Topological Signatures vs. Gradient Histograms: A Comparative Study for Medical Image Classification

This work presents a comparative evaluation of two fundamentally different feature extraction paradigms--Histogram of Oriented Gradients (HOG) and Topological Data Analysis (TDA)--for medical image classification, with a focus on retinal fundus imagery. HOG captures local structural information by modeling gradient orientation distributions within spatial regions, effectively encoding texture and edge patterns. In contrast, TDA, implemented through cubical persistent homology, extracts global topological descriptors that characterize shape, connectivity, and intensity-based structure across images. We evaluate both approaches on the publicly available APTOS retinal fundus dataset for two classification tasks: binary classification (normal vs. diabetic retinopathy (DR)) and five-class DR severity grading. From each image, 26,244 HOG features and 800 TDA features are extracted and independently used to train seven classical machine learning models, including logistic regression, random forest, XGBoost, support vector machines, decision trees, k-nearest neighbors, and Extra Trees, using 10-fold cross-validation. Experimental results show that XGBoost achieves the best performance across both feature types. For binary classification, accuracies of 94.29% (HOG) and 94.18% (TDA) are obtained, while multi-class classification yields accuracies of 74.41% and 74.69%, respectively. These results demonstrate that gradient-based and topological features provide complementary representations of retinal image structure and highlight the potential of integrating both approaches for interpretable and robust medical image classification.