Adaptive Point-Wise Error Metric Design for LiDAR Scan Matching Using Deep Neural Networks

Abstract

Iterative Closest Point (ICP) is one of the most widely used and powerful algorithms for LiDAR scan registration, yet its performance is highly dependent on the design of the underlying error metric. Con- ventional choices such as point-to-point or point-to-plane distances are often based on hand-crafted heuristics, which limits their robustness and generalization across diverse environments. To overcome this limitation, we propose a deep learning–based framework that adaptively learns point-wise error metrics for ICP. Inspired by the probabilistic formulation of Generalized ICP (GICP), which models uncertainty through point-wise covariance matrices, we directly learn anisotropic covariance represen- tations using a neural network. The network interprets geometric structures of LiDAR scan and predicts point-wise covariance matrices that parameterize the registration error metric. To enable stable training, we introduce mathematical approximations for direct supervision of loss and propose prospective drift loss that balances scale between rotation and translation component in transformation matrix. We eval- uate our approach on LiDAR odometry tasks and demonstrate that the learned error metric significantly improves registration accuracy compared to traditional ICP variants that rely on hand-crafted metrics. Furthermore, we provide empirical analysis on proposed method. Our results highlight the potential of data-driven metric design for scan matching and open new directions for integrating deep learning with classical LiDAR scan matching algorithms.