Data: A fixed spherical image F and moving spherical image M.

Result: Diffeomorphism Γ so that M ∘ Γ is “close” to F.

Set ϒ0 = identity transformation (or some a-priori transformation, e.g., from a previous registration)

repeat

Step 1. Given ϒ(t),

foreach vertex n do

Compute ${\overrightarrow{\upsilon }}_n^{(t)}$ using Eq. (28).

end

Compute Γ(t) = exp(v̄) using “scaling and squaring”.

Step 2. Given Γ(t),

foreach vertex n do

Compute ${\overrightarrow{\Upsilon }}_n^{(t)}$ using Eq. (48) implemented via iterative smoothing.

end

until convergence;