Fast point cloud registration in multidirectional affine transformation

This paper proposed a fast multidirectional affine registration (FMDAR) algorithm for matching two three-dimensional point clouds after multidirectional affine transformation with disorder, noise and missing points. The FMDAR algorithm is based on the statistical characteristics and shape features of point clouds. First, the eigenvalues of the point clouds matrix and the scaling rations are used to establish a system of nonlinear equations by the Vieta's Formulas. In addition, the rotational invariance of global vector features as a constraint is introduced and the cost function is established. Secondly, the scaling rations are calculated by using the Trust Region method to optimize the cost function. Finally, the multidirectional affine registration is transformed into a rigid registration after the scale rations are obtained. The FMDAR algorithm is robust in the presence of noises and we validate the FMDAR algorithm on three-dimensional point clouds with varying degrees of deformation in complex cases. What's more, results of the simulation show that the FMDAR algorithm has faster registration speed and higher accuracy compared with some existing algorithms.