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Welcome to the Tuesday morning session. Before we start and continue with the registration problem,

let me briefly summarize the storyline of the lecture, because that is an important question within the evaluation.

I hope you did already the course evaluation. No? Who did the course evaluation already?

Okay. Three. I have three extremely negative votes, so I know who did that.

Thank you. The story of the lecture is basically we have four columns, right? Four columns.

Modalities, pre-processing that takes into account the physics and the artifacts implied by the physics.

We talked about reconstruction. So what can I do if I have very much enhanced projection data or acquired data?

How can I lift these data to higher dimensional information using multiple views?

That was the chapter on 3D reconstruction. And now the fourth part of the lecture is dealing with the problem.

How can I use images at different time points respectively, images acquired by different modalities?

What can I do to merge all the information that was acquired? That's the big picture.

This is your boyfriend. Should I take off? Should I take the phone and answer it?

Okay. I mean, I can tell this guy that you have no time and that I am the big guy now.

So just tell him the truth about us, you know?

Okay. So that's the cloud of diagnostic medical image processing, and then we have the four columns.

We have a brief introduction to modalities. Then we have the topic on pre-processing.

We talked about 3D reconstruction, and now we are dealing with a chapter on image fusion.

And along this storyline, we have provided tons of mathematical tools that are required.

Basically, you should be aware of that you should remember these tools from the basic lectures on engineering mathematics.

What topics did we consider? We talked a lot about linear equations, matrices, properties of matrices,

and the key role of the normal form SVD that you can decompose matrices using SVD.

And this decomposition is very powerful and can be used basically to solve from the scratch easily tons of problems that show up in image processing.

We have learned also some mathematical tools to compare signals.

One crucial similarity measure, for instance, was the Kalbheg-Leibler divergence.

We did some basic probability theory in that statistical reconstruction.

So that's what we did. We talked a little bit about optimization, gradients, and the points where the gradient vanishes.

And here we discussed image undistortion, defect pixel interpolation, elimination of inhomogeneities.

We also talked about the bilateral filter, if I did that a few lectures ago.

Here we talked about 3D reconstruction, Fourier slice theorem, algebraic reconstruction methods, statistical reconstruction methods.

We have learned about exact reconstruction methods, the role of the Hilbert transform, and many of these things.

So be aware of that, that I know what Andreas did. Be aware of that.

He did way more than I usually do on 3D reconstruction. And now we are waiting for Michael.

Did you have snow? Did you have snow? Or what was the problem?

Just say yes.

Now say you called her to tell her that you will be late. That would perfectly fit into the context.

You can watch the video to clear things up.

Fusion. And with respect to fusion, we talk about 2D-2D fusion using point correspondencies.

In summer semester, we will also learn methods to find the points.

Here we just assume that we know where the points are. SIFT, surf features, for the guys who attended this lecture already.

So this is something we omit here. We assume that we have points and point correspondencies.

Very hard problem to find the points, to compute the point correspondences.

But based on the correspondences, it's rather straightforward, two lines of Matlab code to compute the rotation and translation in plane.

That means a 2D rotation and translation. Very easy. We use complex numbers to do that.

Very easy. I wish you would have heard about this in the first semester in the math lecture,

because it's way more motivating to use complex numbers instead of using the square root of minus one, which sounds kind of strange.

Now we are considering the 3D situation and we say, okay, we have the point correspondencies and we want to estimate the rotation matrix.

And we have seen three different types of rotation matrix representations, Sebastian.

Doesn't matter.

Rotation matrices in 3D.