# Linear transforms to displacement field
**URL:** https://discourse.itk.org/t/linear-transforms-to-displacement-field/2992
**Category:** Beginner Questions
**Tags:** python
**Created:** [April 22, 2020, 3:08pm UTC](https://discourse.itk.org/t/linear-transforms-to-displacement-field/2992 "2020-04-22T15:08:33Z")
**Posts on this page:** 2
**Page:** 1
### Author:  [@alixchcl](https://discourse.itk.org/u/alixchcl)
#### Post date: [April 22, 2020, 3:08pm UTC](https://discourse.itk.org/t/linear-transforms-to-displacement-field/2992/1 "2020-04-22T15:08:33Z")
Hi!
I would like to create a deformation field from 2 linear transforms, which are defined on different regions of my image.
So, I have two different linear transforms (one for the right hemisphere, and one for the left hemisphere of the brain). I also have 2 masks, corresponding to the two hemispheres. And I would like to create a deformation field where I get the left linear transform applied over the left hemisphere mask, and the right linear transform applied over the right mask.
I get that this should lead to some discontinuities at the jonction, but I don’t think that this should be a problem for my further calculation.
I am just starting with ITK, so any help will probably be a lot to me,
Thanks in advance !! 🤗
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### Author:  [@dzenanz](https://discourse.itk.org/u/dzenanz)
#### Post date: [April 22, 2020, 6:27pm UTC](https://discourse.itk.org/t/linear-transforms-to-displacement-field/2992/2 "2020-04-22T18:27:32Z")
You could [iterate](https://itk.org/ITKExamples/src/Core/Common/IterateRegionWithAccessToIndexWithWriteAccess/Documentation.html) through your desired deformation field image, and for each pixel check whether it belongs to one of the masks, and if so calculate displacement for it using [TransformContinuousIndexToPhysicalPoint and TransformPhysicalPointToIndex from image](https://discourse.itk.org/t/solved-transformindextophysicalpoint-manually/1031/10) and [TransformPoint](https://itk.org/Doxygen/html/classitk_1_1Transform.html#a4e2ff88e9abbf728d7320be5df203de0) from the corresponding linear transform. Pay attention to the direction of transform (moving to registered). Good luck!