Algorithm 2 Neighborhood recognition of feature points

Input: $p_i,p_i\in$$P_F$; Output: $p_i$‘s mollification neighborhood ${\overline{N}}_i$; 1: for $i=0$ to $P_F$.size() do 2:   Seek $\tilde{S}$ nearest neighborhood $\tilde{N}$; 3:   View every point $\left\{p_1,p_2,...p_{\tilde{S}}\right\}$ as a single cluster $\{{\tilde{N}}_1,{\tilde{N}}_2,...,{\tilde{N}}_{\tilde{S}}\}$;    //see Section 5.1 and Figure 4 4:   for $j=1$ to $\tilde{S}$ do 5:     Compute similarity: $D_{ave}({\tilde{N}}_p,{\tilde{N}}_q), p\ne q$ based on Equation (4); 6:     $T=\min \{D_{ave}({\tilde{N}}_p,{\tilde{N}}_q)\}$; 7:     if ($T<\delta$) then 8:      Find two cluster ${\tilde{N}}_m, {\tilde{N}}_n$ with minimum similarity; 9:      Merge (${\tilde{N}}_m,{\tilde{N}}_n$); 10:     else 11:      Obtain the ultimate cluster result: $\{{\overline{N}}_1,{\overline{N}}_2,...,{\overline{N}}_K\}$; 12:      break; 13:   end For 14:   $\{{\epsilon }_1,{\epsilon }_2,...,{\epsilon }_S\}=$computeResidual ($p_i,\{{\overline{N}}_1,{\overline{N}}_2,...,{\overline{N}}_S\}$); //see Section 5.2 15:   ${\overline{N}}_i=\min \{{\epsilon }_1,{\epsilon }_2,...,{\epsilon }_S\}$corresponding to ${\overline{N}}_c$, $c\in \{1,2,...,S\}$; 16: end for 17: return ${\overline{N}}_i$ with ${\overline{S}}_i$ neighbors;