Abstract. Purpose: Deformable registration problems are conventionally posed in a regularized optimization framework, where balance between fidelity and prescribed regularization usually needs to be tuned for each case. Even so, using a single weight to control regularization strength may be insufficient to reflect spatially variant tissue properties and limit registration performance. In this study, we proposed to incorporate a spatially variant deformation prior into image registration framework using a statistical generative model. Approach: A generator network is trained in an unsupervised setting to maximize the likelihood of observing the moving and fixed image pairs, using an alternating back-propagation approach. The trained model imposes constraints on deformation and serves as an effective low-dimensional deformation parametrization. During registration, optimization is performed over this learned parametrization, eliminating the need for explicit regularization and tuning. The proposed method was tested against SimpleElastix, DIRNet, and Voxelmorph. Results: Experiments with synthetic images and simulated CTs showed that our method yielded registration errors significantly lower than SimpleElastix and DIRNet. Experiments with cardiac magnetic resonance images showed that the method encouraged physical and physiological feasibility of deformation. Evaluation with left ventricle contours showed that our method achieved a dice of (0.93 ± 0.03) with significant improvement over all SimpleElastix options, DIRNet, and VoxelMorph. Mean average surface distance was on millimeter level, comparable to the best SimpleElastix setting. The average 3D registration time was 12.78 s, faster than 24.70 s in SimpleElastix. Conclusions: The learned implicit parametrization could be an efficacious alternative to regularized B-spline model, more flexible in admitting spatial heterogeneity.

中文翻译：

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使用统计生成模型对可变形图像配准施加隐式可行性约束

摘要。目的：可变形配准问题通常在正则化优化框架中提出，其中保真度和规定正则化之间的平衡通常需要针对每种情况进行调整。即便如此，使用单个权重来控制正则化强度可能不足以反映空间变化的组织特性并限制配准性能。在这项研究中，我们建议使用统计生成模型将先验空间变化变形合并到图像配准框架中。方法：在无监督环境中训练生成器网络，以使用交替反向传播方法最大化观察移动和固定图像对的可能性。训练后的模型对变形施加约束，并用作有效的低维变形参数化。在注册过程中，对这个学习的参数化进行优化，消除了显式正则化和调整的需要。所提出的方法针对 SimpleElastix、DIRNet 和 Voxelmorph 进行了测试。结果：合成图像和模拟 CT 的实验表明，我们的方法产生的配准误差明显低于 SimpleElastix 和 DIRNet。心脏磁共振图像实验表明，该方法促进了变形的物理和生理可行性。对左心室轮廓的评估表明，我们的方法取得了 (0.93 ± 0.03) 的骰子，并且比所有 SimpleElastix 选项、DIRNet 和 VoxelMorph 都有显着改进。平均表面距离为毫米级别，可与最佳 SimpleElastix 设置相媲美。平均 3D 配准时间为 12.78 秒，在 SimpleElastix 中比 24.70 秒快。结论：学习到的隐式参数化可能是正则化 B 样条模型的有效替代方案，在承认空间异质性方面更灵活。