RiTex: Harmonization of Radiomic Features Based on Riemannian Geometry

Batch effects arising from variations in hardware, acquisition protocols, and reconstruction parameters present a critical challenge in radiomics, limiting the generalizability of models across multicentre studies. Existing harmonization methods, such as ComBat, CovBat, z-score normalization, and Generative Adversarial Networks, exhibit significant limitations when applied to high-dimensional radiomic data. ComBat assumes a linear feature space and tends to leave residual center-specific information recoverable by downstream classifiers. This paper introduces RiTex (Riemannian Texture Harmonization), a framework that solves a generalized eigenvalue problem between class-aware biological scatter and Ledoit-Wolf-regularized per-batch covariances, with the SPD-manifold Fréchet mean used as a principled averaging step. We evaluate RiTex on the 50-dataset radMLBench benchmark and on a new four-center head-and-neck benchmark with known center labels (n = 380 patients, k = 4 centers from TCIA: HGJ, MDACC, Maastro, QIN). On radMLBench, RiTex reduces the batch auto-detection AUC in 48/50 (96%) datasets, 42/50 (84%) reductions remain significant after Benjamini-Hochberg correction; the mean Batch AUC reduction is ΔBatch = -0.365 (95% bootstrap CI [-0.418, -0.312]), with no significant degradation in biological AUC (mean ΔBio = +0.018, 95% CI [-0.011, +0.047]). On the H&N benchmark with real center labels, RiTex reduces the Batch AUC from 0.74 to 0.59, while ComBat and CovBat leave it at ≈0.98. A component-wise ablation shows that the dominant source of empirical performance is the GEVD step, together with Ledoit-Wolf shrinkage. The SPD Fréchet mean acts as a theoretical scaffold with a negligible empirical contribution (ΔBatch AUC = -0.014 vs. arithmetic mean).