[2311.16157] GeoTop: Advancing Image Classification with Geometric-Topological Analysis

Computer Science > Computer Vision and Pattern Recognition arXiv:2311.16157 (cs) [Submitted on 8 Nov 2023 (v1), last revised 4 Mar 2026 (this version, v2)] Title:GeoTop: Advancing Image Classification with Geometric-Topological Analysis Authors:Mariem Abaach, Ian Morilla View a PDF of the paper titled GeoTop: Advancing Image Classification with Geometric-Topological Analysis, by Mariem Abaach and 1 other authors View PDF HTML (experimental) Abstract:A fundamental challenge in diagnostic imaging is the phenomenon of topological equivalence, where benign and malignant structures share global topology but differ in critical geometric detail, leading to diagnostic errors in both conventional and deep learning models. We introduce GeoTop, a mathematically principled framework that unifies Topological Data Analysis (TDA) and Lipschitz-Killing Curvatures (LKCs) to resolve this ambiguity. Unlike hybrid deep learning approaches, GeoTop provides intrinsic interpretability by fusing the capacity of persistent homology to identify robust topological signatures with the precision of LKCs in quantifying local geometric features such as boundary complexity and surface regularity. The framework's clinical utility is demonstrated through its application to skin lesion classification, where it achieves a consistent accuracy improvement of 3.6% and reduces false positives and negatives by 15-18% compared to conventional single-modality methods. Crucially, GeoTop directly addresses the proble...