We are currently in the chapter on image registration and sensor data fusion.

And what we have considered so far is basically how to make use of point correspondences to

estimate the rotation and translation.

And we have considered 2D points and rigid registration, and we know that complex numbers

help us a lot to come up with a linear solver for the problem.

And we have considered three-dimensional point correspondences, and we know that quaternions

help us out to come up with a linear solver to estimate the rotation parameters.

And then last time, sorry, I should have stayed at home, but unfortunately I had a very important

project meeting this morning in Regensburg.

So I drove up from Regensburg, and since then I'm close to dead.

And then last week, we also, sorry, we should not record it today.

Last week we looked at 3D, 2D registration.

You remember the example when you want to use preoperative CT data and intraoperative

X-ray data, and you want to combine them if you have point correspondences.

The registration problem is basically nothing else but a calibration problem that we have

considered right before Christmas to calibrate C-arm systems.

So we just estimate the components of the projection matrix out of the corresponding

2D, 3D points.

So the trick in this situation is basically the application of homogeneous coordinates.

And that's usually the picture I draw.

If you have feature-based image registration using point correspondences, you have, sorry,

not corrections, correspondences.

If you have 2D, 2D, the mathematical tools are complex numbers.

If you have 3D, 3D, the mathematical tool is basically the concept of quaternions.

And if you have a 2D, 3D correspondence problem, then you use homogeneous coordinates.

So we see that rather advanced mathematical concepts, which usually appear to us like

nice theoretical tools without any practical implication, these tools turn out to be or

to provide very high value for solving these practical problems.

And basically, once you understood this, you can use SVD, and you need just three lines

of code to solve the particular registration problem.

And that's some kind of funny, and it's nice.

And what you should really know and what you should do before you show up in the oral exam

is sit down, define yourself a few point correspondences, write down the measurement matrix and the

system of linear equations, and solve it and play around with it, because it's sometimes

not that obvious how to generate the measurement matrices.

At least for students, it's sometimes not so obvious.

And my personal experience is that quite often people are somehow surprised that I ask such

a detailed question in the oral exam.

It's not very detailed.

I give you a few points, and I say estimate the rotation.

And you should be able to write down the matrix equation.

And if you want to get the 7.5 ECTS points, then you should also be able to type in MATLAB

expressions.

Right?

Good.

So what we want to do now is today and tomorrow is we would like to look into registration

methods.

I see.

Okay.

I will push you a little bit more.