Algorithm 1.

Spherical Demons Registration Algorithm

1:	Input: n roughly registered subjects, each subject has a surface map indicating subfield distribution, which is marked as M.
2:	Output: Diffeomorphism Γ so that min dist(F − M ◦ Γ) achieved, where F is created by averaging all 12 registered subjects.
3:	while iter <= 4 do
4:	Template Surface Atlas $F=\frac{\sum M}{n}$
5:	for each subject with label map M do
6:	4-level multi-precision registration:
7:	for each level do
8:	repeat
9:	Step 1: Given γ(t)
10:	for each vertex k do
11:	Compute:
	$${\overrightarrow{v}}_k^{(t)}=\frac{F(x_k)-M\circ {\gamma }^{(t)}(x_k)}{{\sigma }_k^2}{E}_k{[E_k^T(\frac{{\overrightarrow{m}}_k{\overrightarrow{m}}_k^T}{{\sigma }_k^2}+\frac{S_k{(G_k^2)}^T{G}_k^2{S}_n^T}{{\sigma }_x^2})E_n+\epsilon I_{2\times 2}]}^{-1}{E}_k^T{\overrightarrow{m}}_k$$ (4)
12:	${\mathrm{\Gamma }}^{(t)}={\gamma }^{(t)}\circ \text{exp}({\overrightarrow{v}}^{(t)})$
13:	Step 2: Given Γ(t)
14:	for each vertex k do
15:	Update γ:
	$${\overrightarrow{\gamma }}^{(t+1)}=\underset{\overrightarrow{\gamma }}{\text{argmin}}\frac{1}{{\sigma }_x^2}{\displaystyle \sum _{k=1}^K{\Vert \overrightarrow{{\gamma }_n}-{\overrightarrow{{\gamma }_n}}^{(t)}\Vert }^2+\frac{2}{{\sigma }_T^2}{\Vert \overrightarrow{\gamma }\Vert }_V}$$ (5)
16:	until Convergence
17:	iter = iter + 1