Abstract
Topological data analysis (TDA) is a relatively new field that is gaining rapid adoption due to its robustness and ability to effectively describe complex datasets by quantifying geometric information. In imaging contexts, TDA typically models data as filtered cubical complexes from which we can extract discriminative features using persistence homology. Meanwhile, convolutional neural networks (CNNs) have been shown to be biased towards texture based local features. To address this limitation, we propose a TDA feature engineering pipeline and a simple method to integrate topological features with deep learning models on remote sensing classification. Our method improves the performance of a ResNet18 model on the EuroSAT dataset by 1.44% achieving 99.33% accuracy, which surpasses all previously reported single-model accuracies, including those with larger architectures, such as ResNet50 (2x larger) and XL Vision Transformers (197x larger). We additionally show that our method's accuracy is 1.82% higher than our ResNet18 baseline on the RESISC45 dataset. To our knowledge, this is the first application of TDA features in satellite scene classification with deep learning. This demonstrates that TDA features can be integrated with deep learning models, even on datasets without explicit topological structures, thereby increasing the applicability of TDA. A clean implementation of our method will be made publicly available upon publication.
Abstract (translated)
拓扑数据分析（TDA）是一个相对较新的领域，由于其鲁棒性和能够通过量化几何信息有效地描述复杂数据集的能力，正在迅速被采用。在成像背景下，TDA通常将数据建模为过滤后的立方复形，并从中提取持久同调特征以区分不同的数据特征。同时，卷积神经网络（CNN）已被证明倾向于基于局部纹理的特征。为了克服这一局限性，我们提出了一种用于遥感分类的TDA特征工程管道以及一种简单的方法来将拓扑特征与深度学习模型集成起来。 我们的方法提高了在EuroSAT数据集上ResNet18模型的表现，使其准确率达到了99.33%，比之前所有单独模型报告的准确性都高，包括架构更大的ResNet50（是其两倍大）和XL视觉变换器（几乎是其197倍）。此外，在RESISC45数据集上，我们的方法相比基线ResNet18模型提高了1.82%的准确率。据我们所知，这是首次将TDA特征应用于卫星场景分类与深度学习结合的应用中，这表明TDA特征可以被集成到深度学习模型中，即使是在没有明确拓扑结构的数据集上也能增强TDA的应用范围。 在发布时，我们的方法会提供一个干净的实现版本供公众使用。
URL
https://arxiv.org/abs/2507.10381
