“GeoTop: Geometric-topological fusion for interpretable image classification” (2026), by Mariem Abaach et al. Computer Science research paper. Original abstract below, unchanged. A free PDF is available.

GeoTop: Geometric-topological fusion for interpretable image classification

Mariem Abaach, Ian Morilla · November 4, 2026 · Computer Science

Abstract

Persistent homology cannot separate two images whose intensity filtrations are related by a homeomorphism, even when their excursion sets differ in area or perimeter. We study GeoTop , an interpretable 184-dimensional feature vector that concatenates 64 cubical persistent-homology descriptors with 120 summaries of Lipschitz–Killing curvature (LKC) curves—the area, perimeter and Euler characteristic of the excursion sets—and classifies it with a random forest. A short lemma states when the area and perimeter curves separate images that persistent homology cannot; this is an identifiability result, not a stability or performance guarantee. On a public skin-lesion dataset, GeoTop reached an accuracy of 0.874 (95% CI 0.847–0.900) and an AUROC of 0.945 (0.927–0.961), matching a fine-tuned ResNet-18 and ViT-Base/16 and outperforming HOG features with a support vector machine. Notably, none of six alternative fusion strategies differed significantly from plain concatenation, making the simple concatenation competitive on this dataset. That said, It is not shown to be optimal—an HSV re-extraction of the same pipeline was more accurate on the same split (0.908)—and the fused representation has no formal stability bound. All skin-lesion results come from one public source without patient or lesion identifiers: patient-level separation could not be verified, a near-duplicate-image proxy is the only leakage control, and no external validation was performed, so the results are not clinically validated. We also report a synthetic benchmark of topology-matched image pairs and a preliminary application to plant signalling peptides.

Free PDF DOI: 10.1016/j.array.2026.101417