Algorithm 1.

Registration Mapping and Propagation

Input: {Ii, i = 1, 2, …, N}: original serial images
Output: $\{{\stackrel{\sim }{I}}_i,i=1,2,\dots ,N\}$: registered serial images
Operator: ${\text{ℒ}}_{i:j}\triangleq {\text{ℒ}}_j(\cdots ({\text{ℒ}}_{i+\text{sign}(j-i)\times 2}({\text{ℒ}}_{i+\text{sign}(j-i)\times 1}({\text{ℒ}}_i(\cdot )))))$
1:	Compute reference image index $i^{\ast }\leftarrow \lfloor \frac{N}{2}\rfloor$
2:	Compute $\overline{\mathcal{T}},{\overline{\mathcal{T}}}^{-1}$, and $\mathcal{D}$ by Eqn (2) and (3), respectively
3:	for all i ∈ (i* − 1, i* − 2, …, 1) do
4:	for all $(x_1,x_2)\in \mathrm{\Omega }(I_{i\ast })$ do
5:	Set (X1, X2) ← (x1, x2)
6:	Set j ← i* − 1
7:	while j ≥ i do
8:	Local deformation: $(X_1,X_2)\leftarrow (X_1,X_2)-{\mathcal{D}}_j(X_1,X_2)$
9:	j ← j − 1
10:	${\stackrel{\sim }{I}}_i(x_1,x_2)\stackrel{\text{interpolate}}{\leftarrow }{I}_i\left({\overline{\mathcal{T}}}_{(i\ast -1):i}^{-1}(X_1,X_2)\right)$
11:	for all i ∈ (i* + 1, …, N) do
12:	for all (x1, x2) ∈ Ω (Ii*) do
13:	Set (X1, X2) ← (x1, x2)
14:	Set j ← i* + 1
15:	while j ≤ i do
16:	Local deformation: $(X_1,X_2)\leftarrow (X_1,X_2)-{\mathcal{D}}_j(X_1,X_2)$
17:	j ← j + 1
18:	${\stackrel{\sim }{I}}_i(x_1,x_2)\stackrel{\text{interpolate}}{\leftarrow }{I}_i\left({\overline{\mathcal{T}}}_{i\ast :(i-1)}^{-1}(X_1,X_2)\right)$