Very well. So this brings us to the actual lecture. Great. We spent 15 minutes only talking

about organizational details. So now I would like to welcome you to interventional medical

image processing. And today we will talk about 3D ultrasound and starting from 3D ultrasound,

we will then switch to a very interesting topic, which to a very interesting method,

which is called factorization. And you will see factorization is also really, really cool

thing. So this is a very, very nice method and also mathematics are quite beautiful.

And we will use our most favorite tool. What's our most favorite tool? SVD. Yes, we will

use SVD again. And you will see that this is also a very... No, no, this time it's

SVD. It's not the Fourier transform this time. But let's first talk a bit about 3D ultrasound.

It's also interesting that we just talked about endoscopes and now we're talking about

ultrasound. So also the different modalities and also the way that these modalities work.

Of course, interesting, but they are not that relevant, of course, for the oral exam. Okay.

So let's have a look at ultrasound. And in fact, medical ultrasound was already developed

in 1942, when they discovered it for medical applications. And in 1984, there was the first

3D ultrasound system that has been proposed. But in fact, sound has been used for measurements

already before that. And you can see that first applications range back to Aristoteles.

And they did, for example, ecometry by measuring the time until the reflection arrives. So

actually the echo arrives. You can measure, for example, depth of a well or something

like this. And in fact, a lot of this ultrasound technology has been driven by military applications.

So before it came to medical ultrasound, a lot of these technologies have been involved

by sonar systems and they were using it to detect submarines. And so there's a lot of

military applications where these things have been involved on. But from 1942, this has

been also used for medical applications. So we should always be aware that if you're exploring

technology, there's always most of the technology you can use for different purposes. And there

may be good sides that you can use it for medical applications. But some of the technologies

can also be directly related to military applications or for military intelligence operations if

you want to tap phones or so. If you consider, for example, speech recognition, a lot of

speech recognition funding actually comes from military. And in fact, they have been

also, some parties, some funding agencies have been highly interested in developing

speech recognition for Arabic speech. You may wonder why people fund speech recognition

for Arabic speech, but this has been a very hot topic in speech recognition in recent

years. Well, yeah. Now that they caught Osama bin Laden, it's probably not as interesting

as it used to be. No. Yeah. Okay. So keep that in mind. And whenever you work on these

things. So some researchers say, well, ethical considerations are not of their interest.

But my personal opinion is if you're working on technology and there is clearly foreseeable

misuse how this technology could be used, then you should be careful and also consider

these things when you're developing certain algorithms. Well, but in our case, there's

nothing to worry about because this is all medical and we will just use it for good purposes.

Okay. So what you do in order to use ultrasound, first of all, you have to generate some, you

have some sound waves and this is essentially changes in pressure and you can by pressurization.

So like a loudspeaker does, you change the local pressure in air and the change in air

pressure propagates through the air, which is then if it's audible sound, it's perceived

by your ears. So this is what you're currently hearing too. So this is the change in sound

pressure in the air and you can also do this at higher frequencies and then you will observe

the phenomenon of ultrasound. So here's some examples. So if you change pressurization,

you can generate waves and those waves will then propagate through the medium, indicated

as bars here. In general, you have three different principles or three different effects that

occur. There is reflection and this is typically at the boundary of two media. So then the

waves are not transmitted, but they're reflected. Then you have refraction. Then the wave is

bended by refraction and absorption where there is a loss in acoustic energy. And here