3D Point Cloud Registration Using Iterative Closest Point Algorithm with Quaternion-Based Rotation Estimation

In this article, we explore the implementation of the Iterative Closest Point (ICP) algorithm for 3D point cloud registration, coupled with quaternion-based rotation estimation. The ICP algorithm is a widely-used computational method for aligning point cloud datasets by iteratively finding closest point correspondences between two point clouds. The algorithm typically follows these implementation steps: point selection, correspondence matching, transformation estimation, and error minimization through iterative refinement. For rotation computation, we employ quaternions as they provide superior numerical stability and avoid gimbal lock issues compared to Euler angles. The quaternion approach represents 3D rotations using four-dimensional complex numbers, enabling more accurate and efficient rotation calculations. In practical implementation, the quaternion-based rotation estimation involves constructing a covariance matrix from corresponding point pairs and performing eigenvalue decomposition to extract the optimal rotation quaternion. Through the combination of these two methodologies, we achieve precise 3D point cloud alignment with robust rotation estimation. The implementation typically includes key functions such as nearest_neighbor_search() for correspondence establishment, compute_transformation() for estimating rigid transformation parameters, and apply_transform() for updating point positions during iterative optimization.