Usage: 3dNwarpFuncs [options]
This program reads in a nonlinear 3D warp (from 3dQwarp, etc.) and
computes some functions of the displacements. See the OPTIONS below
for information on what can be computed.
OPTIONS:
--------
-nwarp www = 'www' is the name of the 3D warp dataset
(this is a mandatory option!)
++ This can be computed on the fly, as in 3dNwarpApply.
-prefix ppp = 'ppp' is the name of the new output dataset
-bulk = Compute the (fractional) bulk volume change.
++ e.g., Jacobian determinant minus 1.
-shear = Compute the shear energy.
-vorticity = Compute the vorticity enerty.
If none of '-bulk', '-shear', or '-vorticity' are given, then '-bulk'
will be assumed.
NOTES:
------
Denote the displacement vector field (warp) by
[ p(x,y,z) , q(x,y,z) , r(x,y,z) ]
Define the Jacobian matrix by
[ 1+dp/dx dp/dy dp/dz ] [ Jxx Jxy Jxz ]
J = [ dq/dx 1+dq/dy dq/dz ] = [ Jyx Jyy Jyz ]
[ dr/dx dr/dy 1+dr/dz ] [ Jzx Jzy Jzz ]
* The '-bulk' output is the determinant of this matrix (det[J]), minus 1.
* It measures the amount of volume distortion.
* The '-shear' output is the sum of squares of the J matrix elements --
which equals the sum of squares of its eigenvalues -- divided by
det[J]^(2/3), then minus 3.
* It measures the amount of shearing distortion (normalized by the amount
of volume distortion).
* The '-vorticity' output is the sum of squares of the skew part of
the J matrix = [ Jxy-Jyx , Jxz-Jzx , Jyz-Jzy ], divided by det[J]^(2/3).
* It measures the amount of twisting distortion (also normalized).
* All 3 of these functions are dimensionless.
* The penalty used in 3dQwarp is a combination of the bulk, shear,
and vorticity functions.
++ Compile date = Jan 27 2020 {AFNI_20.0.03:linux_ubuntu_16_64}