HYED-Net: unified hierarchical feature refinement for co-registered nuclei segmentation and virtual IHC-to-mpIF staining

Achieving precise nuclei delineation from routine immunohistochemistry (IHC) images remains challenging because of staining variability and densely touching cells. In this work, we propose HYED-Net, a unified framework that jointly synthesizes co-registered virtual staining channels and predicts nuclei segmentation. The generated staining channels are used as auxiliary features within a segmentation-oriented refinement pathway. The segmentation head combines an Evidence-weighted Dirichlet Gate (ED-Gate) for dual-branch feature fusion, SS2D spatial mixing at selected encoder and decoder stages, and HyperKernel Skip Injection (HKSI) for auxiliary-conditioned depthwise skip modulation. Across three random seeds, HYED-Net obtains a Dice coefficient of 0.758± 0.005 and an AJI of 0.588± 0.010 on BCData, and a Dice coefficient of 0.764± 0.002 and an AJI of 0.470± 0.001 on DeepLIIF. Together, these results demonstrate stable in-domain performance and support the feasibility of joint virtual staining and nuclei segmentation within a unified feature-refinement framework.