Let's first look at
Invariant to Rotation.
Here's a simple example again.
Let's look at this.
And I have the same corner in this
instance is appearing in another image
with a rotation.
Now in this case, if we were to
go through the whole process, and
computing the details that would
actually let us do the ellipse,
which basically would have
the eigenvalues and stuff like that.
Again, we're not doing this directly,
but we actually look at
second movements, which allows
us to get similar information.
For this point and this point,
the eigenvalues should be the same.
The size of the ellipse that we're
looking at should be the same,
but what should not be,
is of course, the rotation.
So it's orientation has
changed from this to this, but
the eigenvalues remain the same.
Since r is only dependent on
the eigenvalues of the ellipse,
it basically suggests that
the corner response function, r,
is invariant to image rotation.
So, this object can be
rotated completely,
as long as these values are the same.
We should still get the same r function,
and with threshold and stuff,
we'll still get the same point.
And in fact, that's what would
suggest that these two corners of
this image would be
identified in both the pairs.
