GeoTop: Advancing Image Classification with Geometric-Topological Analysis

Researchers Mariem Abaach and Ian Morilla have introduced GeoTop, a novel framework that addresses a critical challenge in medical imaging: topological equivalence, where benign and malignant structures share similar global shapes but differ in crucial geometric details. This ambiguity leads to diagnostic errors in both conventional methods and deep learning models. GeoTop provides a mathematically principled solution by unifying Topological Data Analysis (TDA), which identifies robust topological signatures through persistent homology, with Lipschitz-Killing Curvatures (LKCs), which precisely quantify local geometric features like boundary complexity and surface regularity. This fusion creates an interpretable alternative to black-box deep learning approaches.

The framework's clinical utility was demonstrated in skin lesion classification, where it achieved a consistent 3.6% accuracy improvement and reduced false positives and negatives by 15-18% compared to conventional single-modality methods. Beyond performance metrics, GeoTop offers inherent mathematical interpretability through persistence diagrams and curvature-based descriptors, computational efficiency (processing 224x224 pixel images in ≤0.5 seconds), and demonstrated generalizability to molecular-level data. By providing both theoretical guarantees via formal lemmas and empirical validation through controlled benchmarks, GeoTop represents a significant advancement toward more reliable, transparent, and mathematically grounded diagnostic AI systems.