Regularized variational functional use a rough alignment for point clouds registration

Abstract

Alignment two point clouds means finding the orthogonal or affine transformation in three-dimensional space that maximizes the consistent overlap between two clouds. The ICP (Iterative Closest Points) algorithm is the most known technique of the point clouds registration based on the exclusively geometric characteristics. The ICP algorithm consists of the following iteratively applied main steps: determine the correspondence between the points of the two clouds; minimize error metrics (variational subproblem of the ICP algorithm). The key element of the ICP algorithm is the search for an orthogonal or affine transformation, which is the best in sense of a metric combining two clouds of points with a given correspondence between the points. The correspondence between point clouds in real applications is far from ideal. The bad correspondence significantly reduces the probability to obtain a good answer for orthogonal variants of the variational problem. Thus, the probability of obtaining an acceptable transformation as a result of the ICP algorithm with poor correspondence is the comparative criterion for different types of variational problems. In this paper, we propose a regularized variant of the ICP variational problem use a rough point clouds alignment that improved convergence frequency in the case of poor correspondence between point clouds. The proposed modified approach essentially increases the performance of the algorithm. Computational experiments show that the proposed point clouds alignment approach calculates true transformation for almost all synthetic 3D models for any relative placement of the point clouds.