Algorithm 1 Point set registration algorithm

1: Input: reference point set $P\in {\mathbb{R}}^{n\times 3}$; measured point set $Q\in {\mathbb{R}}^{m\times 3}$; maximum accepted deviation $\sigma$ of Euclidean point distances   2: Output: rotation matrix $R\in {\mathbb{R}}^{3\times 3}$, translation vector $t\in {\mathbb{R}}^3$ representing the rigid transformation from the camera coordinate system to the sample coordinate system   3:    4: Compute distance matrices $D_P\in {\mathbb{R}}^{n\times n}$, $D_Q\in {\mathbb{R}}^{m\times m}$; $d_{p,k,l}\in D_P$ corresponds to the Euclidean distance between the points $p_k$, $p_l\in P$ and $d_{q,i,j}\in D_Q$ to the distance between $q_i$, $q_j\in Q$;   5:   ▹ Identify candidate points that could be a match:   6: Initialize empty list $candidates\left[q_i\right]$ for candidate points from P that could be a match for the points $q_i$ from Q; only unique points, no double entries;   7: for each point $q_i$ in Q do   8:       for each $d_{p,k,l}$ with $k<l$ do   9:             if $|d_{q,i,i+1}-d_{p,k,l}|<\sigma$ then 10:                  Add $p_k,p_l$ to the list $candidates\left[q_i\right]$ 11:                  Add $p_k,p_l$ to the list $candidates\left[q_{i+1}\right]$ 12:             end if 13:       end for 14: end for 15:   ▹ Find all matches with candidate points: 16: $matches[q,p]\in {\mathbb{R}}^{m\times n}$ contains number of matching edges for points $q\in Q$ and $p\in P$ 17: Initialize $matches$ with zeros 18: for each $d_{q,i,j}$ do 19:       for each $d_{p,k,l}$ with $p_k$ in $candidates\left[q_i\right]$ do 20:             if $|d_{q,i,j}-d_{p,k,l}| <\sigma$ then 21:                  $matches[q_i,p_k]=matches[q_i,p_k]+1$ 22:                  Continue with next $p_k$ 23:             end if 24:       end for 25: end for 26:  27: $q_i\in Q$ and $p_k\in P$ with the highest values in $matches[q,p]$ are matched together 28: Get $R\in {\mathbb{R}}^{3\times 3}$, $t\in {\mathbb{R}}^3$ with Kabsch algorithm 29: Fine tuning: remove the point pair with the highest distance after registration and check if the overall registration quality improves 30:  31: return $R,t$