A Variational Screened Poisson Reconstruction for Whole-Slide Stain Normalization

Stain variability in digital pathology affects both cross-center diagnostic consistency and the robustness of downstream computational analysis. In this work, we formulate stain normalization as a variational inverse problem and derive a Screened Poisson Normalization (SPN) model from the steady-state reaction–diffusion mechanism underlying histological staining. In the CIE L*a*b* space, the model couples a gradient-domain fidelity term with a chromatic anchoring term, yielding a screened Poisson equation that preserves tissue morphology while enforcing color consistency. We prove that the corresponding variational problem is well-posed in H1(Ω) and stable with respect to perturbations of the input data. We further show that the screening term induces an intrinsic localization length 𝓁c∼λc−1/2, so that boundary perturbations decay exponentially away from tile interfaces. Based on this locality, we develop a non-overlapping tiled DCT-based spectral solver for gigapixel whole-slide images, enabling consistent tile-wise stain normalization and seamless whole-slide reassembly without heuristic boundary blending. Experiments on multi-scanner, multi-protocol, and archival-fading pathology datasets show that SPN achieves stable stain normalization with competitive chromatic alignment and strong preservation of diagnostically relevant microstructure, particularly in full-slide and tiled reconstruction settings. Supplementary experiments on synthetic pathology-like images further support the robustness of SPN under controlled color perturbations and indicate good generalization across diverse staining variations.