Intra-fraction motions are commonly estimated using deformable image registration (DIR). However, the conventional voxel-based methods can compromise accuracy, especially for large changes, affecting processes like dose accumulation and 4D dose optimization. Therefore, we introduce a novel way of representing the registration process, conceptualizing it as a continuous flow in both spatial and temporal realms. This innovative model effectively addresses the inherent limitations of voxel-based discretization, while offering a robust solution to challenges posed by large deformations. Most significantly, the sliding boundary problem, a challenge for classical methods like B-splines [1], can be solved effectively.
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