Abstract
The registration of point clouds in a three-dimensional space is an important task in many areas of computer vision, including robotics and autonomous driving. The purpose of registration is to find a rigid geometric transformation to align two point clouds. The registration problem can be affected by noise and partiality (two point clouds only have a partial overlap). The Iterative Closed Point (ICP) algorithm is a common method for solving the registration problem. Recently, artificial neural networks have begun to be used in the registration of point clouds. The drawback of ICP and other registration algorithms is the possible convergence to a local minimum. Thus, an important characteristic of a registration algorithm is the ability to avoid local minima. In this paper, we propose an ICP-type registration algorithm (λ-ICP) that uses a multiparameter functional (λ-functional). The proposed λ-ICP algorithm generalizes the NICP algorithm (normal ICP). The application of the λ-functional requires a consistent choice of the eigenvectors of the covariance matrix of two point clouds. The paper also proposes an algorithm for choosing the directions of eigenvectors. The performance of the proposed λ-ICP algorithm is compared with that of a standard point-to-point ICP and neural network Deep Closest Points (DCP).
Highlights
IonescuPoint cloud registration is a key element in the reconstruction of a 3D spatial environment for robots and sensors
The analysis shows that the NICP yields better results and a higher robustness compared to the state-of-the-art methods [4]
We show that the proposed λ-iterative closest points algorithm (ICP) algorithm converges well to a suitable orthogonal transformation for a wide class of regularization tasks
Summary
Point cloud registration is a key element in the reconstruction of a 3D spatial environment for robots and sensors. Closed-form solutions to the point-to-point problem in the class of orthogonal transformations are obtained [9,10,11]. A closed-form solution to the NICP variational problem is proposed [5]. Gauss–Newton iterative method [4] and the closed-form solution to the NICP variational problem are obtained [5]. These three steps provide a closed-form solution to the variational problem of the λ-ICP algorithm that approximates the exact solution. We propose an algorithm for reorienting eigenvectors that are computed in a neighborhood within a point cloud. The paper is organized as follows: In Section 2, we propose a closed-form approximation of the exact solution to the variation problem with λ-functional.
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