用拓扑不变量识别虹膜，准确率超97%，比深度学习更可解释。
Topological Invariant-Based Iris Identification via Digital Homology and Machine Learning
- 从虹膜图像提取数字同调的拓扑特征，构建紧凑特征矩阵。
- 逻辑回归模型达97.78%准确率，方差小于0.82%，优于CNN。
- 适合需要可解释性或数据少的安防、医疗等场景。
本研究提出一种基于二维虹膜图像拓扑不变量的生物特征识别方法，通过形式化定义的数字同调表征虹膜纹理，并评估分类性能。每幅归一化虹膜图像（48×482像素）被划分为网格（如6×54或3×27），对每个子区域计算Betti0、Betti1及其比值，采用最新算法求解二维数字图像的同调群。所得不变量构成特征矩阵，结合逻辑回归、KNN和SVM（含PCA，100次随机重复）进行分类。同时训练卷积神经网络（CNN）在原始图像上作对比。结果表明，逻辑回归达到97.78±0.82%准确率，优于CNN的96.44±1.32%及其他基于特征的模型。拓扑特征表现出高精度与低方差。这是首次将正式数字同调的拓扑不变量用于虹膜识别。该方法提供紧凑、可解释且准确的替代方案，适用于深度学习难以胜任的场景，尤其在可解释性或数据有限的情况下。其应用可拓展至其他生物识别、医学影像、材料科学、遥感及可解释人工智能领域，且可在仅含CPU的系统上高效运行，生成鲁棒、可解释的特征，适用于安全关键领域。
原文摘要 · Abstract (English)
Objective - This study presents a biometric identification method based on topological invariants from 2D iris images, representing iris texture via formally defined digital homology and evaluating classification performance. Methods - Each normalized iris image (48x482 pixels) is divided into grids (e.g., 6x54 or 3x27). For each subregion, we compute Betti0, Betti1, and their ratio using a recent algorithm for homology groups in 2D digital images. The resulting invariants form a feature matrix used with logistic regression, KNN, and SVM (with PCA and 100 randomized repetitions). A convolutional neural network (CNN) is trained on raw images for comparison. Results - Logistic regression achieved 97.78 +/- 0.82% accuracy, outperforming CNN (96.44 +/- 1.32%) and other feature-based models. The topological features showed high accuracy with low variance. Conclusion - This is the first use of topological invariants from formal digital homology for iris recognition. The method offers a compact, interpretable, and accurate alternative to deep learning, useful when explainability or limited data is important. Beyond iris recognition, it can apply to other biometrics, medical imaging, materials science, remote sensing, and interpretable AI. It runs efficiently on CPU-only systems and produces robust, explainable features valuable for security-critical domains.
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