Medical images acquired from standardized protocols show consistent macroscopic or microscopic anatomical structures, and these structures consist of composable/decomposable organs and tissues, but existing self-supervised learning (SSL) methods do not appreciate such composable/decomposable structure attributes inherent to medical images. To overcome this limitation, this paper introduces a novel SSL approach called ACE to learn anatomically consistent embedding via composition and decomposition with two key branches: (1) global consistency, capturing discriminative macro-structures via extracting global features; (2) local consistency, learning fine-grained anatomical details from composable/decomposable patch features via corresponding matrix matching. Experimental results across 6 datasets 2 backbones, evaluated in few-shot learning, fine-tuning, and property analysis, show ACE's superior robustness, transferability, and clinical potential. The innovations of our ACE lie in grid-wise image cropping, leveraging the intrinsic properties of compositionality and decompositionality of medical images, bridging the semantic gap from high-level pathologies to low-level tissue anomalies, and providing a new SSL method for medical imaging.

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