Liver registration by overlaying preoperative 3D models onto intraoperative 2D frames can assist surgeons in perceiving the spatial anatomy of the liver clearly for a higher surgical success rate. Existing registration methods rely heavily on anatomical landmark-based workflows, which encounter two major limitations: 1) ambiguous landmark definitions fail to provide efficient markers for registration; 2) insufficient integration of intraoperative liver visual information in shape deformation modeling. To address these challenges, in this paper, we propose a landmark-free preoperative-to-intraoperative registration framework utilizing effective self-supervised learning, termed \ourmodel. This framework transforms the conventional 3D-2D workflow into a 3D-3D registration pipeline, which is then decoupled into rigid and non-rigid registration subtasks. \ourmodel~first introduces a feature-disentangled transformer to learn robust correspondences for recovering rigid transformations. Further, a structure-regularized deformation network is designed to adjust the preoperative model to align with the intraoperative liver surface. This network captures structural correlations through geometry similarity modeling in a low-rank transformer network. To facilitate the validation of the registration performance, we also construct an in-vivo registration dataset containing liver resection videos of 21 patients, called \emph{P2I-LReg}, which contains 346 keyframes that provide a global view of the liver together with liver mask annotations and calibrated camera intrinsic parameters. Extensive experiments and user studies on both synthetic and in-vivo datasets demonstrate the superiority and potential clinical applicability of our method.