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As I wrote here (InsightSoftwareConsortium/ITKElastix#145 (comment)), I tested the methods and for me the output is wrong.

@ntatsisk To avoid any mistake on my part I completely 1:1 took your code from this commit hash: https://github.com/InsightSoftwareConsortium/itk-torch-transform-bridge/tree/affa7b375ad885f3489fdb12bec624b064dc8241/src

But the test case output is:

TEST: registration with direction different than identity
ITK equals result: False
MONAI equals result: False
MONAI equals ITK: True

I used the same files as I previously shared and you said you tested the method with.
real_fixed.nii.gz
real_moving.nii.gz

I also checked out your initial commit state: https://github.com/InsightSoftwareConsortium/itk-torch-transform-bridge/tree/414f85487b71a5bf066dbf54ac9939b08fe7ae46/src

But same output. In that code you also stored the itk transformed image transformed_itk.nii.gz but it's not even showing up in the same space as the original image.

I'm not sure what to make of this.
Could you please help explain this.

I'm quite confused by this.

I'm using the following (and only these - make sure to have a clean venv) dependency versions:

itk-elastix==0.15.0
monai==1.1.0
nibabel==5.0.0
numpy==1.24.1
torch==1.8.1