Table 1.

Deformation model, approximate number of degrees of freedom (dof), similarity measure, and regularization method for each of the algorithms evaluated in this study

Algorithm	Deformation	≃dof	Similarity	Regularization
FLIRT	Linear, rigid-body	9, 6	normalized CR
AIR	5th-order polynomial warps	168	MSD (optional intensity scaling)	Incremental increase of polynomial order; MRes: sparse-to-fine voxel sampling
ANIMAL	Local translations	69K	CC	MRes, local Gaussian smoothing; stiffness parameter weights mean deformation vector at each node
ART	Non-parametric, homeomorphic	7 M	normalized CC	MRes median and low-pass Gaussian filtering
Diffeomorphic Demons	Non-parametric, diffeomorphic displacement field	21 M	SSD	MRes: Gaussian smoothing
FNIRT	Cubic B-splines	30 K	SSD	Membrane energy*; number of basis components; MRes: down- to up-sampling
IRTK	Cubic B-splines	1.4 M	normalized MI	None used in the study; MRes: control mesh spacing and Gaussian smoothing
JRD-fluid	Viscous fluid: variational calculus (diffeomorphic)	2 M	Jensen–Rényi divergence	Compressible viscous fluid governed by the Navier–Stokes equation for conservation of momentum; MRes
ROMEO	Local affine (12 dof)	2 M	Displaced frame difference	First-order explicit regularization method, brightness constancy constraint; MRes: adaptive multigrid (octree subdivision), Gaussian smoothing
SICLE	3-D Fourier series (diffeomorphic)	8 K	SSD	Small-deformation linear elasticity, inverse consistency; MRes: number of basis components
SyN	Bi-directional diffeomorphism	28 M	CC	MRes Gaussian smoothing of the velocity field; transformation symmetry
SPM5:
“SPM2-type”	Discrete cosine transforms	1 K	MSD	Bending energy, basis cutoff
Normalization
Normalization	Discrete cosine transforms	1 K	MSD	Bending energy, basis cutoff
Unified Segmentation	Discrete cosine transforms	1 K	Generative segmentation model	Bending energy, basis cutoff
DARTEL Toolbox	Finite difference model of a velocity field (constant over time, diffeomorphic)	6.4 M	Multinomial model (“congealing”)	Linear-elasticity; MRes: full-multigrid (recursive)

The dof is estimated based on the parameters and data used in the study; approximate equations, where available, are given in each algorithm's description in the Supplementary section 8. Software requirements, input, and run time for the algorithms are in the Appendix B.

^*Since this study was conducted, FNIRT uses bending energy as its default regularization method. MRes=multiresolution; MSD=mean squared difference; SSD=sum of squared differences; CC=cross-correlation; CR=correlation ratio; MI=mutual information.