Semantic segmentation under domain shift remains a fundamental challenge in computer vision, particularly when labelled training data is scarce. This challenge is particularly exemplified in histopathology image analysis, where the same tissue structures must be segmented across images captured under different imaging conditions (stains), each representing a distinct visual domain. Traditional deep learning methods like UNet require extensive labels, which is both costly and time-consuming, particularly when dealing with multiple domains (or stains). To mitigate this, various unsupervised domain adaptation based methods such as UDAGAN have been proposed, which reduce the need for labels by requiring only one (source) stain to be labelled. Nonetheless, obtaining source stain labels can still be challenging. This article shows that through self-supervised pre-training -- including SimCLR, BYOL, and a novel approach, HR-CS-CO -- the performance of these segmentation methods (UNet, and UDAGAN) can be retained even with 95% fewer labels. Notably, with self-supervised pre-training and using only 5% labels, the performance drops are minimal: 5.9% for UNet and 6.2% for UDAGAN, averaged over all stains, compared to their respective fully supervised counterparts (without pre-training, using 100% labels). Furthermore, these findings are shown to generalise beyond their training distribution to public benchmark datasets. Implementations and pre-trained models are publicly available \href{https://github.com/zeeshannisar/resource-effecient-multi-stain-kidney-glomeruli-segmentation.git}{online}.

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