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Good afternoon everybody. Today we continue the chapter on image registration and in contrast to winter semester,

we will consider non-rigid image registration.

That means we want to transform two datasets into a joint coordinate system, into a common coordinate system,

and we allow for deformations during this registration process.

In winter we just have considered rotations and translations, maybe scaling, but now we also allow deformations.

That's very crucial. We have seen yesterday quite a few examples where this is required, this type of registration.

It's also intuitively clear if somebody goes to the hospital and you put them into one scanner,

and then you do something with them and you put them into another scanner, let me say one hour later or two hours later,

then things might have deformed. The stomach is working and the bladder is filling up.

Things are changing and deforming and somehow we have to compensate for this type of deformation.

The question is how can we do this in terms of algorithms?

Just saying we need a deformation is one thing, that's what marketing people do,

and now we have to think about what can we do to implement this.

What marketing people usually do, they hire a student, an intern who is going to do that.

They want to prepare you for this type of job within this lecture.

How do we implement deformable registration or we call it also non-rigid image registration in the literature?

In German, nicht rigide, it sounds so strange.

There are good reasons to give this lecture in English.

Broken English.

I will introduce the whole stuff, then I will do a mathematical formulation for the fifth time, I guess.

We have seen the objective function several times.

Now, in contrast to all the previous sections, we will also talk about the Euler-Lagroshian differential equation

that follows out of these functionals that we are considering.

The program for today, introduction, non-rigid image registration methods are required for.

A typical question in the oral exum is, give me five examples where non-rigid image registration is important,

and then I will do do do do do, and if you come up with three you will get a four.

So simple, it's straightforward.

Non-rigid image registration is a limitation for many medical applications because patients do deform.

Then CT scans, hands up.

Usually the patient has to put the hands up.

Why that? If he gets a thorax or a cardiac CT, why is that required?

What do you think?

Why should you expose this to x-rays if you are just interested in this?

You basically lose energy on this path and on this path, and so you have to squeeze in more energy than is actually required.

So patients sit on the table like this.

Don't bring out the snapshot of this.

In spect scans, the story is different.

Think about having a tumor here. You put your hands up, it goes up here.

You have a motion of three centimeters or something like that.

If you ask some patient, can you please sit on the table or lie on the table of a spect?

Now we will have a procedure that takes just 30 minutes.

You have to keep still, do not swallow, breathe, and so on for 30 minutes.

You have to sit like this. You have a tumor here. You can't do that.

So patients sit there like this.

So we have completely different situations.

Difficult how to deal with a registration problem here.

Patients are repositioned on different acquisition types.

So depending on the shape of the table where you lie on, things deform differently.

Patient change, filled bladder, for instance, or motion compensation, for instance.