Filter-based Tchebichef moment analysis for whole slide image reconstruction

Abstract

In digital pathology, accurate diagnosis and prognosis critically depend on robust feature representation of Whole Slide Images (WSIs). While deep learning offers powerful solutions, its “black box” nature presents significant challenges to clinical interpretability and widespread adoption. Handcrafted features offer interpretability, yet orthogonal moments, particularly Tchebichef moments (TMs), remain underexplored for WSI analysis. This study introduces TMs as interpretable, efficient, and scalable handcrafted descriptors for WSIs, alongside a novel two-dimensional digital filter architecture designed to enhance numerical stability and hardware compatibility during TM computation. We conducted a comprehensive reconstruction analysis using H&E-stained WSIs from the MIDOG++ dataset to evaluate TM effectiveness. Our results demonstrate that lower-order TMs accurately reconstruct both square and rectangular WSI patches, with performance stabilising beyond a threshold moment order, confirmed by SNIRE, SSIM, and BRISQUE metrics, highlighting their capacity to retain structural fidelity. Furthermore, our analysis reveals significant computational efficiency gains through the use of pre-computed polynomials. These findings establish TMs as highly promising, interpretable, and scalable feature descriptors, offering a robust alternative for computational pathology applications that prioritise both accuracy and transparency.