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arXiv 2603.13771cs.CVcs.LG

基于持久同调和Betti特征的3D MRI脑肿瘤分类:一种拓扑数据分析方法用于BraTS2020

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

Faisal Ahmed

AI总结:

本文提出利用拓扑数据分析方法,通过持久同调提取Betti特征,对3D MRI图像进行脑肿瘤分类,实验显示随机森林结合Betti特征在BraTS2020数据集上达到89.19%的准确率。

摘要:

准确且可解释的脑肿瘤分类仍是一个挑战,因为MRI图像具有高维性和复杂的结构模式。本文提出基于拓扑数据分析(TDA)的框架,直接应用于三维MRI体积。具体来说,分析BraTS2020数据集中的3D流体衰减反转恢复(FLAIR)图像,并使用持久同调提取可解释的拓扑描述符。持久同调通过Betti数捕捉数据的内在几何和结构特征,包括连通组件(Betti-0)、环(Betti-1)和空洞(Betti-2)。从3D MRI体积中提取100个紧凑的拓扑特征,总结了脑肿瘤结构的拓扑。这些描述符代表复杂的3D肿瘤形态,同时显著减少数据维度。与许多需要大规模训练数据或复杂架构的深度学习方法不同,该框架依赖于计算高效且直接从图像中提取的拓扑特征。这些特征用于训练经典机器学习分类器,包括随机森林和XGBoost,用于高阶胶质瘤(HGG)和低阶胶质瘤(LGG)的二分类。在BraTS2020数据集上的实验结果表明,结合选定Betti特征的随机森林分类器达到89.19%的准确率。这些发现突显了持久同调作为分析复杂3D医学图像和进行脑肿瘤分类的有效且可解释的方法的潜力。

英文摘要:

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.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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