How can I accurately get the fringes of this profile.

I have the following profile and I want to get the fringes (peaks along the fringes) that are shown.

What I want is accurately get the sape of this fringes I did edge detection but I don't think it's rigorous for this type of calculations. I have attached the .mat file if you want to look. All I want to is accuratly follow the local maxima of these fringes as shown in the figure below:

Did someone encounter similar problem. Thank you very much for the help.

[Walter Roberson]

I wonder if it would work to do a findpeaks() across each row of the image, and trace the evolution?

It might help to start from the middle row and track down until each peak disappears, and then go up and track upwards until each peak disappears.

[Vahram Voskerchyan]

yes! I think it's a good idea here is my approach based on your comment.

load('fringes.mat'); % Load Data

T = abs(P_resize); % Convert to absolute values
figure, imagesc(T), colormap(jet);
colorbar;
hold on;

minpeakdist = 3;  % Minimum distance between peaks
minpeakh = 3e-5;  % Minimum peak height

x_coords = [];
y_coords = [];

% Process all rows from top to bottom
for k = 1:size(T,1)
    tex = T(k,:);
    [pks, locs] = findpeaks(tex, 'MinPeakDistance', minpeakdist, 'MinPeakHeight', minpeakh);
    
    if ~isempty(locs)
        x_coords = [x_coords, X(k, locs)];
        y_coords = [y_coords, Y(k, locs)];
    end
end

% Plot detected fringes
figure;
plot(x_coords, y_coords, 'r*', 'markersize', 2);
hold on;
xlabel('X Coordinate');
ylabel('Y Coordinate');
title('Detected Fringes in Real-World Coordinates');
colorbar;

Answer 1

[Mathieu NOE]

hello

this is a very simple (simplistic ?) approach

I used peakseek for faster execution vs findpeaks but you can use your own prefered tool for this job

PeakSeek - File Exchange - MATLAB Central

of course I suspect you would have prefered a solution where each line data is stored in a specific cell array

here it's just the whole points , not yet organized.

load('fringes.mat')

T = abs(P_resize);
figure,imagesc(T)
colorbar
hold on

minpeakdist = 3;
minpeakh = 3e-5;
for k = 20:size(T,1)
    tex = T(k,:);
    [locs{k}, pks{k}]=peakseek(tex,minpeakdist,minpeakh);
    plot(locs{k},k*ones(size(locs{k})),'r*','markersize',2);

end

[Mathieu NOE]

maybe with a good clustering algorithm you could separate each line

made some attempts with for example

Mean Shift Clustering - File Exchange - MATLAB Central

T = abs(P_resize);
figure,imagesc(T)
colorbar
hold on

minpeakdist = 3;
minpeakh = 1e-5;

xlocs_all= [];
ylocs_all= [];
    
for k = 20:size(T,1)
    tex = T(k,:);
    [locs, pks]=peakseek(tex,minpeakdist,minpeakh);
    xlocs = locs;
    ylocs = k*ones(size(locs));
    
    %plot(xlocs,ylocs,'r.','markersize',2);
    xlocs_all= [xlocs_all xlocs];
    ylocs_all= [ylocs_all ylocs];

end

%% Run DBSCAN Clustering Algorithm
x = [xlocs_all;ylocs_all];
radius = 10;
tic
[clustCent,point2cluster,clustMembsCell] = MeanShiftCluster(x,radius); % NB : x must be row oriented (bcse : [numDim,numPts] = size(x))
toc

numClust = length(clustMembsCell);

Colors=jet(numClust);

for k = 1:numClust
    myMembers = clustMembsCell{k};
    myClustCen = clustCent(:,k);
    plot(x(1,myMembers),x(2,myMembers), '.','color',Colors(k,:))
%     plot(myClustCen(1),myClustCen(2),'o','MarkerEdgeColor','k','MarkerFaceColor',Colors(k,:), 'MarkerSize',10)
end

[Mathieu NOE]

similar stuff with dbscan

DBSCAN Clustering Algorithm - File Exchange - MATLAB Central

load('fringes.mat')

T = abs(P_resize);
figure,imagesc(T)
colorbar
hold on

minpeakdist = 3;
minpeakh = 1e-5;

xlocs_all= [];
ylocs_all= [];
    
for k = 20:size(T,1)
    tex = T(k,:);
    [locs, pks]=peakseek(tex,minpeakdist,minpeakh);
    xlocs = locs;
    ylocs = k*ones(size(locs));
    
    %plot(xlocs,ylocs,'r.','markersize',2);
    xlocs_all= [xlocs_all xlocs];
    ylocs_all= [ylocs_all ylocs];

end

%% Run DBSCAN Clustering Algorithm

epsilon=2;
MinPts=3;
X = [xlocs_all' ylocs_all']; 
tic
IDX=DBSCAN(X,epsilon,MinPts);
toc


%% Plot Results

PlotClusterinResult(X, IDX);

[Vahram Voskerchyan]

Thanks a lot this is exactly what I wanted!

[Mathieu NOE]

Glad I could help ! I was quite unsure I would be able to propose a solution that works good enough

In the mean time I was trying to improve the results , so I implemented some new features , maybe you will be interested to see the results

• resampled the data to a higher dimensions to better separate each fringe line from its neighbours - of course this will slow down the code but the wait is worth
• when doing the peaks search in each slice of data , I apply first a baseline correction to the data so when the peaks are in a low amplitude area it's easier to catch them (so at the end the fringe data collected is larger in size and we have less "holes" between segments)
• modified a bit the plot function after the clustering and added some code to store each individual fringe data in cell array Data{kk} .
• we don't store the small segments : here I opted to store only what is above this threshold :

% minimum size of data to be plotted (we don't want to plot the tiny bits)
minsize = 100;

• if the code works the same on your side , you should now have Data is a cell array of size 1x 25, so you have each individual fringe coordinates at your disposal

result should look like : (see the improvement vs the first code with dbscan )

load('fringes.mat')

T = abs(P_resize);
[m,n] = size(T);
% resample at higher resolution
upsample_factor = 4;
[x, y] = meshgrid(1:n, 1:m);
[xq, yq] = meshgrid(linspace(1, n, upsample_factor*n), linspace(1, m, upsample_factor*m));
T = interp2(x, y, T, xq, yq);

% plot
figure,imagesc(T)
colorbar
hold on

% parameters for baseline correction function
minpeakdist = 3*upsample_factor;
minpeakh = 1e-6;

% init
xlocs_all= [];
ylocs_all= [];
    
for k = 15*upsample_factor:size(T,1)
    tex = T(k,:);
    % baseline correction
    [Base, texc]=baseline(tex(:));
    % find the peaks in each slice of T
    [locs, ~]=peakseek(texc,minpeakdist,minpeakh);
    xlocs = locs;
    pks = tex(locs);
    ylocs = k*ones(size(locs));
    %plot(xlocs,ylocs,'r*','markersize',2);
    % store new data;
    xlocs_all= [xlocs_all xlocs];
    ylocs_all= [ylocs_all ylocs];

end

%% Run DBSCAN Clustering Algorithm
epsilon=2*upsample_factor;
MinPts=2;
X = [xlocs_all' ylocs_all']; 
tic
IDX=DBSCAN(X,epsilon,MinPts);
toc

% minimum size of data to be plotted (we don't want to plot the tiny bits)
minsize = 100;

%% Plot Results
k=max(IDX);
Colors=hsv(k);
Legends = {};
kk = 0;

for i=0:k
    Xi=X(IDX==i,:);
    if i~=0
        Style = '.';
        MarkerSize = 12;
        Color = Colors(i,:);
        Legends{end+1} = ['Cluster #' num2str(i)];
    else
        Style = 'o';
        MarkerSize = 6;
        Color = [0 0 0];
        if ~isempty(Xi)
            Legends{end+1} = 'Noise';
        end
    end
%         if ~isempty(Xi)  % original code
    if size(Xi,1)>=minsize % modified code
        plot(Xi(:,1),Xi(:,2),Style,'MarkerSize',MarkerSize,'Color',Color);
        % store the data if the size is large enough
        kk = kk + 1;
        Data{kk} = Xi;
    end
end
hold off;
axis equal;
grid on;

[Mathieu NOE]

forgot to say : you will need the below and attached functions for the baseline correction

here I had to make a tiny modification in baseline to avoid sometimes an error :

%     if A(i-1)<A(i-2) && A(i-1)<A(i)         % original code
    if (A(i-1)<A(i-2) && A(i-1)<A(i)) || n>=l % mod MN : added condition (n>=l) to avoid error

        
function [Base, Corrected_Spectrum]=baseline(Spectrum)

%Input
%-------
%Spectrum: vector of size (N*1)

%Output
%-------
%Base: Identified Baseline vector of size (N*1)
%Corrected_Spectrum: Corrected Spectrum vector of size (N*1)

l=length(Spectrum);  

lp=ceil(0.5*l);

initial_Spectrum=[ones(lp,1)*Spectrum(1) ; Spectrum ; ones(lp,1)*Spectrum(l)];

l2=length(initial_Spectrum);

S=initial_Spectrum;

n=1;

flag1=0;

while flag1==0
    
n=n+2;
    
i=(n-1)/2;
    
[Baseline, stripping]=peak_stripping(S,n);

A(i)=trapz(S-Baseline);

Stripped_Spectrum{i}=Baseline;

S=Baseline;

if i>3
%     if A(i-1)<A(i-2) && A(i-1)<A(i)         % original code
    if (A(i-1)<A(i-2) && A(i-1)<A(i)) || n>=l % mod MN : added condition (n>=l) to avoid error
        i_min=i-1;
        flag1=1;
    end 
end



end


Base=Stripped_Spectrum{i_min}; 

Corrected_Spectrum=initial_Spectrum-Base; Corrected_Spectrum=Corrected_Spectrum(lp+1:lp+l);

Base=Base(lp+1:lp+l);
end

[Mathieu NOE]

I don't have the Stats Toolbox, but if you have , you could try with Spectral Clustering

spectralcluster