So, good morning everybody.

Medical image processing, interventional medical image processing.

Tuesday morning, 90 minutes, we start as usual with a storyline.

So what is this all about?

So we talk about interventional image processing.

It's the German version.

Interventional medical image processing.

Now I got it.

That's the cloud where we want to get a better understanding.

And what did we discuss so far?

We were basically very much in geometry.

Up to now, we were very much in geometry.

We tried to understand how points are projected into the image plane.

What can I do if I have different projections from various views?

How can I do reconstruction?

How can I estimate the motion parameters?

So it's all about geometry, what we are discussing so far.

And the geometry we have considered was basically driven by very concrete applications.

So what type of applications did we see so far?

Well, sorry for my voice.

We talked the first week about magnetic navigation.

And the idea that is behind magnetic navigation is very simple.

You have a catheter and the catheter tip holds a little magnet.

And on the left and right, you also have huge magnets.

And these magnets generate a magnetic field.

And by the orientation of the B field, of the magnetic field, you can induce some forces

on the catheter tip.

So you can push the catheter tip to certain directions.

And that's required for minimally invasive interventions.

For instance, if you want to work on the cerebral vessel system to fill an aneurysm with coils,

then you need a technique to get there.

And today it's mostly done by mechanical manipulations at the end of the catheter.

So this requires tons of experience.

And with the magnetic navigation system, we have a way to just manipulate the catheter

tip.

The problem we have considered was basically how to build a user interface for this, how

to build a user interface for magnetic navigation.

And at this point, we came up with the concept of epipolar geometry.

And the epipolar geometry basically states the relationship between two images.

I rotate and translate my camera from C1 to C2.

I can look at the geometric relationship between the 3D points, the 2D points, and the rotation

and translation.

And basically, we came up with the statement that Q transposed E times P is zero, and that

was the epipolar constraint.

That was the epipolar constraint, where E is the essential matrix that basically consists

of R times this Q matrix generated by the translation vector.

And we can compute the extrinsics up to scaling.

So that means we get the direction of the translation, but not the absolute value.

So epipolar geometry, and in this context, we have also seen one algorithm.

You might say it's far too theoretical.