  Relative pose estimation for RGBD cameras is crucial in a number of
applications. Previous approaches either rely on the RGB aspect of the images
to estimate pose thus not fully making use of depth in the estimation process
or estimate pose from the 3D cloud of points that each image produces, thus not
making full use of RGB information. This paper shows that if one pair of
correspondences is hypothesized from the RGB-based ranked-ordered
correspondence list, then the space of remaining correspondences is restricted
to corresponding pairs of curves nested around the hypothesized correspondence,
implicitly capturing depth consistency. This simple Geometric Depth Constraint
(GDC) significantly reduces potential matches. In effect this becomes a filter
on possible correspondences that helps reduce the number of outliers and thus
expedites RANSAC significantly. As such, the same budget of time allows for
more RANSAC iterations and therefore additional robustness and a significant
speedup. In addition, the paper proposed a Nested RANSAC approach that also
speeds up the process, as shown through experiments on TUM, ICL-NUIM, and RGBD
Scenes v2 datasets.
