Point cloud registration using congruent pyramids

We present a method to compute an initial alignment for pairwise registration of point clouds. This method uses the properties of a rigid body transformation - the ratio of lengths is preserved, the euclidean distance between points is preserved - to find congruent pyramids in two point clouds. The corresponding vertices of the congruent pyramids are used to derive a closed form solution for initial alignment. The alignment is refined further using the Iterative Closest Point algorithm. We validate the method on challenging datasets - which include airborne LIDAR, outdoor, and indoor - having initial offsets and varying densities.