P2Π: A Minimal Solution for Registration of 3D Points to 3D Planes

This paper presents a class of minimal solutions for the 3D-to-3D registration problem in which the sensor data are 3D points and the corresponding object data are 3D planes. In order to compute the 6 degrees-of-freedom transformation between the sensor and the object, we need at least six points on three or more planes. We systematically investigate and develop pose estimation algorithms for several configurations, including all minimal configurations, that arise from the distribution of points on planes. The degenerate configurations are also identified. We point out that many existing and unsolved 2D-to-3D and 3D-to-3D pose estimation algorithms involving points, lines, and planes can be transformed into the problem of registering points to planes. In addition to simulations, we also demonstrate the algorithm's effectiveness in two real-world applications: registration of a robotic arm with an object using a contact sensor, and registration of 3D point clouds that were obtained using multi-view reconstruction of planar city models.