  The surgical environment imposes unique challenges to the intraoperative
registration of organ shapes to their preoperatively-imaged geometry.
Biomechanical model-based registration remains popular, while deep learning
solutions remain limited due to the sparsity and variability of intraoperative
measurements and the limited ground-truth deformation of an organ that can be
obtained during the surgery. In this paper, we propose a novel \textit{hybrid}
registration approach that leverage a linearized iterative boundary
reconstruction (LIBR) method based on linear elastic biomechanics, and use deep
neural networks to learn its residual to the ground-truth deformation (LIBR+).
We further formulate a dual-branch spline-residual graph convolutional neural
network (SR-GCN) to assimilate information from sparse and variable
intraoperative measurements and effectively propagate it through the geometry
of the 3D organ. Experiments on a large intraoperative liver registration
dataset demonstrated the consistent improvements achieved by LIBR+ in
comparison to existing rigid, biomechnical model-based non-rigid, and
deep-learning based non-rigid approaches to intraoperative liver registration.
