Unsupervised Liver Deformation Correction Network Using Optimal Transport for Image-Guided Liver Surgery

Abstract

In this paper, we propose a novel unsupervised intraoperative liver deformation correction method, called Learning Coherent point drift Network (LCNet), for image-guided liver surgery (IGLS). We first estimate the correspondences between the preoperative and intraoperative point sets in the optimal transport (OT) module by leveraging both original points and extracted features. Afterwards, we compute the point-wise displacement vector by solving the involved matrix equation in the Transformation module, where the point localisation noise is explicitly considered and modeled. Additionally, we present three variants of the proposed approach, i.e., LCNet, LCNet-ED and LCNet-WD, where better registration performances of LCNet against the other two demonstrate the superiority of the utilised Chamfer loss. We have extensively evaluated LCNet on the MedShapeNet dataset consisting of 615 different liver shapes of real patients, and the 3Dircadb dataset comprising 20 liver models of real patients. Extensive experimental results under different deformation and noise magnitudes demonstrate that LCNet outperforms existing state-of-the-art registration algorithms and holds significant application potential in IGLS. For example, when the overlapping ratio between the preoperative and intraoperative point sets is 25%, the deformation magnitude is 8 mm, the maximum point localization noise magnitude is 2 mm and the rotation angle lies in the range of [−45°, 45°], LCNet achieves a root-mean-square error (RMSE) value being 3.21 mm on MedShapeNet dataset, significantly outperforming those of Lepard and RoITr being 5.41 mm (p < 0.001) and 4.90 mm (p < 0.001) respectively.