Algorithm 1.

Task-Optimal Registration

Data: A set of training images {In}
Result: Parameters w that minimize the regularized task performance G [see (2.4)]
Initialize w0.
repeat
Step	1.	Given current values of w, estimate ${\mathrm{\Gamma }}_n^{*}(w)={\text{arg min}}_{{\mathrm{\Gamma }}_n}$, fn (w, Γn), i.e., perform registration of each training subject n.
Step	2.	Given current estimates (w, {Γn (w)}), compute the ∂wG gradient using either (Eq. 2.12) via ∂wΓ* in (2.9) for the addition model or (Eq. 2.16) via ∂wυ* in (2.14) for the composition model.
Step	3.	Perform line search in the direction opposite to ∂wG [47].