vice versa. After we get the solution of $s_3$, we can back-substitute it into (\[equ:33\]) and set $s_0 = 1$, then solve the resulting linear system for $s_1$ and $s_2$. After we get $s_1, s_2, s_3$, we can recover $\bf{R}$ by (\[equ:5\]) and calculate $\bf{y}$ using (\[equ:28\]). Then $\bf{t}$ can be recovered from (\[equ:24\]). We summarize our minimal solution in Algorithm \[alg:Min\].

**Input:** a minimal configuration\
**Output:** $\bf{R}$ and $\bf{t}$\

  ---- ---------------------------------------------------------------------------------------------------------------------------------------------------
  1.   Compute the coefficient matrices in (\[equ:27\]).
  2.   Compute the coefficients in (\[equ:29\]).
  3.   Solve (\[equ:29\]) for $s_1,s_2,s_3$ by the hidden variable method described in section \[subsec:hidden\] and recover $\bf{R}$ using (\[equ:5\]).
  4.   Compute $\bf{y}$ using (\[equ:28\]) and recover $\bf{t}$ by (\[equ:24\]).
  ---- ---------------------------------------------------------------------------------------------------------------------------------------------------

Experiments
===========

In this section, we compare our algorithm with the state-of-the-art algorithms, including Briales’s algorithm [@briales2017convex], BnB [@olsson2009branch], Olsson’s algorithm [@olsson2008solving] and Wientapper’s algorithm [@wientapper2018universal]. We also consider the point-to-point case alone, as it has closed-form solution. We adopt Arun’s algorithm [@arun1987least] implemented in OpenGV [@kneip2014opengv]. The algorithms are evaluated in terms of accuracy and computational time using synthetic and real data.

  --------------------------------------- --------------------- ------------------------- ---------- --------------------- ------------------------- ---------- --------------------- ------------------------- ----------
                                                                                                                                                                                                                
                                          $\bf{t}$ Err ($\%$)   $\bf{R}$ Err ($^\circ$)   Time (s)   $\bf{t}$ Err ($\%$)   