用曲率流与熵增强特征，98.6%准确率区分阿尔茨海默病患者与健康人。
Entropy-Enhanced Conformal Features from Ricci Flow for Robust Alzheimer's Disease Classification
- 基于曲率流生成共形特征，再用香农熵压缩为紧凑向量
- 多层感知机和逻辑回归达到98.62%准确率与F1分数
- 适合脑结构形态分析与神经退行性疾病早期诊断
背景与目标：在脑成像中，几何表面模型对分析解剖结构的3D形状至关重要。阿尔茨海默病（AD）伴随显著皮层萎缩，使形状分析成为有价值的诊断工具。本研究旨在提出并验证一种新型局部表面表示方法，用于自动化、精准诊断AD。方法：使用来自阿尔茨海默病神经影像计划（ADNI）的160名参与者（80名AD患者与80名健康对照）的T1加权MRI扫描。通过Freesurfer重建皮层表面模型，并从3D网格计算关键几何属性。利用曲率流进行共形参数化，得到面积畸变与共形因子；直接从网格计算高斯曲率。对这三个特征应用香农熵，生成紧凑且信息丰富的特征向量。使用多种分类器（如XGBoost、MLP、逻辑回归等）训练与评估。结果：通过配对韦尔奇t检验评估分类器性能差异的统计显著性。该方法在区分AD患者与健康对照方面表现出色。多层感知机（MLP）与逻辑回归分类器表现最优，准确率与F₁分数均达98.62%。结论：本研究证实，共形衍生几何特征的熵是皮层形态测量的强大且稳健指标。高分类准确率凸显该方法在提升阿尔茨海默病研究与诊断中的潜力，为临床研究提供一种简单而强大的工具。
原文摘要 · Abstract (English)
Background and Objective: In brain imaging, geometric surface models are essential for analyzing the 3D shapes of anatomical structures. Alzheimer's disease (AD) is associated with significant cortical atrophy, making such shape analysis a valuable diagnostic tool. The objective of this study is to introduce and validate a novel local surface representation method for the automated and accurate diagnosis of AD. Methods: The study utilizes T1-weighted MRI scans from 160 participants (80 AD patients and 80 healthy controls) from the Alzheimer's Disease Neuroimaging Initiative (ADNI). Cortical surface models were reconstructed from the MRI data using Freesurfer. Key geometric attributes were computed from the 3D meshes. Area distortion and conformal factor were derived using Ricci flow for conformal parameterization, while Gaussian curvature was calculated directly from the mesh geometry. Shannon entropy was applied to these three features to create compact and informative feature vectors. The feature vectors were used to train and evaluate a suite of classifiers (e.g. XGBoost, MLP, Logistic Regression, etc.). Results: Statistical significance of performance differences between classifiers was evaluated using paired Welch's t-test. The method proved highly effective in distinguishing AD patients from healthy controls. The Multi-Layer Perceptron (MLP) and Logistic Regression classifiers outperformed all others, achieving an accuracy and F$_1$ Score of 98.62%. Conclusions: This study confirms that the entropy of conformally-derived geometric features provides a powerful and robust metric for cortical morphometry. The high classification accuracy underscores the method's potential to enhance the study and diagnosis of Alzheimer's disease, offering a straightforward yet powerful tool for clinical research applications.
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