Find the barycenter of luminance in an image
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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.
More Answers (1)
Image Analyst on 30 Oct 2015
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 * ...
See file for a complete demo.