标题： 通过深度平衡模型弥合经典和基于学习的迭代配准 显示英文标题

标题： Bridging Classical and Learning-based Iterative Registration through Deep Equilibrium Models

摘要： 可变形医学图像配准传统上被表述为一个优化问题。 虽然经典方法通过迭代解决这个问题，但最近的基于学习的方法使用循环神经网络（RNN）通过在固定步骤数内展开形变场的预测来模仿这一过程。 然而，经典方法通常在足够迭代后收敛，但基于学习的展开方法缺乏理论上的收敛保证，并且在实践中表现出不稳定性。 此外，展开方法在训练时有一个实际的瓶颈：由于时间反向传播（BPTT），GPU内存使用量随着展开步骤线性增长。 为了解决理论和实践上的挑战，我们提出了DEQReg，一种基于深度平衡模型（DEQ）的新配准框架，它将配准表述为寻找平衡的问题，建立了经典优化方法和基于学习的展开方法之间的自然联系。 DEQReg保持恒定的内存使用量，从而实现理论上无限的迭代步骤。 通过在公开的脑部MRI和肺部CT数据集上的广泛评估，我们表明DEQReg可以实现具有竞争力的配准性能，同时相比最先进的展开方法显著减少了内存消耗。 我们还揭示了一个有趣的现象：当推理步骤超过训练配置时，现有展开方法的性能先略有提高，然后不可逆地下降。 相比之下，DEQReg通过其内置的平衡寻找机制实现了稳定的收敛，弥合了基于经典优化和现代基于学习的配准方法之间的差距。 显示英文摘要

摘要： Deformable medical image registration is traditionally formulated as an optimization problem. While classical methods solve this problem iteratively, recent learning-based approaches use recurrent neural networks (RNNs) to mimic this process by unrolling the prediction of deformation fields in a fixed number of steps. However, classical methods typically converge after sufficient iterations, but learning-based unrolling methods lack a theoretical convergence guarantee and show instability empirically. In addition, unrolling methods have a practical bottleneck at training time: GPU memory usage grows linearly with the unrolling steps due to backpropagation through time (BPTT). To address both theoretical and practical challenges, we propose DEQReg, a novel registration framework based on Deep Equilibrium Models (DEQ), which formulates registration as an equilibrium-seeking problem, establishing a natural connection between classical optimization and learning-based unrolling methods. DEQReg maintains constant memory usage, enabling theoretically unlimited iteration steps. Through extensive evaluation on the public brain MRI and lung CT datasets, we show that DEQReg can achieve competitive registration performance, while substantially reducing memory consumption compared to state-of-the-art unrolling methods. We also reveal an intriguing phenomenon: the performance of existing unrolling methods first increases slightly then degrades irreversibly when the inference steps go beyond the training configuration. In contrast, DEQReg achieves stable convergence with its inbuilt equilibrium-seeking mechanism, bridging the gap between classical optimization-based and modern learning-based registration methods.