Intra-operative data captured during image-guided surgery lacks sub-surface information, where key regions of interest, such as vessels and tumors, reside. Image-to-physical registration enables the fusion of pre-operative information and intra-operative data, typically represented as a point cloud. However, this registration process struggles due to partial visibility of the intra-operative point cloud. In this research, we propose a patient-specific point cloud completion approach to assist with the registration process. Specifically, we leverage VN-OccNet to generate a complete liver surface from a partial intra-operative point cloud. The network is trained in a patient-specific manner, where simulated deformations from the pre-operative model are used to train the model. First, we conduct an in-depth analysis of VN-OccNet’s rotation-equivariant property and its effectiveness in recovering complete surfaces from partial intra-operative surfaces. Next, we integrate the completed intra-operative surface into the Go-ICP registration algorithm to demonstrate its utility in improving initial rigid registration outcomes. Our results highlight the promise of this patient-specific completion approach in mitigating the challenges posed by partial intra-operative visibility. The rotation equivariant and surface generation capabilities of VN-OccNet hold strong promise for developing robust registration frameworks for variations of the intra-operative point cloud.