Okay, so folks, now we should continue in the text.

We have discussed variational calculus.

We have discussed different approaches based on functional optimization.

We have discussed different approaches for non-rigid image registration based on variational

calculus and different functional equations.

We have seen the SSD as a similarity measure.

We have seen the mutual information as a similarity measure.

We have seen the curvature regularizer.

We have seen the diffusion regularizer.

And there are many, many, many more different approaches out there.

And then we have computed the Gatot derivative of the sum of squared differences and the

regularizers.

And I also have shown to you last Tuesday the Gatot derivative of the mutual information.

And I told you that you can find publications from the year 2000, 2001 where people state

that you cannot use gradient descent methods, for instance, to solve a mutual information

based non-rigid registration approach.

That's not true.

In fact, we now are able to compute these things.

And what we started to do last Tuesday is we did a few remarks on image registration.

And I discussed various approaches for image registration and how it can be used in interventions

and interventional imaging.

For instance, I have made you aware of the fact that different images as they are used

in angiography today are basically making use of registration methods.

We have discussed image registration using prior.

So we hooked up on an idea that we have already discussed in winter semester.

And what I'm going to talk about today is I will talk about MR intensity normalization,

an idea that we have worked on for two years and we have a very nice publication or had

a very nice publication in January this year in the IEEE Transactions on Medical Imaging.

So one of the highly reputed journals in our field where we have demonstrated that this

is a good idea.

It's important to know that MR images are not normalized in a sense like CT images.

If you read out in a CT image the intensity value, you look at the intensity value, they

are usually given in Hounsfield units.

So you read the intensity value and you can immediately conclude what type of material

is at this position in or at this point in 3D.

In MR imaging these intensities are telling us nothing.

You look at the image and you see of course different intensity values and you see the

anatomy, you see the morphology.

But if you pick out for brain image a certain voxel, a certain volume element and you read

the intensity value, it does not tell you is it border, is it bone, is it… you just

don't know because these values are not normalized.

And we were working on ideas how to do that and we have presented a very nice idea, I

mean how this can be done by using image registration methods.

And then I will talk about a problem that is very, very, very, very important for interventions.

It's 4D reconstruction of the beating heart using a C-arm device during the intervention.

That means that you can do a 3D reconstruction of the heart while the patient is on the table

and this is a problem that was unsolvable so far.

And what I want to present to you are results that Markus Prümer came up with in his PhD

thesis project.

So quite challenging and quite interesting what we are doing here and these are all current