Periodic Boundary condition feature in image analysis tools

I'm doing some image analysis. Consider the image below with periodic boundary conditions.

Essentially, I want to count how many clusters there are automatically. Now, I understand that MATLAB has a comprehensive list of circle detection features like imfindcircles. But I am unable to find a circle detection algorithm/setting that recognises periodic boundary conditions in the image. As with my case, I would be left with double counting. I have tried creating my own methods of removing the double counting problem. But my methods are somewhat convoluted so I'm mildly sceptical. My question is if anyone knows of a quickfix/setting/feature that could implement periodic boundary conditions in something like imfindcircles?

Thank you

[Mar]

Hello. Did you ever figure this out. I have the same situation where I need to label clusters, but I have periodic boundaries conditions. Please help. Thanks.

[palaciosg226]

Hello, I have the same question. In many applications such as percolation detection, this tool is necessary.

[Rachel]

I have the same question. I am using an algorithm to identify clusters within a 3D cube. The result that I have right now double-counts the clusters at the edges/corners of the box. Is there a way to account for PBC in MATLAB to avoid double-counting?

Answer 1

[Image Analyst]

It can be done but it's a bit tricky. You can call imclearborder and then use find() to find out which blobs have pixels in common (actually somewhat different. It would take probably 15 minutes or so to do but first I'd like to know under what circumstances in the real world would give rise to this. Why are the partial blobs on opposite sides of the image actually the same physical object? Give me the real world use case. I don't want to spend time solving what ends up being an XY Problem.

Answer 2

[Rachel]

The provided coordinates for the clusters are already in wrapped form.

Answer 3

[Image Analyst]

Here is a way to "complete" the boundary (edge) blobs. However the blobs are now duplicated on the sides. We could use imclearborder to remove blobs on two of the sides, but if a blob is in a corner, it's replicated 4 times and you'd have to decide which one to keep.

% Demo by Image Analyst
% Initialization steps:
clc;    % Clear the command window.
close all;  % Close all figures (except those of imtool.)
clear;  % Erase all existing variables. Or clearvars if you want.
workspace;  % Make sure the workspace panel is showing.
format long g;
format compact;
fontSize = 12;
%--------------------------------------------------------------------------------------------------------
%    READ IN IMAGE
folder = pwd;
baseFileName = "spots wrapped.png";
fullFileName = fullfile(folder, baseFileName);
% Check if file exists.
if ~isfile(fullFileName)
    % 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
% Read in image file.
grayImage1 = imread(fullFileName);
% Get size
[rows, columns, numberOfColorChannels] = size(grayImage1)

rows =    603

columns =    601

numberOfColorChannels =      3

% Get gray scale version of it.
if numberOfColorChannels == 3
    grayImage1 = grayImage1(:, :, 1); % Take red channel.
end
mask = grayImage1 > 128;
% Display the image.
subplot(2, 2, 1);
imshow(mask);
axis('on', 'image');
impixelinfo;
caption = sprintf('Original image : %s', baseFileName);
title(caption, 'FontSize', fontSize, 'Interpreter', 'None');
% Maximize window.
g = gcf;
g.WindowState = 'maximized';
g.Name = 'Demo by Image Analyst';
g.NumberTitle = 'off';
drawnow;

%--------------------------------------------------------------------------------------------------------
% Replicate the image on all sides
mask2 = repmat(mask, 3, 3);
blank = false(rows, columns);
markerImage = [blank, blank, blank; blank, mask, blank; blank, blank, blank];

%--------------------------------------------------------------------------------------------------------
% REPLICATE THE MASK ON ALL SIDES.
% GET BORDER BLOBS ONLY
% borderBlobs = imkeepborder(mask);
% Display the image.
subplot(2, 2, 2);
imshow(mask2);
axis('on', 'image');
impixelinfo;
title('Replicated Mask', 'FontSize', fontSize, 'Interpreter', 'None');
% Display the marker image.
subplot(2, 2, 3);
imshow(markerImage);
axis('on', 'image');
impixelinfo;
title('Marker Blobs', 'FontSize', fontSize, 'Interpreter', 'None');

%--------------------------------------------------------------------------------------------------------
%  RECONSTRUCT THE INSIDE BLOBS
mask3 = imreconstruct(markerImage, mask2, 4);
% Display the image.
subplot(2, 2, 4);
imshow(mask3);
axis('on', 'image');
impixelinfo;
title('Reconstructed image', 'FontSize', fontSize, 'Interpreter', 'None');

%--------------------------------------------------------------------------------------------------------
% CROP THE IMAGE TO THE LARGEST BOUNDING BOX.
[r, c] = find(mask3);
row1 = min(r, [], 'all');
row2 = max(r, [], 'all');
col1 = min(c, [], 'all');
col2 = max(c, [], 'all');
mask4 = mask3(row1 : row2, col1 : col2);
% Display the image.
subplot(2, 2, 4);
imshow(mask4);
axis('on', 'image');
impixelinfo;
title('Reconstructed image', 'FontSize', fontSize, 'Interpreter', 'None');