A non‐iterative method for approximation of the exact solution to the point‐to‐plane variational problem for orthogonal transformations

The most popular algorithm for aligning of three‐dimensional point data is the iterative closest point (ICP). In this paper, a new algorithm for orthogonal registration of point clouds based on the point‐to‐plane ICP algorithm is proposed. The algorithm consists of three steps: first, a matrix of affine transformation between two given point clouds are calculated; second, the affine transformation matrix is projected onto the manifold SO(3) of orthonormal matrices; finally, a translation vector is reestimated. The proposed algorithm does not require an approximate initial estimate. At each iterative step of the ICP algorithm, an approximated closed‐form solution for the orthogonal transformation is derived. The performance of the proposed algorithm is compared with that of common algorithms for the geometrical transformations estimation.