# Jacobian of B-spline coefficients

**URL:** https://discourse.itk.org/t/jacobian-of-b-spline-coefficients/3070
**Category:** Algorithms
**Created:** [May 14, 2020, 3:59pm UTC](https://discourse.itk.org/t/jacobian-of-b-spline-coefficients/3070 "2020-05-14T15:59:04Z")
**Posts on this page:** 3
**Page:** 1

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### Author: ![rijobro](https://discourse.itk.org/letter_avatar_proxy/v4/letter/r/53a042/32.png) [@rijobro](https://discourse.itk.org/u/rijobro)
#### Post date: [May 14, 2020, 3:59pm UTC](https://discourse.itk.org/t/jacobian-of-b-spline-coefficients/3070/1 "2020-05-14T15:59:04Z")

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For a motion-estimation algorithm, we’d like to be able to calculate the Jacboian of b-spline coefficients. Alternatively (and less computationally expensive), we’d like to be able to apply this Jacboian onto a pre-existing transformation.

We would like to do this in ITK or VTK, whichever is easier. Matching VTK post is [here](https://discourse.vtk.org/t/jacobian-of-b-spline-coefficients/3310).

Could anyone point us to the relevant classes/methods (dare I say examples) for this?

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### Author: ![matt.mccormick](https://discourse.itk.org/user_avatar/discourse.itk.org/matt.mccormick/32/7_2.png) [@matt.mccormick](https://discourse.itk.org/u/matt.mccormick)
#### Post date: [May 14, 2020, 5:25pm UTC](https://discourse.itk.org/t/jacobian-of-b-spline-coefficients/3070/2 "2020-05-14T17:25:18Z")

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A few pointers:

- `itk::BSplineTransform` [ComputeJacobianFromBSplineWeightsWithRespectToPosition](https://itk.org/Doxygen/html/classitk_1_1BSplineBaseTransform.html#a82b8088088594f93ed53a493b531fec2)
- `itk::BSplineTransform` [ComputeJacobianWithRespectToParameters](https://itk.org/Doxygen/html/classitk_1_1BSplineBaseTransform.html#aae7a9ae6d25612ceec86efa238d1efb6)
- [`itk::TransformToDisplacementFieldFilter`](https://itk.org/Doxygen/html/classitk_1_1BSplineBaseTransform.html#aae7a9ae6d25612ceec86efa238d1efb6)
- [`itk::DisplacementFieldJacobianDeterminantFilter`](https://itk.org/Doxygen/html/classitk_1_1DisplacementFieldJacobianDeterminantFilter.html)

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### Author: ![rijobro](https://discourse.itk.org/letter_avatar_proxy/v4/letter/r/53a042/32.png) [@rijobro](https://discourse.itk.org/u/rijobro)
#### Post date: [May 15, 2020, 12:55pm UTC](https://discourse.itk.org/t/jacobian-of-b-spline-coefficients/3070/3 "2020-05-15T12:55:35Z")

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Hi Matt,  
Great thanks for the pointers!