Laboratoire de Mécanique des Solides, École Polytechnique/C.N.R.S./Université Paris-Saclay, Palaiseau, France; M3DISIM team, Inria / Université Paris-Saclay, Palaiseau, France.
Institute for Biomedical Engineering, University and ETH Zurich, Switzerland.
Med Image Anal. 2018 Dec;50:1-22. doi: 10.1016/j.media.2018.07.007. Epub 2018 Aug 22.
In this paper, we propose a novel continuum finite strain formulation of the equilibrium gap regularization for image registration. The equilibrium gap regularization essentially penalizes any deviation from the solution of a hyperelastic body in equilibrium with arbitrary loads prescribed at the boundary. It thus represents a regularization with strong mechanical basis, especially suited for cardiac image analysis. We describe the consistent linearization and discretization of the regularized image registration problem, in the framework of the finite elements method. The method is implemented using FEniCS & VTK, and distributed as a freely available python library. We show that the equilibrated warping method is effective and robust: regularization strength and image noise have minimal impact on motion tracking, especially when compared to strain-based regularization methods such as hyperelastic warping. We also show that equilibrated warping is able to extract main deformation features on both tagged and untagged cardiac magnetic resonance images.
在本文中，我们提出了一种新的连续有限应变平衡间隙正则化模型，用于图像配准。平衡间隙正则化本质上惩罚任何偏离与边界上任意规定的载荷处于平衡的超弹性体解的偏差。因此，它代表了一种具有强大力学基础的正则化方法，特别适合心脏图像分析。我们在有限元方法的框架内描述了正则化图像配准问题的一致线性化和离散化。该方法使用 FEniCS 和 VTK 实现，并作为一个免费的 Python 库分发。我们表明，均衡变形法是有效和鲁棒的：与基于应变的正则化方法（如超弹性变形）相比，正则化强度和图像噪声对运动跟踪的影响最小。我们还表明，均衡变形法能够在标记和未标记的心脏磁共振图像上提取主要的变形特征。
