the identified consesus set. We still use the synthetic dataset as in the ablation study.

![(a) The number of inliers in the estimated maximal consensus set w.r.t increasing outliers of successful estimation. (b) The number of inliers in the estimated maximal consensus set for 100 runs when the outlier rate is 80%.[]{data-label="fig.robustness"}](inliers2){width="50.00000%"}

**Efficiency of globally optimal methods.** We first compare the efficiency between the proposed method and the LMI. We evaluate the computational cost with respect to the number of feature correspondences and the percentage of outliers. The result is shown in Fig. \[fig.time\], the computational cost of LMI is significantly higher than the proposed methods both for increasing number of correspondences, and the percentage of outliers. The growing gap may also indicate that the complexity of LMI is higher than ours.

**Deterministic convergence.** The vital difference between RANSAC and globally optimal method is the convergence. We compare the number of inliers in the estimated maximal consensus set with respect to increasing outliers when the final pose estimation is successful. The result is shown in Fig. \[fig.robustness\], which indicates that the proposed solution achieves deterministic perfect CCI, while RANSAC gives conservative estimations with less inliers and LMI finds optimistic estimations 