Algorithm 1.

Algorithm for Brain Extraction

Input: Image I, Brain-Extracted Atlas A, Atlas Mask AM
Output: Brain-Extracted Image IB and mask IM
1	I1, ${\mathrm{\Phi }}_1^{-1}=\text{pre-processing}(I)$;
2	for k ← 1 to 6 do
3	if k ≥ 2 then
4	if k ≤ 3 then
5	find ${\mathrm{\Phi }}_k^{-1}$, s.t., $R_{k-1}\circ {\mathrm{\Phi }}_k^{-1}=A$ and ${\mathrm{\Phi }}_k^{-1}$is affine;
6	else if k == 4 then
7	find ${\mathrm{\Phi }}_k^{-1}$, s.t., $R_{k-1}\circ {\mathrm{\Phi }}_k^{-1}=A$ and ${\mathrm{\Phi }}_k^{-1}$is B-spline;
8	else
9	find ${\mathrm{\Phi }}_k^{-1}$, s.t., $(L_{k-1}\circ {\mathrm{\Phi }}_{k-1})\circ {\mathrm{\Phi }}_k^{-1}=A$ and ${\mathrm{\Phi }}_k^{-1}$is B-spline;
10	end
11	$I_k=I_{k-1}\circ {\mathrm{\Phi }}_k^{-1}$;
12	Decompose Ik, s.t., Ik = Lk + Sk + Tk;
13	if k ≤ 3 then
14	Rk = Lk + Sk;
15	end
16	end
17	IB, $I_M=\text{post-processing}(A_M,\{{\mathrm{\Phi }}_k^{-1}\})$