very basic test of jacobian should get a value around 2.14
In conclusion, the sum of the jacobian within the object in the template space -- multiplied by the product of the image spacing -- approximates the volume of the object within the moving image. Assuming you have only applied the SyN transformation by itself.
the rcalc.R compares the following values:
-
the ratio of volumes
-
the estimated volumes
with both jacobian and direct use of segmentations along with image spacing.
From the ants pdf documentation at https://github.com/stnava/ANTsDoc:
Figure 7: Digital invertibility presents some limitations. Here, we see that invertibility is not exact but is gained only by interpolation. Thus, in three-dimensional scenarios in particular, there are fundamental limits to the degree of invertibility that may be achieved. The second and third voxels – from left – in image A undergo an expansion by a factor of 2. That is, under the mapping, 2 voxels are mapped to 4. This gives the definition of the Jacobian – computed by ANTsJacobian – which is a unitless measure defined by the ratio of volumes. Thus, J (x) = V (phi(x))/V (x) where V represents the volume operation and x, here, may be a small object. Thus, if phi – the mapping – causes expansion, then J (x) > 1. In this example phi( x ) is the warp defined in the fixed image space e.g. myOutputWarp.nii.gz
See also Figure 21 and 22.
from within the repo do:
bash runThis.sh