I understood that you want to detect singularities of your data using 2D CWT. Below are my observations on your queries.
- cwtft2 is used for calculating the 2D continuous wavelet transform.
- There are many wavelets supported by cwtft2 based on the requirement. You can find the list of those here https://www.mathworks.com/help/wavelet/ref/cwtftinfo2.html#bt1o3sf-wname
- Based on your data, you can pick one of the listed wavelets in the documentation. Here, I am using mexh as it is sensitive to changes in the signal, such as edges or singularities.
%% Data Generation(Replace your data)
[X, Y] = meshgrid(1:100, 1:100);
Z = zeros(size(X));
Z(40:60, 40:60) = 1; % Introduce singularities
known_singularities = [40, 60, 40, 60]; % [x_start, x_end, y_start, y_end]
%% Set parameters for 2D CWT
wavelet = 'mexh'; % Gaussian wavelet
scales = 1:32;
cwt_result = cwtft2(Z, 'wavelet', wavelet, 'scales', scales);
coef = cwt_result.cfs;
specific_scale = 10;
Z_wavelet = abs(coef(:, :, specific_scale));
%% Singularity Detection
threshold = 0.5 * max(Z_wavelet(:)); % Example threshold
detected_singularities = Z_wavelet > threshold;
% Visualize the wavelet coefficients and detected singularities
figure;
surf(X, Y, Z_wavelet);
title(['2D CWT Coefficients at Scale ', num2str(specific_scale)]);
xlabel('X');
ylabel('Y');
zlabel('Wavelet Coefficient Magnitude');
hold on;
% Highlight detected singularities
[detected_x, detected_y] = find(detected_singularities);
scatter3(detected_x, detected_y, Z_wavelet(detected_singularities), 'r', 'filled');
%% Comapring Detected and known singularities
matches = 0;
x_range = known_singularities(1):known_singularities(2);
y_range = known_singularities(3):known_singularities(4);
for i = 1:length(detected_x)
if ismember(detected_x(i), x_range) && ismember(detected_y(i), y_range)
matches = matches + 1;
end
end
disp(['Number of matches: ', num2str(matches)]);
disp(['Total detected singularities: ', num2str(length(detected_x))]);
Refer the below documentation for further information.
