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.

本研究介绍了一种基于 3D-3D 非刚性配准的图像引导肝脏手术方法，采用有限元模型 (FEM) 作为生物力学模型，在表面匹配项中独特地整合 FEM，确保估算的变形在配准过程中保持几何一致性。此方法通过将软弹簧整合到刚度矩阵中，允许力分布于整个肝脏表面，消除了确定 FEM 中零边界条件和施加力位置的需求。我们还引入了基于力量梯度的正则化技术，强加了空间平滑性，以防止术中数据中的不规则噪音过拟合。通过加速修正梯度算法进行优化，进一步通过我们提出的确定最佳步长的方法来增强效果。该方法在自定义开发的模拟实验和两个公开数据集上进行了评估和比较，始终优于或与基准技术相当。代码和数据集将公开提供。