Study of parameterizations for the rigid body transformations of the scan registration problem

The iterative closest point (ICP) algorithm is the de facto standard for geometric alignment of three-dimensional models when an initial relative pose estimate is available. The basis of the algorithm is the minimization of an error function that takes point correspondences into account. Four closed-form solution methods are known for minimizing this function. This paper presents novel linear solutions to the scan registration problem, i.e., to the problem of putting and aligning 3D scans in a common coordinate system. We extend the methods for registering n-scans in a global and simultaneous fashion, such that the registration of the nth scan influences all previous registrations in one step.