The AIR package uses a variety of spatial models to restrict the type of linear transformation that is being applied when performing registration. While the most general model could be used in all instances, to do so would be both unnecessarily slow and in fact, inaccurate. For example, when if voxel sizes are known exactly, it makes little sense to use anything other than a rigid-body model for intrasubject registration unless there are strong reasons to suspect that the shape and/or size of the brain has changed between image acquisitions. In this context, any values for the nine extra parameters that imply anything other than an exact rigid-body fit might well be considered erroneous.

The following models have been implemented in AIR:

3D linear models

• rigid-body (6 parameters)
• global rescaling (7 parameters)
• traditional (9 parameters)
• affine (12 parameters)
• perspective (15 parameters, not supported for all cost functions)

3D nonlinear models

• first-twelfth order polynomials

2D linear models

• rigid-body (3 parameters)
• global rescaling (4 parameters)
• fixed determinant (5 parameters)
• affine (6 parameters)
• perspective (8 parameters, not supported for all cost functions)

2D nonlinear models

• first-twelfth order polynomials

The pages linked above include detailed mathematical descriptions of each model, including explicit listings of the formal parameters of the models and the initialization file format required for each model.