IV International Conference on "Information Technology and Nanotechnology" (ITNT-2018) Point clouds registration based on the point-to-plane approach for orthogonal transformations A Makovetskii 1 , S Voronin 1 , V Kober 2 , A Voronin 1 and D Tihonkih 1 1 Chelyabinsk State University, Bratiev Kashirinykh str. 129, Chelyabinsk, Russia, 454001 2 Department of Computer Science, CICESE, Carretera Ensenada-Tijuana 3918, Ensenada, B.C., Mexico, 22860 Abstract. The most popular algorithm for aligning of 3D point data is the Iterative Closest Point (ICP). This paper proposes a new algorithm for orthogonal registration of point clouds based on the point-to-plane ICP algorithm for affine transformation. At each iterative step of the algorithm, an approximation of the closed-form solution for the orthogonal transformation is derived. 1. Introduction The Iterative Closest Point (ICP) algorithm [1-5] has become the dominant method for aligning three dimensional models based purely on the geometry. For alignment it is necessary to find a geometric transformation that connects two point clouds in ℝ 3 by the best way with respect to the  2 norm. The ICP algorithm consists of two main stages: 1. Searching of corresponding points (pairs) in two clouds; 2. Minimizing the error metric (variational subproblem of the ICP). There are two basic approaches to choosing the error metric for pairs of points. Within the point-to- point approach [1], the distance between the elements of the pair in ℝ 3 is used. Within the point-to- plane approach [2] the distance between the point of the first cloud and the tangent plane to the corresponding point of the second cloud is used. The key point [6] of the ICP algorithm is the search of either an orthogonal or affine transformations, best in the sense of a quadratic metric that combines two point clouds with a given correspondence between points (the variational subproblem of the ICP algorithm). For the point-to-point metric in the case of orthogonal transformations, the solution in a closed- form was obtained by Horn [7,8]. The solution [7] is based on the use of quaternions, whereas the solution [8] uses orthogonal matrices. The solutions are linear in time with respect to the number of point pairs. The original ICP algorithm is widely used for the rigid objects registration, but it does not work well for the case of the non-rigid objects. An extension of the ICP algorithm is proposed [9], using scaling in addition to rotation and translation. A generalization of this algorithm to the case of an arbitrary affine transformation was done [10,11]. A closed-form solution to the point-to-point problem was derived [12-14]. The above mentioned approaches for solving the variational subproblem of the ICP algorithm are based on the point-to-point metric. The point-to-plane metric has been shown to perform better than the point-point metric in terms of accuracy and convergence rate [15]. A closed-form solution to the point-to-plane case for orthogonal transformations is an open problem. Instead, iterative methods