Objective: In medical imaging, it is often crucial to accurately assess and correct movement during image-guided therapy. Deformable image registration (DIR) consists in estimating the required spatial transformation to align a moving image with a fixed one. However, it is acknowledged that, boundary conditions applied to the solution are critical in preventing mis-registration. Despite the extensive research on registration techniques, relatively few have addressed the issue of boundary conditions in the context of medical DIR. Our aim is a step towards customizing boundary conditions to suit the diverse registration tasks at hand. Approach: We propose a generic, locally adaptive, Robin-type condition enabling to balance between Dirichlet and Neumann boundary conditions, depending on incoming/outgoing flow fields on the image boundaries. The proposed framework is entirely automatized through the determination of a reduced set of hyperparameters optimized via energy minimization. Main results: The proposed approach was tested on a mono-modal CT thorax registration task and an abdominal CT to MRI registration task. For the first task, we observed a relative improvement in terms of target registration error of up to 12% (mean 4%), compared to homogeneous Dirichlet and homogeneous Neumann. For the second task, the automatic framework provides results closed to the best achievable. Significance: This study underscores the importance of tailoring the registration problem at the image boundaries. In this research, we introduce a novel method to adapt the boundary conditions on a voxel-by-voxel basis, yielding optimized results in two distinct tasks: mono-modal CT thorax registration and abdominal CT to MRI registration. The proposed framework enables optimized boundary conditions in image registration without any a priori assumptions regarding the images or the motion.

翻译：目的：在医学影像中，精确评估和纠正图像引导治疗过程中的运动通常至关重要。可变形图像配准（DIR）旨在估计所需的空间变换，以将移动图像与固定图像对齐。然而，人们认识到，应用于解的边界条件对于防止配准错误至关重要。尽管对配准技术进行了广泛研究，但相对较少的研究涉及医学DIR中边界条件的问题。我们的目标是向定制边界条件以适应手头的各种配准任务迈出一步。方法：我们提出了一种通用的、局部自适应的Robin型条件，该条件能够根据图像边界上的流入/流出流场，在Dirichlet和Neumann边界条件之间取得平衡。通过能量最小化优化确定的一组缩减超参数，所提出的框架完全自动化。主要结果：所提出的方法在单模态CT胸部配准任务和腹部CT到MRI配准任务上进行了测试。对于第一个任务，与均匀Dirichlet和均匀Neumann条件相比，我们观察到目标配准误差相对改善了高达12%（平均4%）。对于第二个任务，自动框架提供了接近最佳可实现的结果。意义：本研究强调了在图像边界处定制配准问题的重要性。在这项研究中，我们引入了一种新颖的方法，以逐个体素的方式自适应边界条件，在两个不同的任务（单模态CT胸部配准和腹部CT到MRI配准）中取得了优化结果。所提出的框架能够在不对图像或运动进行任何先验假设的情况下，实现图像配准中的优化边界条件。