Computing Homography
Articles,  Blog

Computing Homography

So let’s think about how
we can compute homography. Let’s start off,
my two images from my scene again. Again, this is
the Lord’s Cricket Ground and what I’m going to do is I’m going
to focus in on a specific region. Let’s say this region here and
this region here. The reason I’m actually picking
these is because there’s a nice planar rectangle in that region and
we can actually use that as an example. Let’s zoom these regions up. So we’ll take this as one of our images
and the second one would be this one and let’s look at them a little
bit more carefully. So here is my two regions, zoom and zoomed in the little
bit of the left panel. It’s done to kind of find this one. This is my equation. We know everything about it by now. What we’re really interested in
computing is a new P-prime from using the transformation
from the original piece. Let’s find four points in this one and I did say there was a reason I found
this region because now I can actually find four points at the corners of
this sign that was on the grass. I can find the same four points here. So, P-prime would be here. P is here, all right? So these are all xys and these would be,
of course, in my new coordinate system, x prime, y prime, using just this
equation, homogenous coordinates. So, again, all ps and all P-primes. So to compute the homography, H here, given pairs of corresponding
points in the two images, we need to set up a set of equations,
where the parameters of H are unknown. So, in essence, these are my two sets. I can most probably get the information
about where these locations are. What I actually don’t know is what H would be between those two images,
right? So that’s what we want to compute. We want to actually model
the transformation that goes from this to this because
if I know this transformation, I can use this for a variety of things.


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