be changed accordingly
plot(C(:,1), C(:,2), 'rx', 'MarkerSize', 15, 'LineWidth', 3);

You can refer to the following Mathworks documentations to know more about these functions:

'fft2': https://www.mathworks.com/help/releases/R2024a/matlab/ref/fft2.html?searchHighlight=fft2&s_tid=doc_srchtitle

'fftshift': https://www.mathworks.com/help/releases/R2024a/matlab/ref/fftshift.html?searchHighlight=fftshift&s_tid=doc_srchtitle

'find': https://www.mathworks.com/help/releases/R2024a/matlab/ref/find.html?searchHighlight=find&s_tid=doc_srchtitle

'detectSURFFeatures': https://www.mathworks.com/help/releases/R2024a/vision/ref/detectsurffeatures.html?searchHighlight=detectSURFFeatures&s_tid=doc_srchtitle

'selectStrongest': https://www.mathworks.com/help/releases/R2024a/vision/ref/kazepoints.selectstrongest.html?searchHighlight=selectStrongest&s_tid=doc_srchtitle

'kmeans': https://www.mathworks.com/help/releases/R2024a/stats/kmeans.html?searchHighlight=kmeans&s_tid=doc_srchtitle

Hope this helps!