Closed form solution of ICP error minimization problem for affine transformations

The iterative closest point (ICP) algorithm is one of the most popular approaches to shape registration. The aim of the algorithm is to calculate the optimal geometric transformation relative to the given metric, combining the two given clouds. An important step in the ICP algorithm is the solution of the problem of minimizing the functional corresponding to a given metric for a given class of geometric transformations. In this paper, a method is presented for solving the variational problem of the ICP algorithm for the point-to-point metric in the class of affine transformations. With the help of computer simulation, the correctness of the proposed method is demonstrated.