Good morning. I'm sorry for the little delay.

Let's start right away with a big picture of the current lecture.

So far we are in third week, so we have not discussed that much.

But what is diagnostic medical image processing about?

It's all about image processing technology that is used in modern environments

for providing tools for diagnostic purposes.

That is not that time relevant or real time relevant like interventional procedures.

But it's a crucial and important area in radiology and it's important to know about these things.

So what we have discussed so far are, we talked a little bit about different modalities.

So we know what a modality is, that's an image acquisition device.

We have seen that there are endoscopes.

We know that there are x-ray systems.

We know that we can do computer tomography.

We know MRI.

We have heard about SPECT and PET a little bit.

And ultrasound was briefly mentioned.

Now we will go through all these modalities and discuss acquisition specific preprocessing methods.

Basically we look at the technology that is used to acquire these images.

And then we look what type of artifacts are implied by these detector technologies we are using.

And how can we compensate for certain artifacts that show up in these images.

And we started out with x-ray imaging.

So we are currently in a chapter on acquisition specific image preprocessing methods.

And currently we look into the domain of x-ray imaging.

And we have seen that there are two detector technologies out there.

And these are the image intensifiers and the flat panel detectors.

And currently we look at the image intensifier.

And we know that there is a vacuum tube.

And within this vacuum tube we have electrons that are accelerated.

And these electrons that are accelerated, they interact with the earth's magnetic field.

And that causes some kind of image distortions.

And we look into algorithms for image undistortion.

So our topic currently is image undistortion.

And we look into algorithms that can be used in such a system on the fly while acquiring the images.

They have to be undistorted.

And today I will also point out that there are software packages out that you can buy for 50,000, 70,000 euros.

That do exactly this type of algorithms that we are currently discussing.

And for image undistortion we have introduced a few concepts.

We have here a distortion or undistortion function that maps the coordinates of the undistorted image to the coordinates of the distorted image.

We have seen that we have to solve a parameter estimation problem.

If we have a parametric mapping from the undistorted image to the distorted image.

We have talked about least squares approaches.

And yesterday we talked about the total least square approach.

What is the difference between least square and total least square?

I actually don't know that because I was here yesterday and you just come up and back.

Okay. Who attended? Yes, you attended, right?

What is the difference?

So if you have to solve a problem like MX is equal to B, right?

And you cannot compute the inverse of the matrix M because B is not in the image space of M.

How do you solve it?

You can say, okay, I solve here the optimization problem that I say this has to be minimized.