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So welcome everybody to the lecture.

Okay, also the guys in the first row please.

Okay, hello. We start with our program.

Okay, so my name is Eva Kolloz. I will give the lecture today and tomorrow and maybe also next week.

Yeah, my name is Eva Kolloz. I'm doing my PhD at the Pattern Recognition Lab.

And yeah, we will talk about today about magnetic resonance intensity in homogeneities.

So you start last week with the topic. So maybe someone can repeat what problem we have and how to solve it.

So maybe someone of you can explain what problem we have in MR.

Nobody?

Okay, so we have images like this.

For example, so this is a phantom image, but we have an ideal image on the right side.

So this would be our ideal MR image.

In the middle we have a gain field or a bias field depending on if we have the multiplicative or the additive model.

And on the left side we have the observed image we get out from the MR scanner.

So what is the problem if you see the left image or maybe it's clearer on this image?

So if you want to post-process the image with some methods, what could be the problem?

Okay, maybe the guy who is laughing. You know the answer? No? Okay.

Okay, so for example, if you do a segmentation, yeah, maybe simple thresholding, okay,

then you would assume a certain gray level.

And you can see on the left side that this is a slice of the brain that you could not segment, for example, the gray matter.

So if you do the segmentation on the right image, you would get out a good segmentation result of the brain.

Okay, you discussed certain methods.

So I think you stopped at the homomorphic filtering.

So maybe someone can explain about the frequency domain filters.

What is the main idea in the frequency domain? Just to give a short intuition how it works.

Maybe you? Yes?

In spatial domain, it's a convolution, so in the frequency domain, it would be multiplication. So we have these basically the hyperspace.

So you can see how it's looking.

Yes, you're right. Okay, as you explained, we have our observed image G and we do a Fourier transform,

and then we have a high-pass filter H, and then we multiply it in the frequency domain, do an inverse Fourier transform,

and we get our ideal image F.

Okay, the homomorphic filtering, it's a little bit different.

So we subtract a low-pass filtered image and normalize the mean.

Okay, you could see here we have the logarithm of our observed image G, and we subtract the low-pass filter.

You could see in the equation above, so the low-pass filter of the logarithmic observed image,

and then we add some mean that we have a mean preserving, preservation,

so that the mean of the log F image is the same mean as of the log G image.

And then we come to the homomorphic unsharp masking.

This is apply a mean normalization. It's one simple method.

Usually you hear it in the literature.

It's used to compare also the methods, how good is your intensity correction with some standard technique,

and it requires the computation of mean computation.

So you see here you want to calculate a global mean value, me, of your observed image Gij.

And then you compute also local mean values, meij, for each pixel in a certain local neighborhood.

If you see the image on the left side, on the upper left, on the lower left side, you see the black rectangle.

This is the image. You calculate the mean. So it's me, it's 1 divided by n.

So n is the number of elements in the image. And then sum over ij, and here is written Fij, but of course it's Gij.

Usually if you come from a usual image processing, you say Fij.

These are your intensity values, but we have here Gij, because this is the observed image of the MR image.