$H$ is the inliers threshold that points with final reprojection errors smaller than $H$ are considered as inliers. The reweighting rule suggests that a point with a large reprojection error will have a small weight during the estimation of camera pose, which is designed under a reasonable assumption that outliers have much larger reprojection errors than inliers. Although inliers may also have larger reprojection errors than $H$ during the iteration process, it is acceptable to assign weights that are smaller than 1 to inliers as long as outliers have much smaller weights. Hence, we simply use $H$ as the benchmark to assign weights.

According to $\bf{R}$ estimation given by equations , we multiply the weight factors with each item of matrices $\bf{A}$ and $\bf{S}$,

$${\bf{A}}_i = w_i {\bf{A}}_i, {\bf{S}}_i = w_i {\bf{S}}_i.$$

Similarity, to update $\mu$ using ,

$${\bf{B}}_{i} = w_i {{\bf{B}}}_{i}, {\bf{C}}_{i} = w_i {{\bf{C}}}_{i}.$$

Since inliers have much larger weights, $\bf{R}$ and $\mu$ are mainly estimated with inliers.

1-Point RANSAC Scheme
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The core algorithm of R1PP$n$P is based on a randomly selected control point $o$. In outlier-free situations, our algorithm works with any control point. However, in situations with outliers, the control point $o$ should be an 