Counting by Points: Density-Guided Weakly-Supervised Nuclei Segmentation in Histopathological Images

Nuclei instance segmentation in histopathological images is pivotal for cancer diagnosis, yet heavily reliant on costly pixel-level annotations. While point-supervised methods reduce annotation burdens, existing approaches struggle to reconstruct accurate nuclear boundaries and fail to leverage spatial distribution cues, particularly in dense or irregularly structured tissues. This paper presents DeNSe, a novel density-guided weakly-supervised framework that integrates nuclei counting with instance segmentation to address these limitations. Unlike conventional methods, DeNSe introduces a multi-task learning architecture, combining density regression and segmentation through two key innovations: (1) a distribution-aware alignment module based on optimal transport theory, which harmonizes feature representations between density maps and segmentation masks to enhance instance differentiation; and (2) a morphology-aware refinement strategy that dynamically adjusts pseudo-labels using density-guided confidence scores, mitigating errors from coarse annotations. By formulating counting as a density regression task, DeNSe captures global nuclei distribution, enabling robust segmentation in densely packed regions. Extensive experiments on three benchmarks demonstrate state-of-the-art performance, achieving significant improvements across various metrics over existing methods. Notably, DeNSe exhibits strong robustness to annotation offsets and generalizes across diverse tissue types, offering a cost-effective and scalable tool for clinical applications. The code is available at https://github.com/lingboboo/DENSE.