Centroid of irregular polygons

[jonnylane]

Hi there,

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 I am trying to come up with a scientific definition of a centroid. I've tried "point of rotation at which ACW moment = CW moment = 0,and a few others, but this doesn't sound right in the purely mathematical context.

any ideas?
thanks

 

[dg]

The centroid is simply more known to physicist as "center of mass"...

Anyway this will help: http://mathworld.wolfram.com/GeometricCentroid.html

If not ask again... ;) Dario

 

[tacman]

Hi there,

The centroid of an irregular polygon is defined as the point at which the polygon could be balanced on a pin. It is often referred to as the "center of mass" or "center of gravity" of the polygon. This point is calculated by taking the average of the coordinates of all the vertices of the polygon. In mathematical terms, it can be represented as (x̅, y̅), where x̅ is the average of all the x-coordinates and y̅ is the average of all the y-coordinates.

In your case, where you are working with ROI's of anatomical features, the centroid can be thought of as the point that represents the "center" of the feature. This can be useful in determining the location of the feature in relation to other structures or for measuring its position within the scan.

I hope this helps in your dissertation writing. Best of luck!