Welcome back to Pattern Recognition. So today we want to talk a bit about applications of the EM

algorithm and I want to show one example from medical imaging where you can see how sophisticated

those algorithms can get and I think that it will be very interesting for you to see how many

additional steps we can actually model with this EM algorithm.

So let's have a look at the slides that I have for you. So this is adaptive segmentation of MRI

data and note that what I'm showing to you today this is something that is let's say an application

but it also involves many steps. So I would say topics like this one are very good for your

understanding of how to bring these things into practice but I don't think that this algorithm

presented in this video will be too relevant for the exam. So this is an application at MRI. So MRI

is magnetic resonance imaging. It's an important medical image acquisition technique. It has high

spatial resolution, good soft tissue contrast and does not involve any ionizing radiation.

There are several applications that require segmentation. So here we do a voxel-wise

classification whether this voxel belongs into a certain tissue class and then you essentially

assign every point in the image a class to which it belongs and these are typically tissue types.

Now a problem arises in MRI that the intensities are not normalized, they're not standardized. In

CT and computer tomography you would have things like the Hounsfield unit that would allow really

a relation to a physical quantity. In MRI this is very difficult and in many acquisition sequences

it is simply not standardized to a physical quantity. This then gives rise to intensity

in homogenities that are also known as the bias field and this is introduced by the radiofrequency

coils and the acquisition sequences. What then happens is that you get images like this one. So

you acquire the image on the left hand side which is now showing essentially the head and the upper

part of the torso and you would assume that in a standardized image all the tissues would essentially

have very similar gray values but you can see that there is this kind of off-rolling effect that you

see towards the boundaries of the image and you have better contrasts in the center than on the

sides but you can correct this with so-called bias field reduction algorithms like the one you have to

see here on the right hand side. By the way this is work by the colleague Florian Jäger who has

actually written his PhD thesis about this topic. So now why is the bias field a problem? Well let's

say you have this checkerboard pattern here and you introduce a bias field then you can see that

the checkerboard is still there so because human perception can compensate for those effects very

efficiently. If you show an image like this one to let's say your medical doctor he will say okay I

can clearly see the checkerboard pattern. Now the bias field is multiplied here into this image and

you can see that it introduces a change in the gray values and if you try to segment just using

the gray value as a kind of tissue class or here indicating which part of the checkerboard you're

in then you get segmentation results like this one. So you see that the actual gray value is not

corresponding to the correct part of the checkerboard. Now of course this is also something

that we typically then also have a couple of discussion with our medical partners because

they say look I can see the checkerboard pattern why is your computer so stupid that it produces

a result like this and you know every monkey can draw a pattern like the one that you see here on

the right hand side so your computer is pretty stupid. Now of course we have methods to deal

with this and what I want to introduce here is actually going back to the work of Sandy Wells

and he already presented the things that I'm showing in the lecture today in a paper in 1996

and it is essentially a statistical approach to intensity based segmentation and MRI. It is

modeling the bias field also statistically using a smoothness constraint and then he also used the

EM algorithm for the simultaneous computation of the tissue classification and the intensity

in homogeneity correction. So the problem here is the missing data is the tissue class assignment

for each pixel. We don't know what is the actual class of the pixel and if the tissue were classified

correctly then we could also very easily compute the bias field because we know it's the deviation

from the correct gray value to the one that we're observing. But if the bias field were known then

also the tissue classification would be much easier. So again we have this kind of missing

information problem here that in order to derive the tissue class from the gray value we need