Liver is an incompressible organ that maintains its volume during the respiration-induced deformation. Quantifying this deformation with the incompressible constraint is significant for liver tracking. The constraint can be accomplished with retaining the divergence-free field obtained by the deformation decomposition. However, the decomposition process is time-consuming, and the removal of non-divergence-free field weakens the deformation. In this study, a divergence-free fitting-based registration method is proposed to quantify the incompressible deformation rapidly and accurately. First, the deformation to be estimated is mapped to the velocity in a diffeomorphic space. Then, this velocity is decomposed by a fast Fourier-based Hodge-Helmholtz decomposition to obtain the divergence-free, curl-free, and harmonic fields. The curl-free field is replaced and fitted by the obtained harmonic field with a translation field to generate a new divergence-free velocity. By optimizing this velocity, the final incompressible deformation is obtained. Moreover, a deep learning framework (DLF) is constructed to accelerate the incompressible deformation quantification. An incompressible respiratory motion model is built for the DLF by using the proposed registration method and is then used to augment the training data. An encoder-decoder network is introduced to learn appearance-velocity correlation at patch scale. In the experiment, we compare the proposed registration with three state-of-the-art methods. The results show that the proposed method can accurately achieve the incompressible registration of liver with a mean liver overlap ratio of 95.33%. Moreover, the time consumed by DLF is nearly 15 times shorter than that by other methods.

中文翻译：

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基于无发散拟合的肝脏不可压缩变形量化

肝脏是不可压缩的器官，在呼吸引起的变形过程中保持其体积。用不可压缩约束量化这种变形对于肝脏跟踪很重要。约束可以通过保留通过变形分解获得的无发散场来实现。然而，分解过程耗时，去除非发散自由场削弱了变形。在这项研究中，提出了一种基于无发散拟合的配准方法来快速准确地量化不可压缩变形。首先，要估计的变形被映射到微分同胚空间中的速度。然后，通过基于快速傅立叶的 Hodge-Helmholtz 分解对该速度进行分解，以获得无发散、无卷曲和谐波场。无旋度场被具有平移场的获得的谐波场替换和拟合，以产生新的无发散速度。通过优化这个速度，得到最终的不可压缩变形。此外，构建了一个深度学习框架（DLF）来加速不可压缩变形的量化。使用所提出的配准方法为 DLF 建立了不可压缩的呼吸运动模型，然后用于扩充训练数据。引入了编码器-解码器网络以在补丁尺度上学习外观速度相关性。在实验中，我们将建议的配准与三种最先进的方法进行比较。结果表明，该方法能够准确实现肝脏不可压缩配准，平均肝脏重叠率为95.33%。而且，