Introduction
With the last step we know where the bottom edges of the pawn are located on the image, we just need to find a way to transform the coordinates of those pixels into game field coordinates.
Given a point
from the Image plane, we’d like to transform it into
from the Game field plane. We can write:

We observe that straight lines are kept straight, thus H is called the homography matrix which can be computed if at least 4 different matching points are given for both planes. 
It’s worth noticing that both
and
points are given in homogeneus coordinates.
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