Linearization of rotations for globally consistent n-scan matching

The ICP (Iterative Closest Point) 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. While four closed-form solution methods are known for minimizing this function, linearization seems necessary for solving the global scan registration problem. This paper presents such linear solutions for registering n-scans in a global and simultaneous fashion. It studies parameterizations for the rigid body transformations of the n-scan registration problem.