There has been remarkable progress in the application of deep learning to 3D point cloud registration in recent years. Despite their success, these approaches tend to have poor generalization properties when attempting to align unseen point clouds at test time. PointNetLK has proven the exception to this rule by leveraging the intrinsic generalization properties of the Lucas & Kanade (LK) image alignment algorithm to point cloud registration. The approach relies heavily upon the estimation of a gradient through finite differentiation -- a strategy that is inherently ill-conditioned and highly sensitive to the step-size choice. To avoid these problems, we propose a deterministic PointNetLK method that uses analytical gradients. We also develop several strategies to improve large-volume point cloud processing. We compare our approach to canonical PointNetLK and other state-of-the-art methods and demonstrate how our approach provides accurate, reliable registration with high fidelity. Extended experiments on noisy, sparse, and partial point clouds depict the utility of our approach for many real-world scenarios. Further, the decomposition of the Jacobian matrix affords the reuse of feature embeddings for alternate warp functions.
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