URICA: A Uniformity Region Affine Identifier Capture Algorithm for Arbitrary Region Retrieval in Pathology Images

Whole slide image (WSI) region retrieval remains an open challenge in computational pathology, as existing methods struggle to represent and preserve information of all possible regions. Current approaches that rely on fixed-size patches or slide-level retrieval are misaligned with real clinical workflows, where pathologists often examine WSI regions of arbitrary orientations and sizes rather than predefined patches or slides. In this work, we redefine WSI retrieval as a semantically optimal matching problem between arbitrary regions under spatial transformations, which necessitates a region-level representation that maintains semantic consistency. To fulfill this requirement, we introduce semantic tessellation, which organizes patch units into flexible, geometry-aware region descriptors. Building on this representation, we develop the affine identifier, a semantic signature that enables rotation- and scale-consistent region matching. We further derive theoretical bounds between the tessellation-derived descriptors and the ideal pixel-level semantic mask objective, showing that they reliably approximate mask-based region similarity. Together, these components form URICA, a theoretically grounded algorithm for robust WSI region retrieval. Experiments on large public datasets demonstrate that URICA achieves strong and consistent performance across diverse WSI retrieval tasks.