基于半群正则化与时间嵌入架构学习微分同胚的医学图像配准
Learning Diffeomorphism for Medical Image Registration with Time-Embedded Architectures Using Semigroup Regularization
把配准形变场建模为 ODE 流，用时间嵌入骨干网络加单一半群正则化替代 scaling-and-squaring 积分与多重辅助约束，可直接迁移到需要可逆形变场的医学配准、可逆光流与图像编辑中的形变建模。
原文依据 models diffeomorphisms using only a single semigroup-based regularization, eliminating explicit integration and auxiliary constraints
摘要译文
由模型翻译 · 术语统一 · 请对照原文核对关键结论微分同胚图像配准（DIR）旨在求取保持拓扑结构的变换，是医学成像中的基础问题。现有 DIR 方法依赖积分格式（如缩放-平方）与多种正则化项来保证可逆性。本文提出 SGDIR，一个连续时间配准框架，以已知的时间嵌入骨干网络为参数化，仅使用单一基于半群的正则化来建模微分同胚，从而无需显式积分与辅助约束。我们从数学上证明该形式直接学习某个底层 ODE 的流，并天然满足逆一致性与循环一致性。我们在八个 2D 与 3D 的 MR 和 CT 数据集上进行评测。在严格施加半群约束时，模型获得近乎完美的微分同胚性质，显著优于现有微分同胚方法，同时与领先的非微分同胚可变形模型相比仍具竞争力。当放宽该正则化时，同一架构即作为可变形方法运行，在配准精度上大幅超越最优的非微分同胚方法。这些结果表明，仅由本文基于半群的正则化所引导的连续时间形变建模，可构成一个统一框架，既能实现严格意义上的微分同胚映射，也能实现最优的可变形配准。
英文原文摘要 1359 字符
Diffeomorphic image registration (DIR) seeks topology-preserving transformations and is fundamental in medical imaging. Existing DIR methods rely on integration schemes (e.g., scaling-and-squaring) and multiple regularizers to enforce invertibility. We introduce **SGDIR**, a continuous-time registration framework, parameterized by known time-embedded backbones, that models diffeomorphisms using only a single semigroup-based regularization, eliminating explicit integration and auxiliary constraints. We mathematically prove that this formulation directly learns the flow of an underlying ODE, inherently enforcing inverse and cycle consistencies. We evaluate on eight 2D and 3D MR and CT datasets. Under strict semigroup enforcement, our model achieves near-perfect diffeomorphism and significantly outperforms existing diffeomorphic methods, while remaining competitive with leading non-diffeomorphic deformable models. When the regularization is relaxed, the same architecture functions as a deformable method and substantially surpasses state-of-the-art non-diffeomorphic approaches in registration accuracy. These results demonstrate that continuous-time deformation modeling, guided solely by our semigroup-based regularization, yields a unified framework capable of both rigorously diffeomorphic mapping and state-of-the-art deformable registration.