Algorithm 1: Estimate and optimize the corresponding points.
	input: ModelS and DataT with normals of size $N\times 6$ (N is the scale of Model/Data)
	output:  2 pairs of corresponding points ${P_1^S}^{\prime }$, ${P_2^S}^{\prime }$, ${P_1^T}^{\prime }$ and ${P_2^T}^{\prime }$
1	extract normals ${\mathbb{N}}_S$ and ${\mathbb{N}}_T$ from S and T
2	${\mathbb{H}}^{\mathbb{S}}\leftarrow \mathcal{H}\left({\mathbb{N}}_S\right)$; ${\mathbb{H}}^{\mathbb{T}}\leftarrow \mathcal{H}\left({\mathbb{N}}_T\right)$;	// see Equations (7) & (8)
3	for$i\leftarrow 1$to 12 do
4	$H_S\left(i\right),I_S\left(i\right)\leftarrow \mathtt{max}\left(H_i^S\right)$;	// maximum intensity and the index
5	$H_T\left(i\right),I_T\left(i\right)\leftarrow \mathtt{max}\left(H_i^T\right)$
6	$N_S\left(i\right)\leftarrow I_S\left(i\right)$; $N_T\left(i\right)\leftarrow I_T\left(i\right)$;	// normals of the max
7	$P_i^S\leftarrow \mathcal{P}\left(N_S\left(i\right)\right)$; $P_i^T\leftarrow \mathcal{P}\left(N_T\left(i\right)\right)$;	// see Equation (6)
8	construct Struct $Q\left(i\right)=\{H\left(i\right),I\left(i\right),P_i\}$
9	end for
10	$Q_S\leftarrow$sortrows ($H_S$; $Q_T\leftarrow$) sortrows ($H_T$);	// descending sort
11	$i=2$
12	$P_{temp}^S=P_2^S$
13	while $arccos(V_i^S,V_{temp}^S)>0.94$ do	// see Eqution (10)
14	$P_{temp}^S=P_{i+1}^S$
15	$i\leftarrow i+1$
16	end while
17	$P_2^S=P_{temp}^S$
18	for$i\leftarrow 2$to 12 do
19	$P_{temp}^T=P_i^T$
20	if $\mid d_{1temp}^S-d_{1temp}^T\mid <0.05$ then	// see Equation (12)
21	$P_2^T=P_{temp}^T$
22	break;
23	end if
24	end for
25	let $n=4$ then calculate ${\mathbb{N}}_1^S,{\mathbb{N}}_2^S,{\mathbb{N}}_1^T,{\mathbb{N}}_2^T$;	// see Equation (13)
26	$\left[a,b,c\right]=V_1^S$
27	create $e_1=(1,1,-\frac{a+b}{c})$ in plane A then $e_2=e_1\times V_1^S$
28	${{\mathbb{N}}_1^S}^{\prime }={(\left[e_i;e_2\right]·{\left({\mathbb{N}}_1^S\right)}^T)}^T$;	// project normals to A
29	calculate $r_1^S$;	// see Equation (14)
30	mesh $r_1^S\times r_1^S$ region into 100 grids;
31	search $(x_p,y_p)$ with the peak intensity in meshed grids;
32	calculate inverse projection point ${P_1^S}^{\prime }$
33	calculate ${P_2^S}^{\prime }$, ${P_1^T}^{\prime }$, ${P_2^T}^{\prime }$