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ITKFixedPointInverseDisplacementField takes a displacement field as input and computes the displacement field that is its inverse. If the input Displacement field was mapping coordinates from a space A into a space B, the output of this filter will map coordinates from the space B into the space A.
The fixed point algorithm is described in the paper:
Mingli Chen, Weiguo Lu, Quan Chen, Knneth J. Ruchala and Gusavo H. Olivera "A simple fixed-point approach to invert a Displacement field", Medical Physics, vol. 35, issue 1, p. 81,
The FixedPointInverseDisplacementFieldImageFilter has been implemented and described in the Insight Journal article:
Luethi M. "Inverting Displacement fields using a fixed point iteration scheme." http://hdl.handle.net/10380/3222 http://www.insight-journal.org/browse/publication/768 October 2010.
Since ITK 4.10.0, this module is available in the ITK source tree as a Remote module. To enable it, set:
Module_FixedPointInverseDisplacementField:BOOL=ON
in ITK's CMake build configuration.