A Geometric Algebra Solution to the 3D Registration Problem

In 1992 Besl and McKay proposed the ICP algorithm, one of the most well known geometry-based registration algorithms, for solving the 3D-3D registration problem. This problem plays a crucial role for computer vision applications in robotics and automation, and it poses an active research topic in many scientific fields, such as object recognition and tracking. Conventionally, it is solved using Linear Algebra. This work presents the development, implementation and evaluation of a fairly simple closed-form solution to the 3D-3D registration problem by calculating the rotation using Geometric Algebra objects, i.e. rotors. The proposed solution effectively follows the standard steps of the ICP algorithm but replaces the rotation matrix calculation step with a rotor-calculation step. The solution is extensively evaluated through various test cases and it is shown that it can reach the same level of accuracy as well-known iterative Linear Algebra methods.