  In the field of medical image segmentation, variant models based on
Convolutional Neural Networks (CNNs) and Visual Transformers (ViTs) as the base
modules have been very widely developed and applied. However, CNNs are often
limited in their ability to deal with long sequences of information, while the
low sensitivity of ViTs to local feature information and the problem of
secondary computational complexity limit their development. Recently, the
emergence of state-space models (SSMs), especially 2D-selective-scan (SS2D),
has had an impact on the longtime dominance of traditional CNNs and ViTs as the
foundational modules of visual neural networks. In this paper, we extend the
adaptability of SS2D by proposing a High-order Vision Mamba UNet (H-vmunet) for
medical image segmentation. Among them, the proposed High-order
2D-selective-scan (H-SS2D) progressively reduces the introduction of redundant
information during SS2D operations through higher-order interactions. In
addition, the proposed Local-SS2D module improves the learning ability of local
features of SS2D at each order of interaction. We conducted comparison and
ablation experiments on three publicly available medical image datasets
(ISIC2017, Spleen, and CVC-ClinicDB), and the results all demonstrate the
strong competitiveness of H-vmunet in medical image segmentation tasks. The
code is available from https://github.com/wurenkai/H-vmunet .
