ALGORITHM I: Inversion of Diffeomorphisms
Input	Input diffeomorphism (ϕ−1) Maximum number of iterations (N) Gradient magnitude tolerance (γI) Step size (ε)
Output	Inverse diffeomorphism (ζ)
1	Initialize ζ = Id and δ = 0 For iteration k < N
2	Compute ∇ζEId(ζk−1) using (16)
3	Compute the maximum gradient magnitude
	$\delta =\underset{\mathit{x}\in \mathrm{\Omega }}{max}\left\{{\Vert {\nabla }_{\mathit{\zeta }}{E}_{Id}({\mathit{\zeta }}^{k-1})(\mathit{x})\Vert }_2\right\}$
4	If δ < γI, Stop.
5	Update the inverses, ζk = ζk−1 − ε∇ζEId (ζk−1)
In this work, we use ε = 0.5, γI = 0.01, and N = 25 iterations.