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

arXiv: https://arxiv.org/abs/2507.03006 · HTML: https://mlsanity.com/paper/2507.03006/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- Builds on 12 of its 42 references that are in the map.
- First posted on arXiv 2 Jul 2025.

## Builds on (most cited first, 12 of 12)

- [A Survey on Deep Learning in Medical Image Analysis](https://mlsanity.com/paper/1702.05747/) (2017)
- [An introduction to Topological Data Analysis: fundamental and practical aspects for data scientists](https://mlsanity.com/paper/1710.04019/) (2017)
- [An overview of deep learning in medical imaging focusing on MRI](https://mlsanity.com/paper/1811.10052/) (2018)
- [A roadmap for the computation of persistent homology](https://mlsanity.com/paper/1506.08903/) (2015)
- [A Stable Multi-Scale Kernel for Topological Machine Learning](https://mlsanity.com/paper/1412.6821/) (2014)
- [giotto-tda: A Topological Data Analysis Toolkit for Machine Learning and Data Exploration](https://mlsanity.com/paper/2004.02551/) (2020)
- [Fast and Accurate Tumor Segmentation of Histology Images using Persistent Homology and Deep Convolutional Features](https://mlsanity.com/paper/1805.03699/) (2018)
- [Uncovering the Topology of Time-Varying fMRI Data using Cubical Persistence](https://mlsanity.com/paper/2006.07882/) (2020)
- [Functional Summaries of Persistence Diagrams](https://mlsanity.com/paper/1804.01618/) (2018)
- [Topological Data Analysis](https://mlsanity.com/paper/1609.08227/) (2016)
- [Blended Multi-Modal Deep ConvNet Features for Diabetic Retinopathy Severity Prediction](https://mlsanity.com/paper/2006.00197/) (2020)
- [Topological Data Analysis of Task-Based fMRI Data from Experiments on Schizophrenia](https://mlsanity.com/paper/1809.08504/) (2018)

## Built on by (most cited first, 10 of 10)

- [HistoViT: Vision Transformer for Accurate and Scalable Histopathological Cancer Diagnosis](https://mlsanity.com/paper/2508.11181/) (2025)
- [Transfer Learning with EfficientNet for Accurate Leukemia Cell Classification](https://mlsanity.com/paper/2508.06535/) (2025)
- [RepViT-CXR: A Channel Replication Strategy for Vision Transformers in Chest X-ray Tuberculosis and Pneumonia Classification](https://mlsanity.com/paper/2509.08234/) (2025)
- [Efficient Breast and Ovarian Cancer Classification via ViT-Based Preprocessing and Transfer Learning](https://mlsanity.com/paper/2509.18553/) (2025)
- [Colormap-Enhanced Vision Transformers for MRI-Based Multiclass (4-Class) Alzheimer's Disease Classification](https://mlsanity.com/paper/2512.16964/) (2025)
- [Hybrid Topological and Deep Feature Fusion for Accurate MRI-Based Alzheimer's Disease Severity Classification](https://mlsanity.com/paper/2602.00956/) (2026)
- [Brain Tumor Classification from 3D MRI Using Persistent Homology and Betti Features: A Topological Data Analysis Approach on BraTS2020](https://mlsanity.com/paper/2603.13771/) (2026)
- [Enhancing Brain Tumor Classification Using Vision Transformers with Colormap-Based Feature Representation on BRISC2025 Dataset](https://mlsanity.com/paper/2603.21234/) (2026)
- [Bridging Topology and Deep Representation Learning: A TDA-ViT Fusion Model for Four-Class Brain Tumor Classification](https://mlsanity.com/paper/2606.00927/) (2026)
- [TopoAgent: An Agentic Framework for Automated Topology Learning in Medical Imaging](https://mlsanity.com/paper/2606.29763/) (2026)

## Abstract (arXiv)

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.