CurvReg: Curvature-aware registration for multi-stain alignment of liver biopsies

Accurate alignment of multi-stain liver biopsy whole-slide images is critical for emerging computational pathology workflows, yet remains challenging due to curved biopsy geometry, non-rigid distortions, and substantial stain-dependent appearance variation. We introduce CurvReg, a curvature-aware, stain-independent registration framework designed to address these challenges by decomposing each biopsy into anatomically coherent segments for piecewise affine alignment, followed by deep learning-based deformable refinement operating directly on tissue segmentation masks rather than raw stained images. By estimating deformation from structural geometry rather than stain intensities, CurvReg enforces anatomically plausible warps and substantially improves robustness to staining, imaging, and device variability. We evaluated CurvReg across three multi-stain liver biopsy datasets and an independent public kidney biopsy dataset from the ANHIR challenge. On the internal multi-stain dataset (Dataset #1) containing hematoxylin-eosin (H&E), Masson's trichrome (MT), and CK7 sections with bile duct annotations, pre-registration mean target registration error (TRE) measured 231.5 μm (H&E-MT), 255.3 μm (MT-CK7), and 188.7 μm (H&E-CK7). After registration, TRE decreased to 51.9 μm, 57.9 μm, and 50.9 μm, respectively, with a >70% reduction across all stain pairs (p p p p 50% reduction; p p p = 0.024) while improving Dice similarity from 0.90 to 0.97 (p < 0.001). To highlight downstream clinical value, we demonstrate that MT-derived portal tract and hepatic vein segmentations can be accurately transferred onto H&E using CurvReg, enabling consistent vascular delineation within the diagnostic stain.