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), into the strain energy term to regularize a surface matching term. We propose a 3D-3D non-rigid registration method that incorporates a modified FEM into the surface matching term. The modified FEM alleviates the need to specify boundary conditions, which is achieved by modifying the stiffness matrix of a FEM and using diagonal loading for stabilization. As a result, the modified surface matching term does not require the specification of boundary conditions or an additional strain energy term to regularize the surface matching term. Optimization is achieved through an accelerated gradient algorithm, further enhanced by our proposed method for determining the optimal step size. We evaluated our method and compared it to several state-of-the-art methods across various datasets. Our straightforward and effective approach consistently outperformed or achieved comparable performance to the state-of-the-art methods. Our code and datasets are available at https://github.com/zixinyang9109/BCF-FEM.

翻译：在图像引导的肝脏手术中，三维-三维非刚性配准方法在估计术前模型与术中点云表面之间的映射关系方面起着关键作用，以应对组织形变的挑战。通常，这些方法将生物力学模型（以有限元模型形式表示）纳入应变能项，以正则化表面匹配项。本文提出一种三维-三维非刚性配准方法，将改进的有限元模型融入表面匹配项。改进的有限元模型通过修正刚度矩阵并采用对角加载技术实现稳定化，从而无需指定边界条件。因此，改进的表面匹配项既不需要边界条件设定，也不需要额外的应变能项进行正则化。优化过程通过加速梯度算法实现，并进一步采用我们提出的最优步长确定方法进行增强。我们在多个数据集上评估了本方法，并与若干先进方法进行了比较。我们提出的简洁高效方法在各项测试中均优于或达到当前先进方法的性能水平。代码与数据集已发布于 https://github.com/zixinyang9109/BCF-FEM。