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

We present the first comparative study of two fundamentally distinct feature extraction techniques: Histogram of Oriented Gradients (HOG) and Topological Data Analysis (TDA), for medical image classification using retinal fundus images. HOG captures local texture and edge patterns through gradient orientation histograms, while TDA, using cubical persistent homology, extracts high-level topological signatures that reflect the global structure of pixel intensities. We evaluate both methods on the large APTOS dataset for two classification tasks: binary detection (normal versus diabetic retinopathy) and five-class diabetic retinopathy severity grading. From each image, we extract 26244 HOG features and 800 TDA features, using them independently to train seven classical machine learning models with 10-fold cross-validation. XGBoost achieved the best performance in both cases: 94.29 percent accuracy (HOG) and 94.18 percent (TDA) on the binary task; 74.41 percent (HOG) and 74.69 percent (TDA) on the multi-class task. Our results show that both methods offer competitive performance but encode different structural aspects of the images. This is the first work to benchmark gradient-based and topological features on retinal imagery. The techniques are interpretable, applicable to other medical imaging domains, and suitable for integration into deep learning pipelines.