Before revision:  Specifically, we (i) propose and construct a series of compatible structures for the registration problem where various invariants can be established, and (ii) design two time-efficient frameworks, one for known-scale registration and the other for unknown-scale registration, to filter out outliers and seek inliers from the invariant-constrained random sampling built upon the compatible structures  .
After revision:  Specifically, we (i) propose and construct a series of compatible structures for the registration problem where various invariants can be established, and (ii) design two time-efficient frameworks, the first for rotation search, the second for known-scale registration and the other for unknown-scale registration, to filter out outliers and seek inliers from the invariant-constrained random sampling built upon the compatible structures .