[Elastix] The determinant of the spatial Jacobian

F.Berendsen at lumc.nl F.Berendsen at lumc.nl
Tue Apr 28 13:31:33 CEST 2015

Dear Tiantian,

You can see the transform in two different directions:
- to transform coordinates from the fixed image to the moving image (i.e. a displacement field)
- to use it to warp the moving image to the fixed image

The Jacobian determinant is >1 if displacement field is locally divergent, but form a warping point of view, the moving image is compressed.
A Jacobian determinant between 0 and 1 placement field is locally convergent, the warped moving image is expanded.
A Jacobian determinant smaller than 0 means folding of the deformation field, the warped moving image is locally 'turned inside-out'. Generally you would see parts of the moving image being repeated (all be it inside-out).

Considering your last question.
Elastix does not take the Jacobian determinant into account for warping images. So, locally stretching an image does not result in a lower intensity.
If you would want to transform an image where the intensities represent some sort of densities, for which a 'preservation of mass' needs to apply, you would need to do the post processing with the Jacobian determinant image yourself.

I hope this answers your questions,


From: elastix-bounces at bigr.nl [mailto:elastix-bounces at bigr.nl] On Behalf Of litiantian
Sent: zondag 26 april 2015 18:57
To: elastix at bigr.nl
Subject: [Elastix] The determinant of the spatial Jacobian

Dear all,

i have a question when i do the registration.....

when I use the command:

transformix -jac all -out outputDirectory -tp TransformParameters.txt

to calculate the determinant of the spatial Jacobian matrix, but i found that it contains minus values in the matrix.

through the elastix manual, i learned that the value of the determinant of the spatial Jacobian matrix identified the amount of local compression or expansion. If it was >1, the pixel was compressed,vise versa. but how does the minus value mean?

in my application, i want to do the registration of the organ position and shape,but keep the value of the corresponding pixel unchanged....(i don't know if this description is clearly to you... )
 And if there is any possible method to do the registration and keep the 3D distribution information at the same time?

I would be appreciate if i can get any help from you!
Thank you very much!!


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