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Forward and inverse warps for warping images, pointsets and Jacobians
Applying the deformations computed by ANTs require the user to specify the correct warps, and to specify them in the correct order. Getting this wrong can cause obvious or subtle errors in the output, depending on the size of the deformations. Common use cases are explained below.
The command
${ANTSPATH}antsRegistrationSyNQuick.sh
-d 3 \
-f fixedImage.nii.gz \
-m movingImage.nii.gz \
-o movingToFixed_ \
-t s
produces
movingToFixed_1Warp.nii.gz
movingToFixed_1InverseWarp.nii.gz
movingToFixed_0GenericAffine.mat
The forward transforms from moving to fixed space are defined as those we use to deform an image in the moving space and produce output in the fixed space. These are movingToFixed_1Warp.nii.gz and movingToFixed_0GenericAffine.mat.
The inverse transforms are the transforms that are used to perform the opposite operation, deforming an image in the fixed space and producing output in the moving space. This operation uses the file movingToFixed_1InverseWarp.nii.gz and the inverse of the forward affine transform movingToFixed_0GenericAffine.mat. The inverse affine transform is not usually stored because it is easy to invert on demand.
Deforming the moving image to fixed space:
${ANTSPATH}antsApplyTransforms \
-d 3 \
-i movingImage.nii.gz \
-r fixedImage.nii.gz \
-t movingToFixed_1Warp.nii.gz \
-t movingToFixed_0GenericAffine.mat \
-o movingToFixedDeformed.nii.gz
If we have regions of interest in fixedLabels.nii.gz, in the fixed image space, we can deform these to moving space:
${ANTSPATH}antsApplyTransforms \
-d 3 \
-i fixedLabels.nii.gz \
-r movingImage.nii.gz \
-t [movingToFixed_0GenericAffine.mat, 1] \
-t movingToFixed_1InverseWarp.nii.gz \
-n GenericLabel[Linear] \
-o movingToFixedDeformed.nii.gz
The option [movingToFixed_0GenericAffine.mat, 1] tells the program to invert the affine transform contained in movingToFixed_0GenericAffine.mat. The option -n GenericLabel[Linear] uses an interpolation function suitable for label images.
Transform points from fixed to moving space:
${ANTSPATH}antsApplyTransformsToPoints \
-d 3 \
-i landmarksInFixedSpace.csv \
-o landmarksInMovingSpace.csv \
-t movingToFixed_1Warp.nii.gz \
-t movingToFixed_0GenericAffine.mat
The forward warps, which we use to deform an image from moving to fixed space, are the warps that transform points from fixed to moving space. To move points in the opposite direction:
${ANTSPATH}antsApplyTransformsToPoints \
-d 3 \
-i landmarksInMovingSpace.csv \
-o landmarksInFixedSpace.csv \
-t [movingToFixed_0GenericAffine.mat, 1]
-t movingToFixed_1InverseWarp.nii.gz \
The input and output to antsApplyTransformsToPoints is in physical space as defined by ITK. This may vary from the coordinates as understood by NIFTI or other file formats. The coordinates need to be carefully validated by users. ANTsR has some capabilities to help with this.
The Jacobian is typically computed in the fixed space, so that Jacobians from a population of moving images can compared directly.
CreateJacobianDeterminantImage 3 movingToFixed1Warp.nii.gz logJacobian.nii.gz 1 1
This outputs the log of the Jacobian determinant in the fixed space.
| Log Jacobian | Moving image volume change |
|---|---|
| < 0 | Expanding |
| = 0 | Zero |
| > 0 | Contracting |
Simple example data and code here, a more complex example here.
In this context the moving image is the subject T1 image on which cortical thickness is computed. The fixed image is a template.
The forward warp computed by antsCorticalThickness.sh is SubjectToTemplate1Warp.nii.gz, and the forward affine is SubjectToTemplate0GenericAffine.mat. The inverse warp is called TemplateToSubject0Warp.nii.gz, and the inverse affine is saved as TemplateToSubject1GenericAffine.mat, so you do not need to use the square brackets on the command line.
To warp an image from subject to template space:
${ANTSPATH}antsApplyTransforms \
-d 3 \
-i subjectImage.nii.gz \
-r registrationTemplate.nii.gz \
-t SubjectToTemplate1Warp.nii.gz \
-t SubjectToTemplate0GenericAffine.mat \
-o subjectImageToTemplateDeformed.nii.gz
To warp an image from template to subject space:
${ANTSPATH}antsApplyTransforms \
-d 3 \
-i templateImage.nii.gz \
-r subjectImage.nii.gz \
-t TemplateToSubject1GenericAffine.mat \
-t TemplateToSubject0Warp.nii.gz \
-o templateImageToSubjectDeformed.nii.gz
The longitudinal pipeline contains multiple runs of antsCorticalThickness.sh. Together, these provide all the transforms necessary to move any of the subject's images to the population template space, via the intermediate single-subject template. The chain of warps required to perform this operation in either direction is composed by the script, and saved as SubjectToGroupTemplateWarp.nii.gz and GroupTemplateToSubjectWarp.nii.gz. This encompasses both the affine and deformable parts.
Note that each time point will have its own warp, and images may be transformed from subject to group template space with:
${ANTSPATH}antsApplyTransforms \
-d 3 \
-i subjectImageTime1.nii.gz \
-r groupTemplate.nii.gz \
-t SubjectTime1/SubjectToGroupTemplateWarp.nii.gz \
-o subjectImageTime1ToGroupTemplateDeformed.nii.gz
Warping to the single-subject template is similar to the cross-sectional usage:
${ANTSPATH}antsApplyTransforms \
-d 3 \
-i subjectImageTime1.nii.gz \
-r groupTemplate.nii.gz \
-t SubjectTime1/SubjectToTemplate1Warp.nii.gz \
-t SubjectTime1/SubjectToTemplate0GenericAffine.mat \
-o subjectImageTime1ToGroupTemplateDeformed.nii.gz
Wherever possible, multiple interpolations of the data should be avoided. Warps between modalities or through intermediate templates can be combined on the command line with multiple -t options to antsApplyTransforms.
Internally, deforming an image involves transforming a point set in the opposite direction to the intuitive direction of the warping. The "moving" image is being resampled into the fixed space, and the warps transform a sample point (ie, a voxel in the output image) into the moving space. A point at the center of a voxel in the fixed space is transformed to moving space by the forward warps, an interpolated intensity value is computed, and the result is placed in the voxel in the output image.
This is why the transform ordering for antsApplyTransforms and antsApplyTransformsToPoints is different, and the use of the forward warp for the Jacobian may be counter-intuitive.
To verify the correct ordering of warps, it's necessary to know the choice of fixed and moving image for each registration. This depends entirely on how antsRegistration was called.