I would like to know if a centroid of points is mapped to the new centroid if the points are mapped via a homography.
How is a centroid determined when using 2D-homographic coordinates.
Lets assume X1 = [1,0,1]' and X2 = [2,1,1]'. The centroid should still be 0.5(X1+X2), right?
X1 = [1,0,1]';X2 = [2,1,1]';Xm = [1.5, 0.5, 1]';H = [1,1,10;2.3,2,20;0.4,1,1];X_1 = H*X1;X_2 = H*X2;X_m = 0.5*(X_1+X_2);result = H*Xm - X_m;
In fact the result 0. So it seems that the centroid is mapped to the centroid. Is this somehow a lucky case or is this the case in general?
The only thing I see, that the third entry of the vectors have to be 1.
Thanks for your help,
Michael