Boundary Constraint-free Biomechanical Model-Based Surface Matching for
  Intraoperative Liver Deformation Correction
Zixin Yang Richard Simon Kelly Merrell Cristian. A. Linte
In image-guided liver surgery, 3D-3D non-rigid registration methods play a
crucial role in estimating the mapping between the preoperative model and the
intraoperative surface represented as point clouds, addressing the challenge of
tissue deformation. Typically, these methods incorporate a biomechanical model,
represented as a finite element model (FEM), used to regularize a surface
matching term. This paper introduces a novel 3D-3D non-rigid registration
method. In contrast to the preceding techniques, our method uniquely
incorporates the FEM within the surface matching term itself, ensuring that the
estimated deformation maintains geometric consistency throughout the
registration process. Additionally, we eliminate the need to determine
zero-boundary conditions and applied force locations in the FEM. We achieve
this by integrating soft springs into the stiffness matrix and allowing forces
to be distributed across the entire liver surface. To further improve
robustness, we introduce a regularization technique focused on the gradient of
the force magnitudes. This regularization imposes spatial smoothness and helps
prevent the overfitting of irregular noise in intraoperative data. Optimization
is achieved through an accelerated proximal gradient algorithm, further
enhanced by our proposed method for determining the optimal step size. Our
method is evaluated and compared to both a learning-based method and a
traditional method that features FEM regularization using data collected on our
custom-developed phantom, as well as two publicly available datasets. Our
method consistently outperforms or is comparable to the baseline techniques.
Both the code and dataset will be made publicly available.