Adaptive local boundary conditions to improve deformable image registration.

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 for DIR methods, boundary conditions applied to the solution are critical in preventing mis-registration. This poses an issue particularly when areas of interest are located near the image border. 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 analyze the behavior of two typical global boundary conditions: homogeneous Dirichlet and homogeneous Neumann. 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 computed tomography (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 close 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 prior assumptions regarding the images or the motion.