[Insight-users] Problems with negative values of Jacobian Determinant in Diffeomorphic Demons

[Harish Mandala]

Hi everyone,

I am currently using itk::DiffeomorphicDemonsRegistrationFilter for 2D
same-modality registration. I am getting negative values in the Jacobian
Determinant of the deformation map. So I looked at the original paper and it
says:

"Since statistical analysis and its biological interpretation often relies
on the assumption that the Jacobian determinant is positive, potential
negative values might appear like a true possible problem. A real solution
to this issue would rely on a more powerfull representation of spatial
transformations that would be consistent with the composition and the
computation of the Jacobian. In practice though, negative Jacobians appear
very seldom and if they do, they are only so slightly negative that
dismissing them should not lead to any problems for biological
interpretation."

1) I did not really understand what this means: "A real solution to this
issue would rely on a more powerfull representation of spatial
transformations that would be consistent with the composition and the
computation of the Jacobian". Can someone please explain?

2) Typically about half the values in the Jacobian Determinant are negative,
and examples of the smallest negative values from each deformation map are:
-0.326896, -0.315346, -0.175188 etc. The largest positive values have
similar magnitudes. So basically, the negative values are neither rare nor
only slightly negative. Also, this is true of every registration I have
tried so far. Why is this happening? Any

3) For the above I had SetStandardDeviations(1.0). I notice that for my data
if I SetStandardDeviations(2.5), then things get better. The negative values
decrease in magnitude - they are more like 0.005 etc. What's the intuition
here?

Thanks in Anticipation,
Harish
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