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Accurate medical imaging segmentation is critical for precise and effectivemedical interventions. However, despite the success of convolutional neuralnetworks (CNNs) in medical image segmentation, they still face challenges inhandling fine-scale features and variations in image scales. These challengesare particularly evident in complex and challenging segmentation tasks, such asthe BraTS multi-label brain tumor segmentation challenge. In this task,accurately segmenting the various tumor sub-components, which varysignificantly in size and shape, remains a significant challenge, with evenstate-of-the-art methods producing substantial errors. Therefore, we proposetwo architectures, FMG-Net and W-Net, that incorporate the principles ofgeometric multigrid methods for solving linear systems of equations into CNNsto address these challenges. Our experiments on the BraTS 2020 datasetdemonstrate that both FMG-Net and W-Net outperform the widely used U-Netarchitecture regarding tumor subcomponent segmentation accuracy and trainingefficiency. These findings highlight the potential of incorporating theprinciples of multigrid methods into CNNs to improve the accuracy andefficiency of medical imaging segmentation.

FMG-Net and W-Net: Multigrid Inspired Deep Learning Architectures For Medical Imaging Segmentation