  Accurate medical imaging segmentation is critical for precise and effective
medical interventions. However, despite the success of convolutional neural
networks (CNNs) in medical image segmentation, they still face challenges in
handling fine-scale features and variations in image scales. These challenges
are particularly evident in complex and challenging segmentation tasks, such as
the BraTS multi-label brain tumor segmentation challenge. In this task,
accurately segmenting the various tumor sub-components, which vary
significantly in size and shape, remains a significant challenge, with even
state-of-the-art methods producing substantial errors. Therefore, we propose
two architectures, FMG-Net and W-Net, that incorporate the principles of
geometric multigrid methods for solving linear systems of equations into CNNs
to address these challenges. Our experiments on the BraTS 2020 dataset
demonstrate that both FMG-Net and W-Net outperform the widely used U-Net
architecture regarding tumor subcomponent segmentation accuracy and training
efficiency. These findings highlight the potential of incorporating the
principles of multigrid methods into CNNs to improve the accuracy and
efficiency of medical imaging segmentation.
