  We present a method that can evaluate a RANSAC hypothesis in constant time,
i.e. independent of the size of the data. A key observation here is that
correct hypotheses are tightly clustered together in the latent parameter
domain. In a manner similar to the generalized Hough transform we seek to find
this cluster, only that we need as few as two votes for a successful detection.
Rapidly locating such pairs of similar hypotheses is made possible by adapting
the recent "Random Grids" range-search technique. We only perform the usual
(costly) hypothesis verification stage upon the discovery of a close pair of
hypotheses. We show that this event rarely happens for incorrect hypotheses,
enabling a significant speedup of the RANSAC pipeline. The suggested approach
is applied and tested on three robust estimation problems: camera localization,
3D rigid alignment and 2D-homography estimation. We perform rigorous testing on
both synthetic and real datasets, demonstrating an improvement in efficiency
without a compromise in accuracy. Furthermore, we achieve state-of-the-art 3D
alignment results on the challenging "Redwood" loop-closure challenge.
