[Insight-users] Jacobian determinant image of the deformation field

[Minjie Wu]

Hello All,


I am trying to get the Jacobian determinant image of a deformation
field. I tested two ways of computing the Jacobian determinant image,
the resulted images are similar in pattern, but different in the
actual image intensity (range or histogram or voxelwise intensity
diffrence).


1. The first way I tried is by using the
itkDeformationFieldJacobianDeterminantFilter filter with the
deformationation field calcuated from 2,  which gives me a jacobian
determinant image of intensity around 0, (-0.2 +0.2).

In the manual page, it says:

"Note that the determinant of a zero vector field is also zero,
whereas the Jacobian determinant of the corresponding identity warp
transformation should be 1.0. In general, in order to obtain the
effective deformation Jacobian determinant, 1.0 must be added to each
Jacobian value in the output."

So I added 1.0 to the resulted image, the final intensity range for
slice 78 is (0.8 1.2).


2. The second way I tried is to using the example code,
DeformableRegistration1.cxx. The jacobian calculation during
itkFEMRegistrationFilter.h registration using ComputeJacobian(). The
result image is similar in pattern as the first one, but for every
voxel, the actual intensity value is different. The final intensity
range for the same slice is (0.02 2.862).


I am very confused by the results. I wonder if the results from 1 and
2 are both jacobian determinant image of the deformation field and
Which method I should use to calculate the precomputed deformation
field?

Any suggestion or help is appreciated. Thank you very much for your help.
-Minjie


-- 
-Minjie