Matlab finding the center of cluster of a few pixels and counting the clusters - arrays

Question

So I have this matrix A, which is made of 1 and zeros, I have about 10 to 14 white spots of many pixels, but I want only 1 white pixel/centers coordinate for every cluster of white, how do I calculate how many cluster there are and their centers.
Try to imagine the matrix A as the night sky with white starts in black sky and how to I count the stars and the stars centers, plus the star are made of cluster of white pixels.
also the clusters are not all exactly the same size.

Answer 1

Here is some code using bwlabel and/or regioprops, which are used to identify connected components in a matrix and a buch of other properties, respectively. I think it suits your problem quite well; however you might want to adapt my code a bit as its more of a starting point.
clear
clc
%// Create dummy matrix.
BW = logical ([ 1 1 1 0 1 1 1 0
1 1 1 0 1 1 1 0
1 1 1 0 1 1 1 0
0 0 0 0 0 0 0 0
0 0 0 0 0 1 1 0
1 1 1 1 0 1 1 0
1 1 1 1 0 1 1 0
1 1 1 1 0 0 0 0]);
%// Identify clusters.
L = bwlabel(BW,4)
Matrix L looks like this:
L =
1 1 1 0 3 3 3 0
1 1 1 0 3 3 3 0
1 1 1 0 3 3 3 0
0 0 0 0 0 0 0 0
0 0 0 0 0 4 4 0
2 2 2 2 0 4 4 0
2 2 2 2 0 4 4 0
2 2 2 2 0 0 0 0
Here you have many ways to locate the center of the clusters. The first one uses the output of bwlabel to find each cluster and calculate the coordinates in a loop. It works and its didactic but it's a bit long and not so efficient. The 2nd method, as mentioned by #nkjt, uses regionprops which does exactly what you want using the 'Centroid' property. So here are the 2 methods:
Method 1: a bit complicated
So bwlabel identified 4 clusters, which makes sense. Now we need to identify the center of each of those clusters. My method could probably be simplified; but I'm a bit out of time so fell free to modify it as you see fit.
%// Get number of clusters
NumClusters = numel(unique(L)) -1;
Centers = zeros(NumClusters,2);
CenterLinIdices = zeros(NumClusters,1);
for k = 1:NumClusters
%// Find indices for elements forming each cluster.
[r, c] = find(L==k);
%// Sort the elements to know hot many rows and columns the cluster is spanning.
[~,y] = sort(r);
c = c(y);
r = r(y);
NumRow = numel(unique(r));
NumCol = numel(unique(c));
%// Calculate the approximate center of the cluster.
CenterCoord = [r(1)+floor(NumRow/2) c(1)+floor(NumCol/2)];
%// Actually this array is not used here but you might want to keep it for future reference.
Centers(k,:) = [CenterCoord(1) CenterCoord(2)];
%// Convert the subscripts indices to linear indices for easy reference.
CenterLinIdices(k) = sub2ind(size(BW),CenterCoord(1),CenterCoord(2));
end
%// Create output matrix full of 0s, except at the center of the clusters.
BW2 = false(size(BW));
BW2(CenterLinIdices) = 1
BW2 =
0 0 0 0 0 0 0 0
0 1 0 0 0 1 0 0
0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0
0 0 0 0 0 0 1 0
0 0 1 0 0 0 0 0
0 0 0 0 0 0 0 0
Method 2 Using regionprops and the 'Centroid' property.
Once you have matrix L, apply regionprops and concatenate the output to get an array containing the coordinates directly. Much simpler!
%// Create dummy matrix.
BW = logical ([ 1 1 1 0 1 1 1 0
1 1 1 0 1 1 1 0
1 1 1 0 1 1 1 0
0 0 0 0 0 0 0 0
0 0 0 0 0 1 1 0
1 1 1 1 0 1 1 0
1 1 1 1 0 1 1 0
1 1 1 1 0 0 0 0]);
%// Identify clusters.
L = bwlabel(BW,4)
s = regionprops(L,'Centroid');
CentroidCoord = vertcat(s.Centroid)
which gives this:
CentroidCoord =
2.0000 2.0000
2.5000 7.0000
6.0000 2.0000
6.5000 6.0000
Which is much simpler and gives the same output once you use floor.
Hope that helps!