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Article Data
Article Ref
1867-UIDC-6529
Date Created
Mon, 31st Mar 2014
Date Modified
Fri, 4th Jul 2014

   Calculating centroids

Question 

How are centroids calculated?

Answer 

Sensor Model G2xxx, G3xxx
Firmware Version 3.x, 4.x
SDK Version n/a

Centroid 2D returns (X,Y), where X is the average of the X positions of all the points in the region of interest (ROI) and Y is the average of the Y positions of all the points in the ROI.

Centroid 3D returns (X,Y) where X is the Z-weighted average of the X positions of all the points in the ROI and Y is the Z-weighted average of the Y positions of all the points in the ROI (weighted arithmetic mean, where the weights are the Z values; see http://en.wikipedia.org/wiki/Weighted_arithmetic_mean.)

This means that the 3D centroid is shifted toward the point where the target is the "highest" (i.e., highest Z value).

Here is a simple example. Let's say you have a profile with 4 points in (X, Z)-coordinates (like in Gocator's Profile Mode) and those points are (1,1), (2,2), (3,3), and (4,4).

Then the 2D centroid is (X1 + X2 + X3 + X4) / 4 = (1 + 2 + 3 + 4) / 4 = 2.5.

And the 3D centroid is (X1*Z1 + X2*Z2 + X3*Z3 + X4*Z4) / (Z1 + Z2 + Z3 + Z4) = (1*1 + 2*2 + 3*3 + 4*4) / (1 + 2 + 3 + 4) = 3.