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arXiv · 2601.11336

Beer-Lambert Autoencoder for Unsupervised Stain Representation Learning and Deconvolution in Multi-immunohistochemical Brightfield Histology Images

Mark Eastwood·Thomas McKee·Zedong Hu·Sabine Tejpar·Fayyaz Minhas
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Abstract

Separating the contributions of individual chromogenic stains in RGB histology whole slide images (WSIs) is essential for stain normalization, quantitative assessment of marker expression, and cell-level readouts in immunohistochemistry (IHC). Classical Beer-Lambert (BL) color deconvolution is well-established for two- or three-stain settings, but becomes under-determined and unstable for multiplex IHC (mIHC) with K>3 chromogens. We present a simple, data-driven encoder-decoder architecture that learns cohort-specific stain characteristics for mIHC RGB WSIs and yields crisp, well-separated per-stain concentration maps. The encoder is a compact U-Net that predicts K nonnegative concentration channels; the decoder is a differentiable BL forward model with a learnable stain matrix initialized from typical chromogen hues. Training is unsupervised with a perceptual reconstruction objective augmented by loss terms that discourage unnecessary stain mixing. On a colorectal mIHC panel comprising 5 stains (H, CDX2, MUC2, MUC5, CD8) we show excellent RGB reconstruction, and significantly reduced inter-channel bleed-through compared with matrix-based deconvolution. Code and model are available at https://github.com/measty/StainQuant.git.

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Mark Eastwood, Thomas McKee, Zedong Hu, Sabine Tejpar, Fayyaz Minhas. 2026-01-16. Beer-Lambert Autoencoder for Unsupervised Stain Representation Learning and Deconvolution in Multi-immunohistochemical Brightfield Histology Images. https://arxiv.org/abs/2601.11336

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