Integrated S-theta, k-means clustering code added.

Data-Analyzer/fourierAnalysis.m

@@ -80,6 +80,7 @@ end
 %% Run Fourier analysis over images
 
 fft_imgs                    = cell(1, nimgs);
+integrated_sf               = zeros(1, nimgs);
 
 % Create VideoWriter object for movie
 videoFile = VideoWriter('Single_Shot_FFT.mp4', 'MPEG-4');
@@ -92,7 +93,7 @@ for k = 1 : length(od_imgs)
     IMG              = od_imgs{k};
     [IMGFFT, IMGBIN] = computeFourierTransform(IMG);
     
-    figure(2);
+    figure(1);
     clf
     set(gcf,'Position',[500 100 1000 800])
     t = tiledlayout(2, 2, 'TileSpacing', 'compact', 'Padding', 'compact'); % 1x4 grid
@@ -146,8 +147,8 @@ for k = 1 : length(od_imgs)
     hYLabel = ylabel('Y (pixels)', 'Interpreter', 'tex');
     hTitle = title('Denoised - Masked - Binarized', 'Interpreter', 'tex');
     
-    set([hXLabel, hYLabel, hL], 'FontName', font)
+    set([hXLabel, hYLabel], 'FontName', font)
-    set([hXLabel, hYLabel, hL], 'FontSize', 14)
+    set([hXLabel, hYLabel], 'FontSize', 14)
     set(hTitle, 'FontName', font, 'FontSize', 16, 'FontWeight', 'bold');  % Set font and size for title
 
     ax3 = nexttile;
@@ -172,11 +173,11 @@ for k = 1 : length(od_imgs)
     hXLabel = xlabel('X (pixels)', 'Interpreter', 'tex');
     hYLabel = ylabel('Y (pixels)', 'Interpreter', 'tex');
     hTitle = title('Fourier Power Spectrum', 'Interpreter', 'tex');
-    set([hXLabel, hYLabel, hL, hText], 'FontName', font)
+    set([hXLabel, hYLabel, hText], 'FontName', font)
-    set([hXLabel, hYLabel, hL], 'FontSize', 14)
+    set([hXLabel, hYLabel], 'FontSize', 14)
     set(hTitle, 'FontName', font, 'FontSize', 16, 'FontWeight', 'bold');  % Set font and size for title
 
-    % Plot the angular structure factor
+    % Plot the angular distribution
     %{
     nexttile
     [theta_vals, angular_intensity] = computeAngularDistribution(zoomedIMGFFT, 10, 20, 100, 75);
@@ -190,19 +191,17 @@ for k = 1 : length(od_imgs)
     % Plot the angular structure factor
     nexttile
     [theta_vals, S_theta] = computeAngularStructureFactor(zoomedIMGFFT, 10, 20, 180, 75, 2);
-
+    integrated_sf(k)      = trapz(theta_vals, S_theta);
     plot(theta_vals/pi, S_theta,'Linewidth',2);
     set(gca, 'FontSize', 14);   % For tick labels only
     hXLabel = xlabel('\theta (\pi)', 'Interpreter', 'tex');
     hYLabel = ylabel('S(\theta)', 'Interpreter', 'tex');
     hTitle = title('Angular Structure Factor', 'Interpreter', 'tex');
-    set([hXLabel, hYLabel, hL, hText], 'FontName', font)
+    set([hXLabel, hYLabel, hText], 'FontName', font)
-    set([hXLabel, hYLabel, hL], 'FontSize', 14)
+    set([hXLabel, hYLabel], 'FontSize', 14)
     set(hTitle, 'FontName', font, 'FontSize', 16, 'FontWeight', 'bold');  % Set font and size for title
     grid on
     
-    
-
     drawnow
     pause(0.5)
     
@@ -214,6 +213,94 @@ end
 % Close the video file
 close(videoFile);
 
+%% Track integrated structure factor across the transition
+
+% Assuming theta_values and integrated_sf are column vectors (or row vectors of same length)
+[unique_theta, ~, idx] = unique(theta_values);
+
+% Preallocate arrays
+mean_sf = zeros(size(unique_theta));
+stderr_sf = zeros(size(unique_theta));
+
+% Loop through each unique theta and compute mean and standard error
+for i = 1:length(unique_theta)
+    group_vals = integrated_sf(idx == i);
+    mean_sf(i) = mean(group_vals);
+    stderr_sf(i) = std(group_vals) / sqrt(length(group_vals)); % standard error = std / sqrt(N)
+end
+
+figure(2);
+set(gcf,'Position',[100 100 950 750])
+errorbar(unique_theta, mean_sf, stderr_sf, 'o--', ...
+    'LineWidth', 1.5, 'MarkerSize', 6, 'CapSize', 5);
+set(gca, 'FontSize', 14);   % For tick labels only
+hXLabel = xlabel('\alpha (degrees)', 'Interpreter', 'tex');
+hYLabel = ylabel('Integrated S(\theta)', 'Interpreter', 'tex');
+hTitle = title('Change during rotation', 'Interpreter', 'tex');
+set([hXLabel, hYLabel], 'FontName', font)
+set([hXLabel, hYLabel], 'FontSize', 14)
+set(hTitle, 'FontName', font, 'FontSize', 16, 'FontWeight', 'bold');  % Set font and size for title
+grid on
+
+%% k-means Clustering
+
+% Reshape to column vector
+X = mean_sf(:);
+
+% Determine the number of clusters to try (you can experiment with different values here)
+optimalClusters = 3;  % Based on prior knowledge or experimentation
+
+% Set the random seed for reproducibility
+rng(42);  
+
+% Specify initialization method ('plus' is the default)
+startMethod = 'plus';  % Options: 'uniform', 'plus', 'sample'
+
+% Apply K-means clustering with controlled initialization
+[idx, C] = kmeans(X, optimalClusters, 'Start', startMethod);
+
+% Plot the results
+figure(3);
+set(gcf,'Position',[100 100 950 750])
+hold on;
+
+% Plot error bars with mean_sf and stderr_sf
+errorbar(unique_theta, mean_sf, stderr_sf, 'o--', ...
+     'LineWidth', 1.5, 'MarkerSize', 6, 'CapSize', 5);
+
+% Scatter plot for data points (showing clusters)
+scatter(unique_theta, X, 50, idx, 'filled');
+
+% Get the current y-axis limits
+current_ylim = ylim;
+
+% Generate colors for each cluster
+colors = lines(optimalClusters);  % Create distinct colors for each cluster
+
+% Loop through each cluster and fill the regions
+for i = 1:optimalClusters
+    % Find indices of data points that belong to the current cluster
+    clusterIdx = find(idx == i);
+    
+    % Find the range of x-values for this cluster
+    x_min = unique_theta(clusterIdx(1));  % Starting x-value for the cluster
+    x_max = unique_theta(clusterIdx(end));  % Ending x-value for the cluster
+    
+    % Fill the region corresponding to the cluster
+    fill([x_min, x_max, x_max, x_min], ...
+         [current_ylim(1), current_ylim(1), current_ylim(2), current_ylim(2)], ...
+         colors(i, :), 'EdgeColor', 'none', 'FaceAlpha', 0.3);  % Add transparency
+end
+
+hXLabel = xlabel('\alpha (degrees)', 'Interpreter', 'tex');
+hYLabel = ylabel('Integrated S(\theta)', 'Interpreter', 'tex');
+hTitle = title('Regimes identified by k-means clustering', 'Interpreter', 'tex');
+set([hXLabel, hYLabel], 'FontName', font)
+set([hXLabel, hYLabel], 'FontSize', 14)
+set(hTitle, 'FontName', font, 'FontSize', 16, 'FontWeight', 'bold');  % Set font and size for title
+grid on;
+hold off;
+
 %% Helper Functions
 function [IMGFFT, IMGBIN] = computeFourierTransform(I)
     % computeFourierSpectrum - Computes the 2D Fourier power spectrum