Inverting deformation fields using a fixed point iteration scheme

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Being able to quickly compute the inverse of a deformation field is often useful in the context of medical image analysis. While ITK supports this functionality, the current algorithms are slow and do not always yield accurate results. In this paper we describe an ITK implementation of a fixed point algorithm for the approximate inversion of deformation fields that was recently proposed by M. Chen and co-workers. The algorithm has been shown to be both faster and more accurate than those currently implemented in ITK.
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minus A useful class. by Matthew Mccormick on 2011-01-15 18:58:36 for revision #1
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The author provides an implementation of the paper by M. Chen that is intended to provide a faster and more accurate inverse displacement image filter.


The algorithm is faster and more accurate than the InverseDeformationFieldImageFilter.


More quantitative test cases and analysis are needed to verify that 1) the class is faster and 2) the class is more accurate.

Open Science:

Source code and input images are provided.  The images and deformation found in the article not included are distributed with ITK.


I compiled it with both ITK 3.20.0 and ITK4 git.  It compiled fine.  The test failed because of an incorrect filename in the CMakeLists.txt.  Only the most basic test code is included.  I also wrote code to run the warping and inverse warping on the input image to reproduce the output of the first example present in the paper.

Open source Contributions:

The code was usable.

Code Quality :

The code was easy to read.  There is a Win32 header included in the test case for unknown reasons.  Some unused code was still present.  In terms of ITK coding styles some changes could be made -- no tabs, bracket location, method definition style.

Quality of the data :

It was a couple of well chosen datasets.

Free comment :

Thanks for this nice contribution.


I have made some suggested changes that can be found here:

Matt McCormick (thewtex) (9):

      Initial import from IJ revision #1.

      Fix testing file names.

      Remove executable permissions.

      The test generates the images shown in the article.

      Replace indentation tabs with spaces.

      Add UseInputImageInformation method.

      rm unused TimeProbe header.

      rm unused WarpVectorImageFilter header.

      Make multi-threaded.


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Comment by Tobias Gass yellow

thanks for the filter, works very good and is fast.

I had one problem, which appears when the inverse is not expected to be in the same physical domain as the deformation itself. It can be resolved by overwriting the following function



which is used to set the requested region of the input to the requested region of the output in the regular filter pipeline. In this filter, this is not necessary.

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Categories: Atlas-based segmentation, Deformable registration, Registration, Segmentation, Transforms
Keywords: Deformation fields, Inversion, Image registration
Toolkits: ITK
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