ALGORITHM II: MIND Demons
Input	Input images (I0 and I1) Number of pyramid levels (Nℓ) Maximum numbers of iterations (Nk) Gradient magnitude tolerance (γS) Metric value convergence tolerance (γF) Convergence window (W) Registration parameters (σp, tp, ∈, σU, and σD)
Output	Diffeomorphism (ψ)
1	Initialize ϕ0(0.5) = ϕ1 (0.5) = Id and δ = 0 For level ℓ < Nℓ
2	If ℓ > 0, upsample ϕ0 and ϕ1  For iteration k <Nk
3	Compute ${\mathit{m}}_{I_0\circ {\mathit{\varphi }}_0}$ and ${\mathit{m}}_{I_1\circ {\mathit{\varphi }}_1}$
4	Compute S, ∇0S, and ∇1S using (20) and (21)
5	Compute the maximum normalized gradient magnitude    $\delta =\underset{\mathit{x}\in \mathrm{\Omega }}{max}\left\{\frac{1}{C}({\Vert {\nabla }_{0}S(\mathit{x})\Vert }_2+{\Vert {\nabla }_{1}S(\mathit{x})\Vert }_2)\right\}$   where $C={\sum }_{\mathit{x}\in \mathrm{\Omega }}({\Vert {\nabla }_{0}S(\mathit{x})\Vert }_2+{\Vert {\nabla }_{1}S(\mathit{x})\Vert }_2)$
6	If k > W, compute a gradient ∇F of a line fitted to S in (20) evaluated from k − W to k.
7	If δ < γS or ∇F < γF, Stop.
8	Compute ${\mathit{v}}_0^k$ and ${\mathit{v}}_1^k$ using (9) and (10) where K is approximated by $G_{{\sigma }_U}$
9	Estimate ${\mathit{\eta }}_0^k$ and ${\mathit{\eta }}_1^k$ using (12)
10	Regularize ${({\mathit{\varphi }}_0^k)}^{-1}$ and ${({\mathit{\varphi }}_1^k)}^{-1}$ based on (14) using $G_{{\sigma }_D}$
11	Estimate ${\mathit{\varphi }}_0^k$ and ${\mathit{\varphi }}_1^k$ using Algorithm I
12	Compute $\mathit{\psi }={\mathit{\varphi }}_0\circ {\mathit{\varphi }}_1^{-1}$
In this work, we use γS = 10−ℓ, γF = 10−6, and W = 20 iterations.