  3D scan registration is a classical, yet a highly useful problem in the
context of 3D sensors such as Kinect and Velodyne. While there are several
existing methods, the techniques are usually incremental where adjacent scans
are registered first to obtain the initial poses, followed by motion averaging
and bundle-adjustment refinement. In this paper, we take a different approach
and develop minimal solvers for jointly computing the initial poses of cameras
in small loops such as 3-, 4-, and 5-cycles. Note that the classical
registration of 2 scans can be done using a minimum of 3 point matches to
compute 6 degrees of relative motion. On the other hand, to jointly compute the
3D registrations in n-cycles, we take 2 point matches between the first n-1
consecutive pairs (i.e., Scan 1 & Scan 2, ... , and Scan n-1 & Scan n) and 1 or
2 point matches between Scan 1 and Scan n. Overall, we use 5, 7, and 10 point
matches for 3-, 4-, and 5-cycles, and recover 12, 18, and 24 degrees of
transformation variables, respectively. Using simulations and real-data we show
that the 3D registration using mini n-cycles are computationally efficient, and
can provide alternate and better initial poses compared to standard pairwise
methods.
