Okay, so one first remark.

Wait, wait, I have some other set of slides. Just one second.

Wait, wait, wait, wait.

I'm borrowing a set of slides from medical engineering one, because what I want to talk about right now, and you don't have to record this, is the lecture evaluation.

Surprise, surprise. Yeah, so I have tons here, and everybody can have one.

So you may want to, so if you come up here, everybody can get a transaction. Do you want to have one? Please evaluate.

So I'm going to hand them out now, and I'm asking you to please evaluate this lecture, and you may have noticed, come on, you can come up here, or you can just pass them through.

Okay, then just pass them through. Have you noticed those nice QR codes on the tons? Who knows what these QR codes are for?

You can just scan it with your mobile phone using your QR app, and you will be directly guided to the questionnaire, and there you only have to answer five questions, so it's very short.

You can do the evaluation really quickly, but evaluation is really important in order to make our lectures better, and there's a couple of questions, and if you're interested, you can do the extended questionnaire,

but if you're not too much interested in the evaluation, there's only five questions, so please do these five questions, and you can do it even now during the lecture.

All the information is on the transaction numbers, so please evaluate. This is important for improving the lecture, and we will go through the evaluation results, what you reported in the last lecture of this term.

So we only have now essentially two lectures left, so we will do non-rigid registration, and we will do interventional reconstruction, motion compensated reconstruction, and then we will finish the lecture.

But in the last lecture of the semester, we will do the evaluation results and the summary of the entire lecture, which will be very closely related to the cloud, and if you go through the summary, it can also, maybe we do it more in an interactive way.

Who wants to do the summary in an interactive way? Who's taking the exam in the first exam period? Quite a few.

So we can go, and so you can already prepare for the last lecture, and then we will talk about the contents in quite some detail for one and a half hours, summarize everything, and then this should also give you a pretty good preparation for the oral exam.

Good. Did everybody get a transaction number? Did you already evaluate? Evaluate, please.

I have to collect the remaining numbers, the remaining tons. Do you also evaluate? Good. You also need to evaluate. We need you for evaluation.

No. So does everybody know what happens to the evaluation? What will be done with it?

So first of all, we will go through the evaluation results and discuss about the pros and cons of the lecture, and I can use that feedback to improve the lecture.

Second part is there's a ranking of all the lectures that will be prepared, and all the lectures that have an evaluation less than a certain level, those lectures will have to write a statement why the evaluation was so bad, and this will be discussed in the study committees.

So evaluation is also important if somebody is not doing a good job in the lecture, he has to explain it to the study committees.

So those are also the people who decide which subjects are going to be part of the lecture and of your study curriculum and which lectures aren't.

So there's multiple effects that the evaluation has. And of course there's a ranking, and the best lectures, the top ten lectures are usually published, and of course it's very prestigious to be part of the top ten lectures.

But yeah, so what often happens in the evaluation is that only people who really liked the lecture and people who didn't like the lecture give feedback, but it would be very nice if we have a more thorough feedback.

So if you want to improve lectures and if you have some remarks how to improve the lecture, please do that. This is very, very dear to us, and I will try to really put that into practice and really improve the lecture.

So this is really important. I mean, good, this is not a first semester class, so I won't go through this entire set of slides, but in the first semesters I really have to explain what happens to the transaction numbers, and your feedback will be looked at not only by me, but also by other people.

So if you complain about stuff in the evaluation, and if somebody has a bad evaluation, then all the points or the critique will also be presented to the study committees. Keep that in mind.

So your evaluation is really able to change lectures. And of course I will try to adopt to your feedback to improve the lecture.

Okay, good. Yeah. So what happens after the evaluation? There's the report and lecture, and it's reported in respective committees, and then the lecture is improved. Okay. Did you know that?

So there's a formal process, and this is, by the way, only the School of Engineering has this formal process. The other schools, like social sciences, they do not have this process. They have no structured way of providing feedback.

And this way, so the evaluation system that we have will probably roll out to the entire university. So everybody will probably use the system in a couple of years.

So if you talk to guys from a different school at this university, they probably don't even know about this evaluation system.

So this is quite an important point. Good.

Now that we have talked about the evaluation, we can go back to the actual content of the lecture.

And what we will talk about today is the actual application of variational calculus into non-rigid image registration.

So let's first start with an introduction, and then we will look a bit into the mathematical formalization, and you will realize that this is a variational problem, that we can formalize this in a variational problem.

And then we will look into the Euler-Lagrange equation for diffusion registration and also for curvature registration, because these are two popular regularizers.

So, and then we will look into the first variation of mutual information.

Okay. So, okay. Good. Let's start.

In the last semester in diagnostic medical image processing, we were talking about rigid registration.

And this is a rigid body motion, so you rotate, you translate, you may even allow scaling, but you generally assume that the motion is somehow rigid.

And rigid motion is, it also happens, so typically if you move your skull, so the skull itself moves in a kind of rigid motion.

Of course you also have non-rigid parts, which actually happen here at the skin.

But the bulk motion of the skull, you can explain with a rigid motion.

And so it's suitable for some applications, but for sure not for general body motion.

And so you can solve different problems with that, but generally if you have the scan of a patient at two different points in time, in particular in the abdomen, you will have significant changes.

So these changes may be just because every time you lay down onto the scanner bed, you have different deformation of your inner organs.

And of course you have breathing motion. So breathing motion is also a motion that you cannot explain by a global rigid transform.

So you can explain parts of breathing motion with local rigid transforms.