Okay, can we start? Good morning everybody for the Tuesday session. Before we continue

with the algebraic reconstruction technique, ART, I will briefly summarize where we are

and what we have discussed so far. You know there is one important question in the evaluation

saying what is the story or does there exist a storyline of the lecture. If you tend to

say no, you are not listening to the first part, the first 10 minutes of each Tuesday

lecture where I try to explain to you the storyline. So the storyline of diagnostic

medical image processing is basically sitting on four columns. First of all, we are aware

of different imaging modalities. You should be able to say if I show an image to you which

modality this image belongs to. So if I show an ultrasound image to you, you should say

this is an MR image and so on. And colleagues of mine, for instance, Peter Haasbreiter,

if you attend his lecture on visualization and if I have the exam together with him,

he usually has some printouts with some pictures, what is this, and then we say MR. And it should

be easy for you to see this is MR or CT or X. So modalities. And then we looked at single

images. There is an A in between, images. So we looked at how our images acquired. We

looked a little bit into the physics but not in detail. And then we talked about image

pre-processing methods. That means methods that generate better images out of the measurements.

We have seen image undistortion. We have seen defect pixel interpolation. We have seen low

frequency elimination in MR images to eliminate homogeneities. We have, I don't know what

else we have discussed. That's basically what we said. Then we looked into multiple images

of a single modality and how we can do reconstruction. Multiple mono images. And here in particular

we have focused on X-ray images. And the problem, how can I compute out of multiple views of

an object using an X-ray device higher dimensional image information. So we talked about reconstruction.

That means we slice theorem, filtered back projection. We have learned about Bayer's

law and these things. And currently we are talking about algebraic methods to solve this

issue. And the third part, and this is what the following three weeks will be considered

in more detail, is on multi model image registration. Now we say we consider images of different

modalities of one and the same patient and we want to combine all these images in a way

that all these images lie in one and the same image coordinate system. And in between we

have learned a little bit about basic math methods like SVD, about optimization. We talked

about least squares. We talked about bootstrapping. And we also learned about camera calibration,

how to calibrate an X-ray system. We learned about homogeneous coordinates and many interesting

other aspects. So it's quite a load that we have experience in this lecture. And if you

prepare for the oral exam you will also experience that it's quite a lot if you want to understand

things in detail and if you want to be in a position that you can answer my smart questions.

My very detailed questions. Good. Okay. Questions so far? Which chapter do you like the most?

I was asking these questions in many evaluations before. Most students like the reconstruction

chapter very much. I don't know why but they seem to like this one in particular. Good.

So let's continue with Nora's example here. What's it? Look at this. That was your experiment

you did yesterday. I was asking you give me the solution and you said right away this

is the solution, right? And then we found an iterative scheme to solve it. So just let's

back up a little bit. We have discretized Bayer's law yesterday. Basically in X-ray

imaging we observe line integrals. Each pixel in the X-ray image is a line integral. So

if you talk to a radiologist, you go skiing, you break your leg, you go to a radiologist

to get an X-ray and then you can say look at these five line integrals. This is exactly

where the bone is broken. Nobody talks like this but basically that's what happens and

what you see. And we can discretize these line integrals and say this is not an integral

with infinitesimism. Say it loud. Small steps but you have discrete steps of a certain size

and it turns out that the integral will become a sum. And computer scientists usually do

not work with small steps but we have discrete steps. And we end up basically with a system

of linear equations. And these W's they form the so-called system matrix that is defined