LCNet: A Robust and Accurate Non-Rigid 3-D Point Set Registration Approach for Image-Guided Liver Surgery

In this paper, we propose a novel unsupervised learning-based non-rigid 3D point set registration method, Learning Coherent Point Drift Network (LCNet), for image-guided liver surgery. We reformulate the classical probabilistic registration approach, i.e., Coherent Point Drift (CPD) into a learning-based paradigm. We first utilise the feature extraction module (FEM) to extract the features of two original point sets, which are robust to rigid transformation. Subsequently, we establish reliable correspondences between the point sets using the optimal transport (OT) module by leveraging both original points and learned features. Then, rather than directly regressing displacement vectors, we compute the displacements by solving the involved matrix equation in the transformation module, where the point localization noise is explicitly considered. In addition, we present three variants of the proposed approach, i.e., LCNet, LCNet-ED and LCNet-WD. Among these, LCNet outperforms the other two, demonstrating the superiority of the Chamfer loss. We have extensively evaluated LCNet on the simulated and real datasets. Under experimental conditions with the rotation angle lies in the range of $[{-}45^{\circ },45^{\circ }]$ and the translation in the range of $[{-}30 mm, 30 mm]$ , LCNet achieves the root-mean-square-error (rmse) value being 3.46 mm on the MedShapeNet dataset, while those using CPD and RoITr are 7.65 mm $(p\lt 0.001)$ and 6.71 mm $(p\lt 0.001)$ respectively. Experimental results show that LCNet exhibits significant improvements over existing state-of-the-art registration methods and shed light on its promising use in image-guided liver surgery.