> I was going through the 2005 paper on unified segmentation by Ashburner and
> Friston. I was hoping to clarify a couple of points from the paper. So the
> paper models intensity distribution using a mixture of gaussians. So my
> questions are as follows
>
> 1. Do the different clusters(Gaussians) correspond to different tissue types
> in the brain viz., Grey Matter, White Matter and CSF? i.e. one is interested
> in measuring the probability of a voxel of a given intensity belonging to a
> certain tissue class?
In practice, more than one Gaussian is used to model the intensity
distribution of each tissue type. The idea here is to allow a bit of
kurtosis in order to try to model some of the partial volume effects.
> 2. In the same paper it is mentioned that 'In a simple MOG, the
>
> probability of obtaining a datum with intensity yi given that it
>
> belongs to the kth Gaussian (ci = k) and that the kth Gaussian is
>
> parameterised by nu_k and sigma_k^2' is given by the probability density
> function of a gaussian distribution. But since we are dealing with a
> continuous data set of intensity, the probability that the voxel intensity
> is equal to a certain value is zero, we can only ask what is the probability
> that the intensity is in a certain range and that too will be given by the
> integral of the gaussian function in that range.
It relates to a probability density function, so I may have been a bit
sloppy in terms of not using P(..) and p(..) to denote probabilities
and probability densities.
Life would be slightly easier if the intensities were continuous. In
practice, images are usually encoded via integer values in the DICOM
files, so we are really dealing with probabilities rather than
densities. The code in SPM does not really account for this, and
assumes continuous intensities.
>
> Could someone please clarify these points for me, especially the second
> question.
I hope this sort of answers the question.
Best regards,
-John
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