# Find the barycenter of luminance in an image

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David Corwin
on 29 Oct 2015

Commented: David Corwin
on 30 Oct 2015

##### 2 Comments

### Accepted Answer

Image Analyst
on 29 Oct 2015

Edited: Image Analyst
on 29 Oct 2015

Since R2008a (or maybe b) regionprops has had a "WeightedCentroid" property that you can ask for. So pass in the L channel and ask for that if you want the centroid weighted by the L value.

If you want it weighted by the distance, that's the inertia or moment. See https://en.wikipedia.org/wiki/Image_moment I don't think there's anything built in for that but you can ask for the PixelList which is the location of every pixel in the blob and you can easily calculate it yourself.

##### 6 Comments

Walter Roberson
on 30 Oct 2015

No, L is not the label matrix here. L is the luminance channel, in accordance with IA's earlier "So pass in the L channel and ask for that if you want the centroid weighted by the L value."

A = imread('figure2.jpg');

LAB = rgb2lab(A);

L = LAB(:,:,1);

imageprops = regionprops(L, 'WeightedCentroid');

result = imageprops.WeightedCentroid;

If you want the "top half" then pass in the top half,

imageprops = regionprops(L(1:end/2,:), 'WeightedCentroid');

upperCent = imageprops.WeightedCentroid;

imageprops = regionprops(L(ceil(end/2):end,:), 'WeightedCentroid');

lowerCent = imageprops.WeightedCentroid;

### More Answers (1)

Image Analyst
on 30 Oct 2015

David:

I wrote a demo for you to compute the first 5x5 central spatial moments, as given by the Wikipedia page https://en.wikipedia.org/wiki/Image_moment. See attached m-file. The key code is this:

% Sum up the powers of the gray levels, weighted by the distance from the centroids.

% Ref: https://en.wikipedia.org/wiki/Image_moment

highestMomentNumber = 5;

mu = zeros(highestMomentNumber, highestMomentNumber); % Allocate up to 5 moment (probably way overkill).

for q = 1 : size(mu, 2) % in the column, x direction.

for p = 1 : size(mu, 1) % in the row, y direction

for location = 1 : length(allX)

% For every pixel in this blob....

% Sum up for moment "mu sub pq" - i.e. the pqth moment.

thisGrayLevel = grayImage(allY(location), allX(location));

mu(p, q) = mu(p, q) + ...

(allX(location) - xCenter).^q * ...

(allY(location) - yCenter).^p * ...

double(thisGrayLevel);

end

end

end

See file for a complete demo.

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