Dear Burkhard,
> but your answer did not satisfy. If the mean <l>=0 that can only
> happen if all
> eigenvalues are zero (unless you allow negative eigenvalues which is
> exactly
> my point: Negative eigenvalues should not be permitted no matter
> what algorithm
> you are going to use to calculate them - they have no physical meaning
> in the diffusion tensor).
Yes, FA outside the range of 0-1 means that an estimated eigenvalue is
negative.
>
> If all li=0 than also <l>=0 but now the ratio of numerator and
> denominator
> in the equation of FA becomes ill-defined sqrt(0/0). Unless you have
> another
> explanation. Jesper mentioned something about the "true FA"
> implicating
> that FSL calculates FA-values by statistical means (which by the way
> is nowhere
> explained or mentioned in the documents).
I am not sure what you mean by "statistical means". The eigenvalues
calculated by FSL are estimates (from the data) of some true (unknown)
eigenvalue. Every estimate is associated with an uncertainty (error),
the magnitude of which depends on the quality of the data. Let us
assume in a given voxel the "true" eigenvalue is very small. The
estimate will then be this true eigenvalue +/- some random number that
depends on the uncertainty. And sometimes this estimate will be
negative.
It would be easy enough to simply (in the FSL code) set any negative
eigenvalue to zero. This is not done because we think that
1. They do no harm as they stand
2. It might do harm to set them to zero since that would skew
distributions.
Is that clearer?
Jesper
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