用神经网络提升2D图像拓扑分析的抗噪能力
Noise-Robust Topology Estimation of 2D Image Data via Neural Networks and Persistent Homology
- 用监督学习的神经网络预测2D二值图像的贝蒂数
- 在噪声环境下，神经网络性能优于传统持久同调方法
- 适合需要抗噪拓扑分析的图像处理研究者
持久同调（PH）与人工神经网络（ANN）为从数据中推断拓扑结构提供了截然不同的方法。本文研究了监督训练的神经网络在预测2D二值图像贝蒂数时的抗噪能力。通过对比基于立方复形和带符号欧氏距离变换（SEDT）的典型PH流程，我们在一个合成数据集和两个真实世界数据集上发现，神经网络在噪声条件下表现更优，可能得益于其从训练数据中学习上下文与几何先验的能力。尽管仍处于发展初期，神经网络在结构化噪声下的拓扑估计已展现出对持久同调的有力替代潜力。
原文摘要 · Abstract (English)
Persistent Homology (PH) and Artificial Neural Networks (ANNs) offer contrasting approaches to inferring topological structure from data. In this study, we examine the noise robustness of a supervised neural network trained to predict Betti numbers in 2D binary images. We compare an ANN approach against a PH pipeline based on cubical complexes and the Signed Euclidean Distance Transform (SEDT), which is a widely adopted strategy for noise-robust topological analysis. Using one synthetic and two real-world datasets, we show that ANNs can outperform this PH approach under noise, likely due to their capacity to learn contextual and geometric priors from training data. Though still emerging, the use of ANNs for topology estimation offers a compelling alternative to PH under structural noise.
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