Renal pathology, as the gold standard of kidney disease diagnosis, requires doctors to analyze a serial of tissue slices stained by H\&E staining and special staining like Masson, PASM, and PAS, respectively. These special staining methods are costly, time-consuming, and hard to standardize for wide use especially in primary hospitals. Advances of supervised learning methods can virtually convert H\&E images into special staining images, but the pixel-to-pixel alignment is hard to achieve for training. As contrast, unsupervised learning methods regarding different stains as different style transferring domains can use unpaired data, but they ignore the spatial inter-domain correlations and thus decrease the trustworthiness of structural details for diagnosis. In this paper, we propose a novel virtual staining framework AGMDT to translate images into other domains by avoiding pixel-level alignment and meanwhile utilizing the correlations among adjacent tissue slices. We first build a high-quality multi-domain renal histological dataset where each specimen case comprises a series of slices stained in various ways. Based on it, the proposed framework AGMDT discovers patch-level aligned pairs across the serial slices of multi-domains through glomerulus detection and bipartite graph matching, and utilizes such correlations to supervise the end-to-end model for multi-domain staining transformation. Experimental results show that the proposed AGMDT achieves a good balance between the precise pixel-level alignment and unpaired domain transfer by exploiting correlations across multi-domain serial pathological slices, and outperforms the state-of-the-art methods in both quantitative measure and morphological details.
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