Okay, so welcome everybody to interventional medical image processing.

And what I would like to do now in the following is give a short summary of the lecture, what

we have done so far, and what is the scope of the lecture and where we're aiming at.

So that you don't lose the overview.

And by the way, if you're preparing for the oral exam, there's a certain likelihood that

the first question in the oral exam will be something like, can you summarize the contents

of the lecture?

What is the lecture about?

Something like this.

And if you can show something like this, then you are very well prepared for the first question.

Okay, good.

So what is the lecture about?

Well, our lecture is about interventional medical image processing.

And if we think about our lecture, we can go back and think, well, what is this lecture

about?

So essentially, the lecture is divided into essentially four or five segments, depends

on how far we go.

And we had a short introduction for a short motivation, what we do in international medical

image processing.

And we came to the conclusion that what we want to do is going to be interventional.

So we need to have methods that will be able to process applications in real time because

we need immediate feedback, or there's very little time during the intervention.

So time constraints are tough, but in general, it's a kind of image processing that has to

be performed.

So we had this introduction, and then we were looking into some tools, right?

And we already talked about a tool called SVD.

And you may remember, we had a small refresher course, and that SVD is very powerful.

If you want to solve certain questions, if you want to solve linear systems, then it's

a very powerful tool.

And one application of SVD, so there's many applications, but one application of SVD

that we have seen is that, for example, we can solve problems like A times X equals B.

And now those two are vectors, and this is a matrix.

And now you can compute, for example, the pseudo inverse in order to get X. And using

SVD, you get a pseudo inverse, and you can just get it like this.

So you can solve problems like that.

Then another tool that we talked about were projection models, and we will see later why

they are very useful.

So projection models and homogeneous coordinates.

And you remember that in the homogeneous coordinates, we had this trick that we added an additional

dimension, and suddenly we could rewrite nonlinear problems into linear ones.

So you remember that we had to divide over the last component in order to compute a perspective

projection.

And now we added, introduced a new component, and by the de-homogenization, we go back into

the original space, and there we divide by the last component, which made our projection

essentially a linear transform.

So we had SVD projection models, and one very nice tool that we also already discussed this

week was filtering.

So filtering, convolution, and with that respect, linear systems, Fourier transforms, and so

on.

So we were using that already in the previous lecture.