# Image registration for DTI

The problem is that image registration is ultimately based on comparing the two (or more) images as the software wiggles them around, and stopping when the comparison is good. The comparison might be least squares (e.g., correlation), mutual information, or whatnot. But if the images aren't that comparable in detail, then the registration might be off, and it is hard to judge how much.

For images going into the DWI-to-DTI calculation, one solution is the DWI-to-DTI calcuation itself. That is, the goal *after* registration is then to compute the DT from the DW data at each voxel, and this computation is itself a fitting of the DT to the DW values. At the end, in each voxel we have residual = what's left after we subtract the DT fit from the DW data. A precise registration method would be to wiggle the DW images around until the overall residuals from the DT fit are small. Schematically:

(1) Do some preliminary standard registration method, just to get things off to a good start;

(2) Compute the DWI-to-DTI fit at each voxel;

(3) Compute the residual variance (or MAD) at each voxel, then average these (or median) over the brain as a measure of the overall goodness-of-fit;

(4) Wiggle the DW images arounds and go back to step (2), with the goal of minimizing the overall residual value computed in (3).

There are many details to be worked out, such as the method used in step (4) to decide upon the image movement parameters.

The principle is to directly attack the problem: misregistration produces bad DTI fits, so use try to minimize this badness.

This is probably a Ph.D. level problem, taking a couple years to get working well, I'd guess, for a decent student.

## image registration for DTI