Find center of mass of parts of a matrix

Hi, Let us say that I have a matrix as shown below:

Then I apply a treshold to this matrix and am left with a region of interest. As such:

How can I find the center of mass for this region of interest (using values from the corresponding indexes in the first matrix) and the location of this center of mass in the original matrix?

Thanks for any help

Answer 1

[Guillaume]

Well, go back to the definition of the centre of mass, which is just a weighted mean:

%inputs:
%originalmatrix: the original matrix
%binarisedmatrix = originalmatrix > threshold; %the thresholded matrix, a logical array
[rows, cols] = ndgrid(1:size(originalmatrix, 1), 1:size(originalmatrix, 2));
rowcentre = sum(rows(binarisedmatrix) .* originalmatrix(binarisedmatrix)) / sum(originalmatrix(binarisedmatrix));
colcentre = sum(cols(binarisedmatrix) .* originalmatrix(binarisedmatrix)) / sum(originalmatrix(binarisedmatrix));

[OH]

Thanks! That works great!

[OH]

Sorry to bring this up again, but I just need to make sure that everything is correct.

I tested the code you wrote on a 10-by-10 matrix as such:

the center bins are all = 2 and the surrounding bins = 1. I then plotted the rowcentre and colcentre (red circle in the image). Should not the centroid be located at the very centre here? That is, rowcentre = 5.5 and colcentre = 5.5? Thanks again.

[Guillaume]

Works fine for me:

originalmatrix = ones(10);
originalmatrix(4:7, 4:7) = 2         %semicolon missing for display
binarisedmatrix = originalmatrix > 1 %semicolon missing for display
[rows, cols] = ndgrid(1:size(originalmatrix, 1), 1:size(originalmatrix, 2));
rowcentre = sum(rows(binarisedmatrix) .* originalmatrix(binarisedmatrix)) / sum(originalmatrix(binarisedmatrix))  %semicolon missing for display
colcentre = sum(cols(binarisedmatrix) .* originalmatrix(binarisedmatrix)) / sum(originalmatrix(binarisedmatrix))  %semicolon missing for display

returns 5.5 for both rowcentre and colcentre

[OH]

You are right, it works. I had just made a silly mistake. Thanks!

Answer 2

[KSSV]

doc mean

[OH]

Hey, thanks. I know how to get the mean value of the region of interest: let us call the first matrix A and the tresholded matrix, where the region of interest indexes = 1 and outside region indexes = 0,B. Then I find the mean value by: mean(A(B==1))

However, I need to find the location of the center of mass in A