# Compute deformation field smoothness

**URL:** <https://discourse.itk.org/t/compute-deformation-field-smoothness/788>\
**Category:** Algorithms\
**Created:** [March 21, 2018, 2:42pm UTC](https://discourse.itk.org/t/compute-deformation-field-smoothness/788 "2018-03-21T14:42:02Z")\
**Posts on this page:** 3\
**Page:** 1

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**Author:** ![c.spanakis83](https://discourse.itk.org/user_avatar/discourse.itk.org/c.spanakis83/32/737_2.png) [@c.spanakis83](https://discourse.itk.org/u/c.spanakis83)\
**Post date:** [March 21, 2018, 2:42pm UTC](https://discourse.itk.org/t/compute-deformation-field-smoothness/788/1 "2018-03-21T14:42:02Z")

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Hello. I am trying to develop and algorithm for deformable image registration and I want to know if there is a way to calculate the smoothness of the deformation field that warps an image.

Thank you in advance

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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:** [March 21, 2018, 2:53pm UTC](https://discourse.itk.org/t/compute-deformation-field-smoothness/788/2 "2018-03-21T14:53:47Z")

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It depends how “smoothness” is defined, but one option is to characterize smoothness with the [strain energy density](https://en.wikipedia.org/wiki/Strain_energy_density_function) computed from the [displacement field strain](http://hdl.handle.net/10380/3573).

HTH,  
Matt

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**Author:** ![blowekamp](https://discourse.itk.org/user_avatar/discourse.itk.org/blowekamp/32/79_2.png) [@blowekamp](https://discourse.itk.org/u/blowekamp)\
**Post date:** [May 11, 2018, 1:35pm UTC](https://discourse.itk.org/t/compute-deformation-field-smoothness/788/3 "2018-05-11T13:35:18Z")

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Split this topic on May 11, 2018, 1:35pm UTC

A post was split to a new topic: [make output deformation smooth](https://discourse.itk.org/t/make-output-deformation-smooth/921)