Donle, L.; Phillips, M.; Gaber, F.; Ramesh, S.; Sacco, M.; Hautaniemi, S.; Virtanen, A.; Bressem, K.; Adams, L.; Goon, K.; Nevins, E.; Robinett, R. A.; Kochanny, S.; Hassan, S.; Dolezal, J.; Pearson, A. T.; Lengyel, E.

Medical foundation models compress biomedical data into embeddings that support diverse downstream clinical tasks. However, successful model deployment is hampered by performance degradation on external data. It is recognized that embeddings capture acquisition signatures, such as hardware and technical differences, in addition to biology. Effective harmonization must remove the acquisition signature while preserving biological signals, a trade-off that current methods fail to balance adequately. Input-level normalization fails to eliminate acquisition signatures from embeddings, whereas embedding-level methods adjust features in an untargeted manner. We present FEATMAP, a harmonization approach that models acquisition signatures as geometric distortions between manifolds of similarly arranged embeddings. Using paired data that isolate the effect of acquisition signatures, FEATMAP fits a single global affine transformation per foundation model to correct acquisition signatures directly in the embedding space. This targeted, reusable correction aims to preserve biological and demographic variation while harmonizing across acquisition signatures. Across scanner and foundation-model harmonization in digital pathology and field-strength harmonization in brain MRI, FEATMAP improves cross-condition embedding similarity, reduces performance gaps without retraining, and suggests potential for the alignment of disparate embedding spaces.