Toward a Unified Framework for Point Set Registration

Point set registration plays a critical role in robotics and computer vision. Early methods considered registration as a purely geometric problem, presenting excellent extensibility for various tasks due to their explicit handling of correspondences; statistical methods were later introduced to handle noise. However, the two categories of algorithms have evolved independently without sharing much in common. In this paper, we leverage the concept of information geometry to theoretically unify the two classes together by interpreting them as the same operation but in different spaces associated with respective metrics. Moreover, based on the proposed unification, we also develop a novel bandwidth estimation strategy to solve the long-standing problem of statistical registration algorithms, and demonstrate its theoretical and practical advantages over deterministic annealing, the most commonly used technique. We also present a case study to show how geometric and statistical approaches can benefit from each other.