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

2026-03-14

AI Summary

This study addresses the challenge of classifying brain tumors in high-dimensional 3D MRI by proposing an interpretable approach based on topological data analysis (TDA). For the first time, persistent homology combined with 0-, 1-, and 2-dimensional Betti numbers is applied to 3D FLAIR images to construct a compact 100-dimensional topological feature vector that effectively captures tumor structure without relying on deep learning. Evaluated on the BraTS2020 dataset using random forest and XGBoost classifiers, the method achieves an accuracy of 89.19% in binary classification between high-grade and low-grade gliomas, demonstrating the efficacy and potential of low-dimensional topological features in medical image analysis.

Technology Category

• Machine Learning: Dimensionality Reduction/Feature Selection
• Computer Vision: Medical and Biological Imaging
• Natural Language Processing: Interpretability, Analysis, and Evaluation of NLP Models

Application Category

• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods
• Search and Retrieval-Augmented AI: Web query analysis, representation and understanding
• User Modeling, Personalization and Recommendation: Explainable and interpretable methods for personalization

Abstract

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.

Problem

• brain tumor classification
• 3D MRI
• topological data analysis
• persistent homology
• Betti features

Innovation

• Persistent Homology
• Betti Features
• Topological Data Analysis
• 3D MRI
• Brain Tumor Classification