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I have a bit of a problem for you. I have recently had to write a program to compute the centroid (centre of area) of a 2d shape. I used a many-point weighted triangle method. The shapes themselves are ROI's of anatomical features on SPECT and MRI scans.

Im writing up my dissertation and im trying to come up with a scientific definition of a centroid. Ive tried "point of rotation at which ACW moment = CW moment = 0,and a few others, but this doesnt sound right in the purely mathematical context.

any ideas?

thanks