So using this, we came up with this
whole description of how to look for
corner or
responses of corners in an image.
And we looked at this diagram.
And again, basically this is showing
you in the two different eigenvalues,
that if the eigenvalue 1 is larger,
the eigenvalue 2 is smaller.
This is the kind of shape you get.
If both of them are smaller
this is what you get.
If eigenvalue second one is larger,
this is the shape you get.
And of course, when both of them
are larger, this is the shape again.
Of course this is the corner.
So we're looking for mostly corners.
This would be an edge,
this would be an edge, and
this would just be a thresholded point.
We also looked at details of
how we can actually now just
if we know the second moment matrix,
we can actually compute all of this
from the straight from
the second moment matrix.
And we actually did look at the
determinant of this matrix and trace and
actually just comes after
the simple calculation.
And we use a small weight factor, a
constant to help us do this calculation.
So if you notice here where R, which
basically is giving us this information
about what is a corner or not,
is only dependent on the eigenvalues
of the second moment matrix,
making it larger when it's a corner.
Negative with large magnitude for
an edge and small.
The magnitude of the R would be small
and that’s where this region would be.
So again, we can do all of this
without any explicit computations of
the eigenvalues because we know how to
compute the M straight from the image,
by just doing the derivatives and
then using the gradient
computation to help us get there.
Which actually is an efficient way of
doing these kind of things, and again
this is one of the reasons this kind
of stuff can be done quite efficiently
in most simple computers.
Again, remember, this was the equation
that now we just have to compute, and
we can actually do this
on a neighborhood with
just image intensities, and
the derivatives of image intensities.
