Integrating Ordinary Differential Equations (ODEs) with U-shaped neural networks has emerged as a novel direction in medical image segmentation. Current networks predominantly employ discretization methods incorporating ODEs. However, these methods face inherent trade-offs between model compactness, computational accuracy, and efficiency. Continuous ODE solutions were rarely studied because they face three limitations: high computational costs, long training time, and poor generalization ability. To address these limitations, we propose an innovative Continuous Neural Memory ODE UNet (CNM-UNet), which replaces all hierarchical decoder layers in vanilla UNet with a single Continuous Neural Memory ODEs Block (CNM-Block) decoder, significantly reducing computation costs and improving training efficiency. CNM-UNet leverages ODEs' dynamic properties to establish continuous temporal feature extraction. For alleviating the generalization problem, a DUal SElf-updated (DUSE) strategy based on test-time adaptation principles is introduced to enhance cross-domain generalization. Experimental results demonstrate CNM-UNet's comprehensive advantages in computational capacity, convergence speed, and cross-domain adaptability, offering new insights for practical deployment of continuous ODE methodologies for medical image segmentation.

Medical image segmentation is a critical task in computer vision, with UNet serving as a milestone architecture. The typical component of UNet family is the skip connection, however, their skip connections face two significant limitations: (1) they lack effective interaction between features at different scales, and (2) they rely on simple concatenation or addition operations, which constrain efficient information integration. While recent improvements to UNet have focused on enhancing encoder and decoder capabilities, these limitations remain overlooked. To overcome these challenges, we propose a novel multi-scale feature fusion method that reimagines the UNet decoding process as solving an initial value problem (IVP), treating skip connections as discrete nodes. By leveraging principles from the linear multistep method, we propose an adaptive ordinary differential equation method to enable effective multi-scale feature fusion. Our approach is independent of the encoder and decoder architectures, making it adaptable to various U-Net-like networks. Experiments on ACDC, KiTS2023, MSD brain tumor, and ISIC2017/2018 skin lesion segmentation datasets demonstrate improved feature utilization, reduced network parameters, and maintained high performance. The code is available at https://github.com/nayutayuki/FuseUNet.

With the rapid advancement of deep learning, computer-aided diagnosis and treatment have become crucial in medicine. UNet is a widely used architecture for medical image segmentation, and various methods for improving UNet have been extensively explored. One popular approach is incorporating transformers, though their quadratic computational complexity poses challenges. Recently, State-Space Models (SSMs), exemplified by Mamba, have gained significant attention as a promising alternative due to their linear computational complexity. Another approach, neural memory Ordinary Differential Equations (nmODEs), exhibits similar principles and achieves good results. In this paper, we explore the respective strengths and weaknesses of nmODEs and SSMs and propose a novel architecture, the nmSSM decoder, which combines the advantages of both approaches. This architecture possesses powerful nonlinear representation capabilities while retaining the ability to preserve input and process global information. We construct nmSSM-UNet using the nmSSM decoder and conduct comprehensive experiments on the PH2, ISIC2018, and BU-COCO datasets to validate its effectiveness in medical image segmentation. The results demonstrate the promising application value of nmSSM-UNet. Additionally, we conducted ablation experiments to verify the effectiveness of our proposed improvements on SSMs and nmODEs.