We are a little delayed in our program for this semester,

so hopefully I can gain some speed now.

We talk about bias field correction,

and what is a bias field?

Briefly.

What is a bias field?

Sir, I forgot your first name again, sorry.

What is a bias field?

There is a difference in intensity.

So some parts of the image have a high intensity

and some a lower, but that's independent of the object

which is on the image.

That means we have some low frequency,

gray level ramps that are overlaid with the original image.

And we want to eliminate these low frequency disturbances

in the image.

And this has several reasons in MR imaging.

What is, for instance, a reason that we get

these intensity variations in MR images?

Johannes?

Because of the magnetic field.

Yeah, the heterogeneity of the magnetic field.

Yeah, basically we have to solve the problem.

We have here the original values, let's call them fi,

and we add some bias component on that,

and we get the observed image.

And this is true for all the image points.

And basically we have to compute out of this,

this decomposition into two components,

elements of the sum, and then we just subtract the bi.

We have to estimate the bi and subtract it.

And of course, if I get multiple equations,

I will never ever be able to do this type of decomposition

because the decomposition into a sum of numbers

is not something that we can do.

There is no unique solution to that,

like prime factorization.

But using the prior knowledge that the bias field

is some low frequency structure,

has some low frequency structure, we can do something.

And we have seen already a few ideas what can be done.

For instance, we have seen that we can do

unsharp masking, we have seen that we can apply

mean filter with a huge kernel

just to get the low frequency behavior in the image,

and then we subtract it.

And last week we also had started to look

to histograms of the images,

and we have observed that the peaks in the histograms

that show the structures, or characterize basically,