Algorithms to solve absolute orientation problem for GL(3), O(3), and SO(3) groups

The most popular algorithm for aligning of 3D point data is the Iterative Closest Point (ICP). The point-to-point variational problem for orthogonal transformations is mathematically equivalent to the absolute orientation problem in photogrammetry. In this paper the survey of the known closed form methods to solve point-to-point ICP variation problem is proposed. Also, the new extension of the Horn algorithm for O(3) group to SO(3) group is obtained. Computer simulation illustrates the difference of performance for considered methods.