# Brain Tumor Classification from 3D MRI Using Persistent Homology and Betti Features: A Topological Data Analysis Approach on BraTS2020

arXiv: https://arxiv.org/abs/2603.13771 · HTML: https://mlsanity.com/paper/2603.13771/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 14 of its 29 references that are in the map.
- First posted on arXiv 14 Mar 2026.

## Builds on (most cited first, 14 of 14)

- [3D U-Net: Learning Dense Volumetric Segmentation from Sparse Annotation](https://mlsanity.com/paper/1606.06650/) (2016)
- [A Survey on Deep Learning in Medical Image Analysis](https://mlsanity.com/paper/1702.05747/) (2017)
- [Identifying the Best Machine Learning Algorithms for Brain Tumor Segmentation, Progression Assessment, and Overall Survival Prediction in the BRATS Challenge](https://mlsanity.com/paper/1811.02629/) (2018)
- [Topological Signatures vs. Gradient Histograms: A Comparative Study for Medical Image Classification](https://mlsanity.com/paper/2507.03006/) (2025)
- [HOG-CNN: Integrating Histogram of Oriented Gradients with Convolutional Neural Networks for Retinal Image Classification](https://mlsanity.com/paper/2507.22274/) (2025)
- [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)
- [3D-TDA -- Topological feature extraction from 3D images for Alzheimer's disease classification](https://mlsanity.com/paper/2511.08663/) (2025)
- [Colormap-Enhanced Vision Transformers for MRI-Based Multiclass (4-Class) Alzheimer's Disease Classification](https://mlsanity.com/paper/2512.16964/) (2025)
- [Addressing High Class Imbalance in Multi-Class Diabetic Retinopathy Severity Grading with Augmentation and Transfer Learning](https://mlsanity.com/paper/2507.17121/) (2025)
- [Four-Stage Alzheimer's Disease Classification from MRI Using Topological Feature Extraction, Feature Selection, and Ensemble Learning](https://mlsanity.com/paper/2601.00918/) (2026)
- [Hybrid Topological and Deep Feature Fusion for Accurate MRI-Based Alzheimer's Disease Severity Classification](https://mlsanity.com/paper/2602.00956/) (2026)

## Built on by (most cited first, 2 of 2)

- [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)

## Abstract (arXiv)

Accurate and interpretable brain tumor classification from medical imaging remains a challenging problem due to the high dimensionality and complex structural patterns present in magnetic resonance imaging (MRI). In this study, we propose a topology-driven framework for brain tumor classification based on Topological Data Analysis (TDA) applied directly to three-dimensional (3D) MRI volumes. Specifically, we analyze 3D Fluid Attenuated Inversion Recovery (FLAIR) images from the BraTS 2020 dataset and extract interpretable topological descriptors using persistent homology. Persistent homology captures intrinsic geometric and structural characteristics of the data through Betti numbers, which describe connected components (Betti-0), loops (Betti-1), and voids (Betti-2). From the 3D MRI volumes, we derive a compact set of 100 topological features that summarize the underlying topology of brain tumor structures. These descriptors represent complex 3D tumor morphology while significantly reducing data dimensionality. Unlike many deep learning approaches that require large-scale training data or complex architectures, the proposed framework relies on computationally efficient topological features extracted directly from the images. These features are used to train classical machine learning classifiers, including Random Forest and XGBoost, for binary classification of high-grade glioma (HGG) and low-grade glioma (LGG). Experimental results on the BraTS 2020 dataset show that the Random Forest classifier combined with selected Betti features achieves an accuracy of 89.19%. These findings highlight the potential of persistent homology as an effective and interpretable approach for analyzing complex 3D medical images and performing brain tumor classification.