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So good afternoon everybody.

Before we continue with the chapter on magnetic navigation,

let me briefly summarize the stories we have considered so far.

This semester we talk about interventional medical image processing.

We are basically considering methods that support the therapeutic procedure of the physician while he or she is treating the patient.

So the picture you have to keep in mind is bloody fingers, patients, and you want to fix a problem by using imaging systems and image guidance and navigation support and things like that.

And what we have considered so far was not so much actually because the semester is still at the beginning.

Hello, hello, hello.

A friend of mine had a nice gift for me last weekend.

It was a book about 30 persons in Erlangen and I found one chapter on you.

Of course you know the book, right? Do you know the book?

You don't know it?

Yes, I am there.

I am fully invited for a function on the 2nd of October between the most popular book in the world here and the most popular function every year in India. We want to inform Germans about India.

Okay, good. I appreciated reading it.

Okay, good. But I lost the concept. Don't worry, I am coming back.

So we did not discuss so much. Maybe that in the first lectures you might have had the impression, oh maybe I mixed this lecture up with a lecture on linear algebra where we considered things like vectors and bundles of vectors and we computed the main direction of a bundle of vectors and things like that.

But that was very important actually because if we want to analyze an image and if we want to find structures, we basically found out a measure for the degree of changes in a local neighborhood and we have used the concept of gradients and then we looked at the gradients in the neighborhood and we were able to classify basically three different types of regions in the image.

One was a flat region where nothing happens. Then there was a region where we say there is an edge and there was another region where we say there was a corner, right?

And this was basically the concept we have considered, how to find homogeneous regions in the image, how we can find edges and how we can actually detect corners.

And this is a very crucial concept that will be following us through the whole lecture series.

And that's why you should really make sure that you got the key messages out of these sections.

And now we are considering the problem of magnetic navigation.

And that's a very exciting field. Why is this very exciting? Because we know that in interventional procedures what the doctor tries to do is he wants to fix the problem of the patient without hurting him too much, with a minimum of a trauma that is necessary.

And with magnetic navigation we want to build now a tool which basically allows us to orient the cathedral in the vessel tree.

I have shown to you last week the videos where you have seen how an external magnetic field can basically reorient the cathedral tip of such a cathedral.

And the task we are now considering is how to build an interface where the doctor sees basically the vessel tree, where the doctor sees where the cathedral is, and the doctor wants to tell the system, please orient the magnetic field into this or that direction, such that the cathedral is pulled over.

So the situation you should keep in mind is the following. You have here, let's say, an image. You have here your patient. Let me just draw here roughly the patient.

And the situation is, and you are laughing here, these are the things you will remember in 10 years from now. If I draw it very seriously you won't remember this. It's also nice to see from a psychological point of view in the oral exams what students do.

Can you draw a patient? They will draw it exactly like this. And then there is the cathedral in, right? It's going through the vessels, right, to the heart, and then here.

And the vessel tree, that's the cathedral, and the vessel tree, I indicate the vessel tree by green color just to make sure that you do not feel bad about these bloody color. So it goes like this and this.

And you want to find a way that the doctor can tell the system, please pull over the cathedral tip here at this bifurcation. This is called bifurcation where the arteries split up.

The arteries split up, pull it up into this direction. So he sees basically the cathedral here in the x-ray image, for instance. There is the cathedral tip.

And then he sees the bifurcation like this of the vessel and he wants to tell the system, please go into this direction with the cathedral. Maybe you can at least roughly see what's going on.

Go into this direction. The task is now, you're an engineer working for a mid-range company like General Motors. They started to build interventional imaging devices.

And your boss asks you, okay, you have a salary of 120,000 euros a year, please build a user interface for this device. That was the task we were facing roughly 10 years ago when I was in industry.

So how can we build a system like that? First of all, we have to be aware of the fact that this is an x-ray image and that this is a 2D image. So this is a 2D image.

And it's flat on the screen. And if the patient sits here on the table or lies on the table, can you lie here? No. And I want to put the cathedral into this direction and I do a projection into the 2D image plane.

You know, I lose a coordinate, a dimension. Sir? What can I do? Yeah, but that would require that I combine the system with two huge magnets with a CT device.

The CT device has this donut structure so the patient disappears basically in there. Yeah, so we want to have an x-ray C arm based system where you can have access to the patient as much as you want basically.

So we restrict ourselves to 2D and 2D images are not good for solving this task as Roman was mentioning because one dimension is missing.

So does the vector point into this direction or in this direction and we only observe the projection into this plane?

What can we do to extend the 2D information in a way that I have three dimensional information?

What do you do if you go and shop a TV that has the 3D option? What is the mandatory requirement of your biological system that you are able to see three dimensions?

You need a second camera. If you have only one eye you see two dimensional things or the world in 2D.

If you have two eyes with an offset and a disparity you can basically use your biological computer and compute the three dimensional information implicitly.

We do it all the time. So the idea was why don't we look at the patient from this direction and the second time from this direction.

You're feeling alright? Do not rotate your head because I don't have a motion compensation here.

The question is how do I deal with the two projections and how can I compute out of the two projections the 3D orientation and the 3D vector.