Persistent topological properties of an image serve as an additional
descriptor providing an insight that might not be discovered by traditional
neural networks. The existing research in this area focuses primarily on
efficiently integrating topological properties of the data in the learning
process in order to enhance the performance. However, there is no existing
study to demonstrate all possible scenarios where introducing topological
properties can boost or harm the performance. This paper performs a detailed
analysis of the effectiveness of topological properties for image
classification in various training scenarios, defined by: the number of
training samples, the complexity of the training data and the complexity of the
backbone network. We identify the scenarios that benefit the most from
topological features, e.g., training simple networks on small datasets.
Additionally, we discuss the problem of topological consistency of the datasets
which is one of the major bottlenecks for using topological features for
classification. We further demonstrate how the topological inconsistency can
harm the performance for certain scenarios.

本文旨在分析拓扑特征在不同训练场景下对图像分类的有效性，并讨论数据集的拓扑一致性问题对于分类性能的影响。